diff --git a/.gitignore b/.gitignore index b77b35370..79784747f 100644 --- a/.gitignore +++ b/.gitignore @@ -15,3 +15,4 @@ JCTBGui/ *.toc build tests +docs/ diff --git a/Makefile b/Makefile index 99ffb190a..8378d9977 100755 --- a/Makefile +++ b/Makefile @@ -120,8 +120,8 @@ htmldoc: detaildoc: createdocs docspdf docshtml removedocs -createdocs: doxy.config - doxygen doxy.config +createdocs: $(LIBRARYDIR)/doxy.config + doxygen $(LIBRARYDIR)/doxy.config docspdf: cd slsDetectorPackageDocs/latex && make diff --git a/doxy.config b/doxy.config deleted file mode 100644 index 18a5ed106..000000000 --- a/doxy.config +++ /dev/null @@ -1,164 +0,0 @@ -# If the EXTRACT_ALL tag is set to YES doxygen will assume all entities in -# documentation are documented, even if no documentation was available. -# Private class members and static file members will be hidden unless -# the EXTRACT_PRIVATE and EXTRACT_STATIC tags are set to YES - -EXTRACT_ALL = YES - -# If the EXTRACT_PRIVATE tag is set to YES all private members of a class -# will be included in the documentation. - -EXTRACT_PRIVATE = NO - - - -# If the EXTRACT_STATIC tag is set to YES all static members of a file -# will be included in the documentation. - -EXTRACT_STATIC = YES - -# If the EXTRACT_LOCAL_CLASSES tag is set to YES classes (and structs) -# defined locally in source files will be included in the documentation. -# If set to NO only classes defined in header files are included. - -EXTRACT_LOCAL_CLASSES = YES - -# This flag is only useful for Objective-C code. When set to YES local -# methods, which are defined in the implementation section but not in -# the interface are included in the documentation. -# If set to NO (the default) only methods in the interface are included. - -EXTRACT_LOCAL_METHODS = YES - -# If this flag is set to YES, the members of anonymous namespaces will be -# extracted and appear in the documentation as a namespace called -# 'anonymous_namespace{file}', where file will be replaced with the base -# name of the file that contains the anonymous namespace. By default -# anonymous namespace are hidden. - -EXTRACT_ANON_NSPACES = NO - -# If the HIDE_UNDOC_MEMBERS tag is set to YES, Doxygen will hide all -# undocumented members of documented classes, files or namespaces. -# If set to NO (the default) these members will be included in the -# various overviews, but no documentation section is generated. -# This option has no effect if EXTRACT_ALL is enabled. - -HIDE_UNDOC_MEMBERS = NO - -# If the HIDE_UNDOC_CLASSES tag is set to YES, Doxygen will hide all -# undocumented classes that are normally visible in the class hierarchy. -# If set to NO (the default) these classes will be included in the various -# overviews. This option has no effect if EXTRACT_ALL is enabled. - -HIDE_UNDOC_CLASSES = NO - -# If the HIDE_FRIEND_COMPOUNDS tag is set to YES, Doxygen will hide all -# friend (class|struct|union) declarations. -# If set to NO (the default) these declarations will be included in the -# documentation. - -HIDE_FRIEND_COMPOUNDS = NO - -INTERNAL_DOCS = NO - -SHOW_INCLUDE_FILES = YES - -SHOW_FILES = YES - -SHOW_NAMESPACES = NO - -COMPACT_LATEX = YES - -PAPER_TYPE = a4 - -PDF_HYPERLINKS = YES - -USE_PDFLATEX = YES - -LATEX_HIDE_INDICES = YES - -PREDEFINED = __cplusplus - -INPUT = slsDetectorSoftware/commonFiles/communication_funcs.h \ - slsDetectorSoftware/commonFiles/error_defs.h \ - slsDetectorSoftware/commonFiles/sls_detector_defs.h \ - slsDetectorSoftware/commonFiles/sls_detector_funcs.h \ - slsDetectorSoftware/f90Interface/externPostProcessing.h \ - slsDetectorSoftware/multiSlsDetector/multiSlsDetectorClient.h \ - slsDetectorSoftware/multiSlsDetector/multiSlsDetectorCommand.h \ - slsDetectorSoftware/multiSlsDetector/multiSlsDetector.h \ - slsDetectorSoftware/slsDetector/slsDetectorActions.h \ - slsDetectorSoftware/slsDetector/slsDetectorBase.h \ - slsDetectorSoftware/slsDetector/slsDetectorCommand.h \ - slsDetectorSoftware/slsDetector/slsDetector.h \ - slsDetectorSoftware/slsDetector/slsDetectorUsers.h \ - slsDetectorSoftware/slsDetector/slsDetectorUtils.h \ - slsDetectorSoftware/slsDetectorAnalysis/angCalLogClass.h \ - slsDetectorSoftware/slsDetectorAnalysis/angleConversionConstant.h \ - slsDetectorSoftware/slsDetectorAnalysis/angularCalibration.h \ - slsDetectorSoftware/slsDetectorAnalysis/angularConversion.h \ - slsDetectorSoftware/slsDetectorAnalysis/AngularConversion_Standalone.h \ - slsDetectorSoftware/slsDetectorAnalysis/angularConversionStatic.h \ - slsDetectorSoftware/slsDetectorAnalysis/badChannelCorrections.h \ - slsDetectorSoftware/slsDetectorAnalysis/detectorData.h \ - slsDetectorSoftware/slsDetectorAnalysis/enCalLogClass.h \ - slsDetectorSoftware/slsDetectorAnalysis/energyCalibration.h \ - slsDetectorSoftware/slsDetectorAnalysis/energyConversion.h \ - slsDetectorSoftware/slsDetectorAnalysis/fileIO.h \ - slsDetectorSoftware/slsDetectorAnalysis/FileIO_Standalone.h \ - slsDetectorSoftware/slsDetectorAnalysis/fileIOStatic.h \ - slsDetectorSoftware/slsDetectorAnalysis/movingStat.h \ - slsDetectorSoftware/slsDetectorAnalysis/postProcessingFileIO_Standalone.h \ - slsDetectorSoftware/slsDetectorAnalysis/postProcessingFuncs.h \ - slsDetectorSoftware/slsDetectorAnalysis/postProcessing.h \ - slsDetectorSoftware/slsDetectorAnalysis/postProcessing_Standalone.h \ - slsDetectorSoftware/slsDetectorAnalysis/runningStat.h \ - slsDetectorSoftware/slsDetectorAnalysis/singlePhotonFilter.h \ - slsDetectorSoftware/slsDetectorAnalysis/single_photon_hit.h \ - slsDetectorSoftware/slsDetectorAnalysis/TSlsDetectorDict.h \ - slsDetectorSoftware/slsReceiverInterface/receiverInterface.h \ - slsDetectorSoftware/threadFiles/CondVar.h \ - slsDetectorSoftware/threadFiles/Global.h \ - slsDetectorSoftware/threadFiles/Multi.h \ - slsDetectorSoftware/threadFiles/Mutex.h \ - slsDetectorSoftware/threadFiles/Single.h \ - slsDetectorSoftware/threadFiles/Task.h \ - slsDetectorSoftware/threadFiles/ThreadPool.h \ - slsDetectorSoftware/usersFunctions/angleFunction.h \ - slsDetectorSoftware/usersFunctions/usersFunctions.h \ - slsReceiverSoftware/include/ansi.h \ - slsReceiverSoftware/include/BinaryFile.h \ - slsReceiverSoftware/include/BinaryFileStatic.h \ - slsReceiverSoftware/include/circularFifo.h \ - slsReceiverSoftware/include/DataProcessor.h \ - slsReceiverSoftware/include/DataStreamer.h \ - slsReceiverSoftware/include/Fifo.h \ - slsReceiverSoftware/include/File.h \ - slsReceiverSoftware/include/GeneralData.h \ - slsReceiverSoftware/include/genericSocket.h \ - slsReceiverSoftware/include/HDF5File.h \ - slsReceiverSoftware/include/HDF5FileStatic.h \ - slsReceiverSoftware/include/Listener.h \ - slsReceiverSoftware/include/logger.h \ - slsReceiverSoftware/include/MySocketTCP.h \ - slsReceiverSoftware/include/receiver_defs.h \ - slsReceiverSoftware/include/RestHelper.h \ - slsReceiverSoftware/include/sls_receiver_defs.h \ - slsReceiverSoftware/include/sls_receiver_funcs.h \ - slsReceiverSoftware/include/slsReceiver.h \ - slsReceiverSoftware/include/slsReceiverTCPIPInterface.h \ - slsReceiverSoftware/include/slsReceiverUsers.h \ - slsReceiverSoftware/include/ThreadObject.h \ - slsReceiverSoftware/include/UDPBaseImplementation.h \ - slsReceiverSoftware/include/UDPInterface.h \ - slsReceiverSoftware/include/UDPRESTImplementation.h \ - slsReceiverSoftware/include/UDPStandardImplementation.h \ - slsReceiverSoftware/include/utilities.h \ - slsReceiverSoftware/include/ZmqSocket.h - - - - -OUTPUT_DIRECTORY = slsDetectorPackageDocs - diff --git a/manual/docs/html/slsDetectors-FAQ/footnode.html b/manual/docs/html/slsDetectors-FAQ/footnode.html index a874b9474..9d4a88914 100644 --- a/manual/docs/html/slsDetectors-FAQ/footnode.html +++ b/manual/docs/html/slsDetectors-FAQ/footnode.html @@ -18,15 +18,15 @@ original version by: Nikos Drakos, CBLU, University of Leeds - +
-
... tab 2.1
+
... tab 3.1
The default name of the calibrated trimfiles is trimbits/beamline/settings/noise.snxxx where settings is the chosen settings. You can change it in src/qDetector.h and then recompile the acquisition program as described in [*]. @@ -62,8 +62,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds .
-
....snxxx 2.2
+
....snxxx 3.2
The default name of the calibration file calibration/settings.snxxx where settings is the chosen settings. You can change it in src/qDetector.h and then recompile the acquisition program. 
.
diff --git a/manual/docs/html/slsDetectors-FAQ/images.pl b/manual/docs/html/slsDetectors-FAQ/images.pl
index 81701e712..91bff74bf 100644
--- a/manual/docs/html/slsDetectors-FAQ/images.pl
+++ b/manual/docs/html/slsDetectors-FAQ/images.pl
@@ -5,73 +5,104 @@
 $key = q/includegraphics[width=textwidth]{imagesslashtrimbitdistribution};AAT/;
 $cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/trimbitdistribution}|; 
 
+$key = q/displaystyleX_ell={ensuremath{displaystyle{frac{{ensuremath{displaystyle{{ensure{{ensuremath{displaystyle{|b|m}}}}{{ensuremath{displaystyle{e}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle X_\ell={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyl...
+...nsuremath{\displaystyle{\vert b\vert m}}}}{{\ensuremath{\displaystyle{e}}}}}}}
+$|; 
+
 $key = q/E_f|; 
 
 $key = q/E_t|; 
 
-$key = q/(108602&0xFFFFFFFE)>>1=54301;MSF=1.6;AAT/;
+$key = q/lambda=;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ (108602\&0xFFFFFFFE)»1 = 54301$|; 
+ WIDTH="31" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
+ SRC="|."$dir".q|img202.png"
+ ALT="$ \lambda =$">|; 
 
-$key = q/includegraphics[width=textwidth]{multi_detector};AAT/;
+$key = q/N_{mathrm{obs}};MSF=1.6;AAT/;
 $cached_env_img{$key} = q|\includegraphics[width=\textwidth]{multi_detector}|; 
+ WIDTH="37" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img142.png"
+ ALT="$ N_{\mathrm{obs}}$">|; 
 
-$key = q/Vthreshold=7;MSF=1.6;AAT/;
+$key = q/displaystylelanglexrangle={ensuremath{displaystyle{frac{{ensuremath{displaystyleath{displaystyle{sqrt{C_1+C_2}}}}}{{ensuremath{displaystyle{2}}}}}}};MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ Vthreshold=7$|; 
+ WIDTH="261" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img178.png"
+ ALT="$\displaystyle \langle x \rangle={\ensuremath{\displaystyle{\frac{{\ensuremath{\...
+...nsuremath{\displaystyle{\sqrt{C_1+C_2}}}}}{{\ensuremath{\displaystyle{2}}}}}}}
+$">|; 
 
-$key = q/includegraphics[width=textwidth]{imagesslashro_trigger_acquisition.eps};AAT/;
+$key = q/displaystylemathsf{GoF}_{(2)}=sqrt{{ensuremath{displaystyle{frac{{ensuremath{dismath{left({langlexrangle^*-langlexrangle_{!mathrm{w(2)}}+1}right)}}};MSF=1.6;AAT/;
 $cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/ro_trigger_acquisition.eps}|; 
+ WIDTH="569" HEIGHT="189" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img169.png"
+ ALT="$\displaystyle \mathsf{GoF}_{(2)}=
+\sqrt{
+{\ensuremath{\displaystyle{\frac{{\ens...
+...{\left({
+\langle x\rangle^*-\langle x \rangle_{\!\mathrm{w(2)}}+1
+}\right)}}
+}
+$">|; 
+
+$key = q/N_k;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ N_k$|; 
 
 $key = q/E_t>4;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ E_t>4$|; 
 
-$key = q/(108602&0x1)=0;MSF=1.6;AAT/;
+$key = q/displaystylePhi_m;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ (108602\&0x1) =0$|; 
+ WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img57.png"
+ ALT="$\displaystyle \Phi_m$">|; 
 
-$key = q/E_t;MSF=1.6;AAT/;
+$key = q/DeltaOmega;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ E_t$|; 
+ WIDTH="29" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="|."$dir".q|img69.png"
+ ALT="$ \Delta\Omega$">|; 
 
-$key = q/includegraphics[width=textwidth]{imagesslashtrimbitplot};AAT/;
+$key = q/displaystyle{ensuremath{displaystyle{frac{{ensuremath{displaystyle{E{ensuremath{mathrm{e}}}^{-2lambda}}}}}{{ensuremath{displaystyle{4lambda^3}}}}}}};MSF=1.6;AAT/;
 $cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/trimbitplot}|; 
+ WIDTH="296" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img191.png"
+ ALT="$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{E{\en...
+...math{\mathrm{e}}}^{-2\lambda}}}}}{{\ensuremath{\displaystyle{4\lambda^3}}}}}}}
+$">|; 
+
+$key = q/s=0ldots+infty;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ s=0\ldots +\infty$|; 
 
 $key = q/{displaymath}textrm{textbf{MEASUREMENTS}}leftUpdownarrow,{array}{l}%textrm{Measuightarrow,textrm{Stopscript}{array}%right.{array}right.{displaymath};MSF=1.6;AAT/;
 $cached_env_img{$key} = q|\begin{displaymath}\textrm{\textbf{MEASUREMENTS}} \\\\
 \left\Updownarrow  
 \be...
@@ -84,149 +115,1469 @@ $cached_env_img{$key} = q|<IMG
 \right.
 \end{displaymath}|; 
 
-$key = q/includegraphics[width=textwidth]{imagesslashbad_ff_col};AAT/;
+$key = q/X;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/bad_ff_col}|; 
+ WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="|."$dir".q|img214.png"
+ ALT="$ X$">|; 
 
-$key = q/includegraphics[width=textwidth]{data_receiver};AAT/;
+$key = q/N_{mathrm{obs}}^*;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|\includegraphics[width=\textwidth]{data_receiver}|; 
+ WIDTH="37" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img149.png"
+ ALT="$ N_{\mathrm{obs}}^*$">|; 
+
+$key = q/displaystyle{sigma}_{langlexrangle_{!mathrm{w}}}^{mathrm{corrected}}=mathsf{GoF}sigma_{langlexrangle_{!mathrm{w}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle {\sigma}_{\langle x \rangle_{\!\mathrm{w}}}^{\mathrm{corrected}} = \mathsf{GoF} \sigma_{\langle x \rangle_{\!\mathrm{w}}}
+$|; 
+
+$key = q/displaystyleY_ell=mathop{sum_{k,j}}_{{ensuremath{left|{b_{k,j}capB_ell}right|}}>displaystyle{B}}}}}}}{ensuremath{left({sigma_{r_{k,j}}}right)}}^{-2};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle Y_\ell=\mathop{\sum_{k,j}}_{ {\ensuremath{\left\vert{ b_{k,j}\cap...
+...th{\displaystyle{B}}}}}}} {\ensuremath{\left({\sigma_{r_{k,j}}}\right)}}^{-2}
+$|; 
+
+$key = q/displaystyleR_ell={ensuremath{displaystyle{frac{{ensuremath{displaystyle{X_ell}}uremath{displaystyle{e(C+1)}}}}{{ensuremath{displaystyle{m|b|}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle R_\ell={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyl...
+...emath{\displaystyle{e(C+1)}}}}{{\ensuremath{\displaystyle{m\vert b\vert}}}}}}}
+$|; 
+
+$key = q/hat{B}_ell;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \hat{B}_\ell$|; 
+
+$key = q/n-m=s-2k;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ n-m=s-2k$|; 
+
+$key = q/displaystyleI_{k,j}={ensuremath{displaystyle{frac{{ensuremath{displaystyle{e_{k,emath{left({C_{k,j}+min{ensuremath{left({1,C_{k,j}}right)}}}right)}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle I_{k,j}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaysty...
+...nsuremath{\left({C_{k,j}+\min{\ensuremath{\left({1,C_{k,j}}\right)}}}\right)}}
+$|; 
 
 $key = q/Resolution=4;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ Resolution=4$|; 
 
 $key = q/E_0;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ E_0$|; 
 
-$key = q/pm;MSF=1.6;AAT/;
+$key = q/displaystylex=langlexrangle^*={ensuremath{displaystyle{frac{{ensuremath{displays}}}}}{{ensuremath{displaystyle{N_{mathrm{obs}}^*}}}}}}}langlexrangle;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ \pm$|; 
+ WIDTH="382" HEIGHT="78" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img150.png"
+ ALT="$\displaystyle x=\langle x\rangle^*={\ensuremath{\displaystyle{\frac{{\ensuremat...
+...obs}}}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}^*}}}}}}}\langle x\rangle
+$">|; 
 
-$key = q/Counts=500;MSF=1.6;AAT/;
+$key = q/sigma_{eta_0};MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ Counts=500$|; 
+ WIDTH="27" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img221.png"
+ ALT="$ \sigma_{\eta_0}$">|; 
 
-$key = q/includegraphics[width=textwidth]{imagesslashtrigger_acquisition.eps};AAT/;
+$key = q/displaystyle{ensuremath{left|{B_ell}right|}}=B;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/trigger_acquisition.eps}|; 
+ WIDTH="66" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img90.png"
+ ALT="$\displaystyle {\ensuremath{\left\vert{B_\ell}\right\vert}}=B$">|; 
 
-$key = q/E_f;MSF=1.6;AAT/;
+$key = q/{ensuremath{{2theta}}};MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ E_f$|; 
+ WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="|."$dir".q|img63.png"
+ ALT="$ {\ensuremath{{2\theta}}}$">|; 
+
+$key = q/displaystylesigma_X=sqrt{langleX^2rangle-langleXrangle^2}=sqrt{eta_0X_0}=eta_0sqrt{C_0}=sqrt{eta_0}sqrt{X_0};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \sigma_X=\sqrt{\langle X^2\rangle-\langle X\rangle^2}=\sqrt{\eta_0 X_0}=\eta_0\sqrt{C_0}=\sqrt{\eta_0}\sqrt{X_0}
+$|; 
+
+$key = q/displaystylePhi_m-{ensuremath{displaystyle{frac{{ensuremath{displaystyle{180}}}}ensuremath{displaystyle{D_m}}}}{{ensuremath{displaystyle{R_m}}}}}}}.;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \Phi_m-{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyl...
+...\frac{{\ensuremath{\displaystyle{D_m}}}}{{\ensuremath{\displaystyle{R_m}}}}}}}.$|; 
 
 $key = q/E_t|; 
 
-$key = q/includegraphics[width=textwidth]{imagesslashnormal_acquisition.eps};AAT/;
+$key = q/displaystylechi_{(0)}^2=mathop{sum}_{j=1}^{N_{mathrm{obs}}}{ensuremath{displaystath{left({F_j-C_j}right)}}^2}}}}{{ensuremath{displaystyle{C_j}}}}}}};MSF=1.6;AAT/;
 $cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/normal_acquisition.eps}|; 
+ WIDTH="160" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img140.png"
+ ALT="$\displaystyle \chi_{(0)}^2 = \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}
+{\ensuremat...
+...remath{\left({F_j-C_j}\right)}}^2
+}}}}{{\ensuremath{\displaystyle{
+C_j
+}}}}}}}
+$">|; 
 
-$key = q/E_t=E_0slash2;MSF=1.6;AAT/;
+$key = q/C_j,quadj=1ldotsN_{mathrm{obs}};MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ E_t=E_0/2$|; 
+ WIDTH="138" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img143.png"
+ ALT="$ C_j,\quad j=1\ldots N_{\mathrm{obs}}$">|; 
+
+$key = q/displaystyleepsilon={ensuremath{displaystyle{frac{{ensuremath{displaystyle{sigmaath{displaystyle{1}}}}{{ensuremath{displaystyle{sqrt{2lambda}}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \epsilon = {\ensuremath{\displaystyle{\frac{{\ensuremath{\display...
+...suremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{\sqrt{2\lambda}}}}}}}}
+$|; 
+
+$key = q/displaystylesigma_X=sqrt{eta_0}sqrt{X_0}=eta_0sqrt{C_0}=eta_0sigma_{C_0};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \sigma_X=\sqrt{\eta_0}\sqrt{X_0}=\eta_0\sqrt{C_0}=\eta_0\sigma_{C_0}
+$|; 
+
+$key = q/N=10^8;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ N=10^8$|; 
+
+$key = q/D_m;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ D_m$|; 
+
+$key = q/displaystyle{ensuremath{displaystyle{frac{{ensuremath{displaystyle{{ensuremath{left|{b_{k,j}capB_ell}right|}}}}}}{{ensuremath{displaystyle{B}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ens...
+...ert{ b_{k,j}\cap B_\ell }\right\vert}}}}}}{{\ensuremath{\displaystyle{B}}}}}}}
+$|; 
+
+$key = q/X_ell=0;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ X_\ell=0$|; 
+
+$key = q/C_1;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ C_1$|; 
+
+$key = q/e_lambda=E_lambdaslashlambda;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ e_\lambda=E_\lambda/\lambda$|; 
+
+$key = q/sigma_{R_ell};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \sigma_{R_\ell}$|; 
+
+$key = q/F_j;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ F_j$|; 
 
 $key = q/includegraphics[width=textwidth]{imagesslashnoise_thresholdscantrimmed};AAT/;
 $cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/noise_thresholdscantrimmed}|; 
 
+$key = q/displaystyle{sigma}_{langlexrangle_{!mathrm{w(2)}}}^{mathrm{corrected}}=mathsf{GoF}_{(2)}sigma_{langlexrangle_{!mathrm{w(2)}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle {\sigma}_{\langle x \rangle_{\!\mathrm{w(2)}}}^{\mathrm{corrected}} = \mathsf{GoF}_{(2)} \sigma_{\langle x \rangle_{\!\mathrm{w(2)}}}
+$|; 
+
+$key = q/displaystylek_m;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle k_m$|; 
+
+$key = q/b_{k,j};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ b_{k,j}$|; 
+
+$key = q/Rightarrow;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \Rightarrow$|; 
+
+$key = q/d;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ d$|; 
+
+$key = q/Phi_m;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \Phi_m$|; 
+
+$key = q/2thetaequiv{ensuremath{{2theta}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ 2\theta\equiv{\ensuremath{{2\theta}}}$|; 
+
+$key = q/displaystyleB_ell=[{ensuremath{{2theta}}}_0+(ell-1)B,{ensuremath{{2theta}}}_0+ellB],qquadell=1,ldots,M;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle B_\ell=[{\ensuremath{{2\theta}}}_0+(\ell-1)B, {\ensuremath{{2\theta}}}_0+\ell B],\qquad \ell=1,\ldots,M
+$|; 
+
+$key = q/includegraphics[width=textwidth]{imagesslashthr_scan_expl};AAT/;
+$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/thr_scan_expl}|; 
+
+$key = q/displaystyle{ensuremath{displaystyle{frac{{ensuremath{displaystyle{D_m}}}}{{ensuremath{displaystyle{p}}}}}}};;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{D_m}}}}{{\ensuremath{\displaystyle{p}}}}}}};$|; 
+
+$key = q/C_{k,j};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ C_{k,j}$|; 
+
+$key = q/displaystylelanglexrangle_{!mathrm{w(2)}}={ensuremath{displaystyle{frac{{ensuremmath{displaystyle{1}}}}{{ensuremath{displaystyle{C_j+1}}}}}}}}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \langle x \rangle_{\!\mathrm{w(2)}}={\ensuremath{\displaystyle{\f...
+...uremath{\displaystyle{1
+}}}}{{\ensuremath{\displaystyle{
+C_j+1
+}}}}}}}
+}}}}}}}
+$|; 
+
+$key = q/e_lambda;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ e_\lambda$|; 
+
+$key = q/displaystyleX_0=eta_0C_0;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle X_0=\eta_0 C_0
+$|; 
+
+$key = q/includegraphics[width=textwidth]{imagesslashsample_with_fluorescence};AAT/;
+$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/sample_with_fluorescence}|; 
+
+$key = q/xi_lambda=sqrt{lambdaslashN};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \xi_\lambda=\sqrt{\lambda/N}$|; 
+
+$key = q/includegraphics[width=textwidth]{imagesslashnoise_thresholdscanuntrimmed};AAT/;
+$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/noise_thresholdscanuntrimmed}|; 
+
+$key = q/C_2;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ C_2$|; 
+
+$key = q/displaystyleint_{-infty}^{+infty}{ensuremath{mathrm{d}{eta},}}mathop{sum}_{n=0}^{+infty}P(n)widehat{P}(eta)=1;;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \int_{-\infty}^{+\infty}{\ensuremath{\mathrm{d}{\eta}  }}\mathop{\sum}_{n=0}^{+\infty}
+P(n)\widehat{P}(\eta)=1 ;
+$|; 
+
+$key = q/R_ell;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ R_\ell$|; 
+
+$key = q/displaystyle{ensuremath{displaystyle{frac{{ensuremath{displaystyle{E{ensuremath{ystyle{E{ensuremath{left({langlexrangle}right)}}}}}}}}}=O(epsilon^2);MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{E{\en...
+...aystyle{E{\ensuremath{\left({\langle x \rangle}\right)}}}}}}}}}=
+O(\epsilon^2)
+$|; 
+
+$key = q/C_1,C_2;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ C_1,C_2$|; 
+
+$key = q/N_{mathrm{obs}}=2;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ N_{\mathrm{obs}}=2$|; 
+
+$key = q/displaystyle{sigma}_{langlexrangle_{!mathrm{w(1)}}}^{mathrm{corrected}}=mathsf{GoF}_{(1)}sigma_{langlexrangle_{!mathrm{w(1)}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle {\sigma}_{\langle x \rangle_{\!\mathrm{w(1)}}}^{\mathrm{corrected}} = \mathsf{GoF}_{(1)} \sigma_{\langle x \rangle_{\!\mathrm{w(1)}}}
+$|; 
+
+$key = q/displaystylelanglexrangle_{mathrm{w(2)}}={ensuremath{displaystyle{frac{{ensuremaystyle{(C_1+1)(C_2+1)}}}}{{ensuremath{displaystyle{C_1+C_2+2}}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \langle x \rangle_{\mathrm{w(2)}}={\ensuremath{\displaystyle{\fra...
+...{\displaystyle{(C_1+1)(C_2+1)}}}}{{\ensuremath{\displaystyle{C_1+C_2+2}}}}}}}}
+$|; 
+
+$key = q/displaystylesigma_{r_{k,j}}={ensuremath{displaystyle{frac{{ensuremath{displaysty,j}}right|}}m_{k,j}}}}}}}}sqrt{{ensuremath{left({C_{k,j}+1}right)}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \sigma_{r_{k,j}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\d...
+...k,j}}\right\vert}}m_{k,j}}}}}}}}\sqrt{{\ensuremath{\left({C_{k,j}+1}\right)}}}
+$|; 
+
+$key = q/Vthreshold=7;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ Vthreshold=7$|; 
+
+$key = q/displaystylesigma_{R_ell}={ensuremath{displaystyle{frac{{ensuremath{displaystyleh{displaystyle{esqrt{(C+1)}}}}}{{ensuremath{displaystyle{|b|m}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \sigma_{R_\ell}={\ensuremath{\displaystyle{\frac{{\ensuremath{\di...
+...isplaystyle{e\sqrt{(C+1)}}}}}{{\ensuremath{\displaystyle{\vert b\vert m}}}}}}}
+$|; 
+
+$key = q/displaystylesigma_{langlexrangle_{!mathrm{w(1)}}}={ensuremath{displaystyle{frac{mathrm{w(1)}}}}}}{{ensuremath{displaystyle{N_{mathrm{obs}}^*}}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \sigma_{\langle x \rangle_{\!\mathrm{w(1)}}} = {\ensuremath{\disp...
+..._{\!\mathrm{w(1)}}}}}}{{\ensuremath{\displaystyle{
+N_{\mathrm{obs}}^*
+}}}}}}}}
+$|; 
+
+$key = q/displaystylelanglen^2rangle=mathop{sum}_{n=0}^{+infty}n^2P(n)=C_0^2+C_0;;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \langle n^2\rangle=\mathop{\sum}_{n=0}^{+\infty}
+n^2 P(n)=C_0^2+C_0 ;
+$|; 
+
+$key = q/k=1,ldots,P;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ k=1,\ldots,P$|; 
+
+$key = q/proptoepsilon_x;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \propto\epsilon_x$|; 
+
+$key = q/o_m;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ o_m$|; 
+
+$key = q/displaystyler_{k,j}={ensuremath{displaystyle{frac{{ensuremath{displaystyle{I_{k,emath{left({C_{k,j}+min{ensuremath{left({1,C_{k,j}}right)}}}right)}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle r_{k,j}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaysty...
+...nsuremath{\left({C_{k,j}+\min{\ensuremath{\left({1,C_{k,j}}\right)}}}\right)}}
+$|; 
+
+$key = q/displaystylesigma_x=sqrt{langlex^2rangle-langlexrangle^2}=sqrt{{ensuremath{displ{mathrm{obs}}}}}}}}}mathop{sum}_{j=1}^{N_{mathrm{obs}}}C_j}right)}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \sigma_x=\sqrt{\langle x^2\rangle-\langle x\rangle^2}=\sqrt{
+{\en...
+...\mathrm{obs}}}}}}}}}
+\mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}C_j
+}\right)}}
+}
+$|; 
+
+$key = q/lambda=1,10,100,ldots,1000000;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \lambda=1,10,100,\ldots,1000000$|; 
+
+$key = q/langlexrangle^*;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \langle x\rangle^*$|; 
+
+$key = q/displaystyleo_m+{ensuremath{displaystyle{frac{{ensuremath{displaystyle{180}}}}{{ensuremath{displaystyle{pi}}}}}}}c_mk_m;;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle o_m+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{180}}}}{{\ensuremath{\displaystyle{\pi}}}}}}}c_mk_m;$|; 
+
+$key = q/displaystylex=langlexrangle={ensuremath{displaystyle{frac{{ensuremath{displaystyystyle{N_{mathrm{obs}}}}}}}}}mathop{sum}_{j=1}^{N_{mathrm{obs}}}C_j.;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle x=\langle x\rangle={\ensuremath{\displaystyle{\frac{{\ensuremath{...
+...aystyle{ N_{\mathrm{obs}}}}}}}}}
+\mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}C_j .
+$|; 
+
+$key = q/O_j=C_j+min{ensuremath{left({1,C_j}right)}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ O_j=C_j+\min{\ensuremath{\left({1,C_j}\right)}}$|; 
+
+$key = q/O(epsilon_x^2);MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ O(\epsilon_x^2)$|; 
+
+$key = q/displaystylelangleXrangle=mathop{sum}_{n=0}^{+infty}eta_0nP(n)=eta_0C_0=X_0;;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \langle X\rangle=\mathop{\sum}_{n=0}^{+\infty}
+\eta_0 nP(n)=\eta_0 C_0=X_0 ;
+$|; 
+
+$key = q/includegraphics[width=textwidth]{data_receiver};AAT/;
+$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{data_receiver}|; 
+
+$key = q/chi^2;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \chi ^2$|; 
+
+$key = q/includegraphics[width=textwidth]{imagesslasheffiThinkBackplanes};AAT/;
+$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/effiThinkBackplanes}|; 
+
+$key = q/M;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ M$|; 
+
+$key = q/K;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ K$|; 
+
+$key = q/displaystylex=langlexrangle_{!mathrm{w}}={ensuremath{displaystyle{frac{{ensurema{displaystyle{1}}}}{{ensuremath{displaystyle{sigma_j^2}}}}}}}}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle x= \langle x \rangle_{\!\mathrm{w}}={\ensuremath{\displaystyle{\f...
+...th{\displaystyle{1
+}}}}{{\ensuremath{\displaystyle{
+\sigma_j^2
+}}}}}}}
+}}}}}}}
+$|; 
+
+$key = q/displaystylealpha_{jm}=o_m+{ensuremath{left({{ensuremath{displaystyle{frac{{ensuarctan{ensuremath{left[{{ensuremath{left({j-c_m}right)}}k_m}right]}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \alpha_{jm}=o_m+{\ensuremath{\left({{\ensuremath{\displaystyle{\f...
+...t)}}\arctan{\ensuremath{\left[{{\ensuremath{\left({j-c_m}\right)}}k_m}\right]}}$|; 
+
+$key = q/E_f;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ E_f$|; 
+
+$key = q/displaystyleR_ell={ensuremath{displaystyle{frac{{ensuremath{displaystyle{X_ell}}}}{{ensuremath{displaystyle{Y_ell}}}}}}};;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle R_\ell={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{X_\ell}}}}{{\ensuremath{\displaystyle{Y_\ell}}}}}}};
+$|; 
+
+$key = q/e_{k,j};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ e_{k,j}$|; 
+
+$key = q/I_0;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ I_0$|; 
+
+$key = q/displaystylesigma_x={ensuremath{displaystyle{frac{{ensuremath{displaystyle{1}}}}e{langlexrangle}}}}{{ensuremath{displaystyle{N_{mathrm{obs}}}}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \sigma_x={\ensuremath{\displaystyle{\frac{{\ensuremath{\displayst...
+...style{\langle x\rangle}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}}}}}}}}}
+$|; 
+
+$key = q/eta_0;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \eta_0$|; 
+
+$key = q/s=n+m;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ s=n+m$|; 
+
+$key = q/b;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ b$|; 
+
+$key = q/x;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ x$|; 
+
+$key = q/C_j=0;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ C_j=0$|; 
+
+$key = q/c_m;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ c_m$|; 
+
+$key = q/R_m;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ R_m$|; 
+
+$key = q/{langlexrangle};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ {\langle x \rangle} $|; 
+
+$key = q/displaystyleP(n)={ensuremath{displaystyle{frac{{ensuremath{displaystyle{C_0^n{ensuremath{mathrm{e}}}^{-C_0}}}}}{{ensuremath{displaystyle{n!}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle P(n)={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{C_0^n{\ensuremath{\mathrm{e}}}^{-C_0}
+}}}}{{\ensuremath{\displaystyle{
+n!}}}}}}}
+$|; 
+
+$key = q/C_j;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ C_j$|; 
+
+$key = q/includegraphics[width=textwidth]{imagesslashthr_scan_fluo};AAT/;
+$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/thr_scan_fluo}|; 
+
+$key = q/displaystylechi^2=mathop{sum}_{j=1}^{N_{mathrm{obs}}}{ensuremath{displaystyle{frft({F_j-O_j}right)}}^2}}}}{{ensuremath{displaystyle{sigma_j^2}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \chi^2 = \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}
+{\ensuremath{\dis...
+...\left({F_j-O_j}\right)}}^2
+}}}}{{\ensuremath{\displaystyle{
+\sigma_j^2
+}}}}}}}
+$|; 
+
+$key = q/displaystylec_mp.;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle c_m p.$|; 
+
+$key = q/O_j=C_j;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ O_j=C_j$|; 
+
+$key = q/includegraphics[width=textwidth]{imagesslashsettings};AAT/;
+$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/settings}|; 
+
+$key = q/displaystyleE{ensuremath{left({sigma_x^2}right)}}=mathop{sum}_{m,n=0}^{+infty}{ensuremath{displaystyle{lambda}}}}{{ensuremath{displaystyle{2}}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle E{\ensuremath{\left({\sigma_x^2}\right)}} = \mathop{\sum}_{m,n=0}...
+...ac{{\ensuremath{\displaystyle{\lambda}}}}{{\ensuremath{\displaystyle{2}}}}}}}}
+$|; 
+
+$key = q/N_E;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ N_E$|; 
+
+$key = q/displaystyle{ensuremath{displaystyle{frac{{ensuremath{displaystyle{p}}}}{{ensuremath{displaystyle{k_m}}}}}}};;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{p}}}}{{\ensuremath{\displaystyle{k_m}}}}}}};$|; 
+
+$key = q/displaystylemathop{sum}_{n=0}^{+infty}P(n)=1;;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \mathop{\sum}_{n=0}^{+\infty}
+P(n)=1 ;
+$|; 
+
+$key = q/hat{b}_{j,k};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \hat{b}_{j,k}$|; 
+
+$key = q/(108602&0xFFFFFFFE)>>1=54301;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ (108602\&0xFFFFFFFE)»1 = 54301$|; 
+
+$key = q/displaystylelanglexrangle_{mathrm{w(2)}}=langlexrangle+1-{ensuremath{displaystyle{(C_1-C_2)^2}}}}{{ensuremath{displaystyle{4(langlexrangle+1)}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \langle x \rangle_{\mathrm{w(2)}}=\langle x \rangle + 1 -{\ensure...
+...style{(C_1-C_2)^2}}}}{{\ensuremath{\displaystyle{4(\langle x \rangle+1)}}}}}}}
+$|; 
+
+$key = q/lambda;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \lambda$|; 
+
+$key = q/includegraphics[width=textwidth]{multi_detector};AAT/;
+$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{multi_detector}|; 
+
+$key = q/displaystylesigma_{langlexrangle_{!mathrm{w}}}={ensuremath{displaystyle{frac{{endisplaystyle{1}}}}{{ensuremath{displaystyle{sigma_j^2}}}}}}}}}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \sigma_{\langle x \rangle_{\!\mathrm{w}}} = {\ensuremath{\display...
+...h{\displaystyle{1
+}}}}{{\ensuremath{\displaystyle{
+\sigma_j^2
+}}}}}}}
+}}}}}}}}
+$|; 
+
+$key = q/2theta;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ 2\theta$|; 
+
+$key = q/O;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ O$|; 
+
+$key = q/includegraphics[width=textwidth]{imagesslashro_trigger_acquisition.eps};AAT/;
+$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/ro_trigger_acquisition.eps}|; 
+
+$key = q/O_n;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ O_n$|; 
+
+$key = q/displaystyleo_m;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle o_m$|; 
+
+$key = q/(108602&0x1)=0;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ (108602\&0x1) =0$|; 
+
+$key = q/ell;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \ell$|; 
+
+$key = q/displaystylesigma_{x^*}={ensuremath{displaystyle{frac{{ensuremath{displaystyle{Nnglexrangle^*}}}}{{ensuremath{displaystyle{N_{mathrm{obs}}^*}}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \sigma_{x^*}= {\ensuremath{\displaystyle{\frac{{\ensuremath{\disp...
+...e{\langle x\rangle^*}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}^*}}}}}}}}
+$|; 
+
+$key = q/O(epsilon_x^3);MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ O(\epsilon_x^3)$|; 
+
+$key = q/k;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ k$|; 
+
+$key = q/displaystylesigma_{R_ell}={ensuremath{displaystyle{frac{{ensuremath{displaystyle{1}}}}{{ensuremath{displaystyle{sqrt{Y_ell}}}}}}}}.;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \sigma_{R_\ell}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{\sqrt{Y_\ell}}}}}}}}.
+$|; 
+
+$key = q/displaystyle=;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle =$|; 
+
+$key = q/displaystylesigma_{langlexrangle_{!mathrm{w(2)}}}={ensuremath{displaystyle{frac{mathrm{w(2)}}}}}}{{ensuremath{displaystyle{N_{mathrm{obs}}^*}}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \sigma_{\langle x \rangle_{\!\mathrm{w(2)}}} = {\ensuremath{\disp...
+..._{\!\mathrm{w(2)}}}}}}{{\ensuremath{\displaystyle{
+N_{\mathrm{obs}}^*
+}}}}}}}}
+$|; 
+
+$key = q/displaystyleqquadhat{b}_{k,j}inB_ell.;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \qquad \hat{b}_{k,j}\in B_\ell .
+$|; 
+
+$key = q/{langlexrangle_{!mathrm{w(1)}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ {\langle x \rangle_{\!\mathrm{w(1)}}}$|; 
+
+$key = q/displaystylelangleX^2rangle=int_{-infty}^{+infty}{ensuremath{mathrm{d}{eta},}}mahop{sum}_{n=0}^{+infty}n^2P(n)=(eta_0^2+sigma_{eta_0}^2)(C_0^2+C_0);;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \langle X^2\rangle=\int_{-\infty}^{+\infty}{\ensuremath{\mathrm{d...
+...p{\sum}_{n=0}^{+\infty}
+n^2 P(n)
+=
+(\eta_0^2+\sigma_{\eta_0}^2)(C_0^2+C_0) ;
+$|; 
+
+$key = q/sigma_{O_n};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \sigma_{O_n}$|; 
+
+$key = q/{langlexrangle^*};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ {\langle x \rangle^*} $|; 
+
+$key = q/Counts=500;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ Counts=500$|; 
+
+$key = q/displaystylesigma_{I_{k,j}}={ensuremath{displaystyle{frac{{ensuremath{displaystyisplaystyle{m_{k,j}}}}}}}}sqrt{{ensuremath{left({C_{k,j}+1}right)}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \sigma_{I_{k,j}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\d...
+...ath{\displaystyle{m_{k,j}}}}}}}}\sqrt{{\ensuremath{\left({C_{k,j}+1}\right)}}}
+$|; 
+
+$key = q/Deltat;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \Delta t$|; 
+
+$key = q/displaystylelanglexrangle_{!mathrm{w(1)}}={ensuremath{displaystyle{frac{{ensuremremath{displaystyle{1}}}}{{ensuremath{displaystyle{C_j}}}}}}}}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \langle x \rangle_{\!\mathrm{w(1)}}={\ensuremath{\displaystyle{\f...
+...nsuremath{\displaystyle{1
+}}}}{{\ensuremath{\displaystyle{
+C_j
+}}}}}}}
+}}}}}}}
+$|; 
+
+$key = q/displaystyleX_ell=mathop{sum_{k,j}}_{{ensuremath{left|{b_{k,j}capB_ell}right|}}>style{B}}}}}}}r_{k,j}{ensuremath{left({sigma_{r_{k,j}}}right)}}^{-2};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle X_\ell=\mathop{\sum_{k,j}}_{ {\ensuremath{\left\vert{ b_{k,j}\cap...
+...aystyle{B}}}}}}} r_{k,j} {\ensuremath{\left({\sigma_{r_{k,j}}}\right)}}^{-2}
+$|; 
+
+$key = q/displaystyleK={ensuremath{displaystyle{frac{{ensuremath{displaystyle{1}}}}{{ensusplaystyle{R_ell}}}}{{ensuremath{displaystyle{sigma_{R_ell}^2}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle K={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+1
+...
+...h{\displaystyle{R_\ell}}}}{{\ensuremath{\displaystyle{\sigma_{R_\ell}^2}}}}}}}
+$|; 
+
+$key = q/sigma_X=sqrt{langleXrangle}=sqrt{X_0};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \sigma_X=\sqrt{\langle X\rangle}=\sqrt{X_0}$|; 
+
+$key = q/O_j;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ O_j$|; 
+
+$key = q/sigma_j^2=C_j+1;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \sigma_j^2=C_j+1$|; 
+
+$key = q/displaystyleE{ensuremath{left({{ensuremath{displaystyle{frac{{ensuremath{displayh{displaystyle{lambda^{n+m}}}}}{{ensuremath{displaystyle{n!m!}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle E{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremat...
+...uremath{\displaystyle{\lambda^{n+m}}}}}{{\ensuremath{\displaystyle{n!m!}}}}}}}
+$|; 
+
+$key = q/displaystylemathsf{GoF}=sqrt{{ensuremath{displaystyle{frac{{ensuremath{displayst}}}}}}}}}}}}}}}}}{{ensuremath{displaystyle{N_{mathrm{obs}}-1}}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \mathsf{GoF}=
+\sqrt{
+{\ensuremath{\displaystyle{\frac{{\ensuremat...
+...
+}}}}}}} }}}}}}}
+}}}}{{\ensuremath{\displaystyle{
+N_{\mathrm{obs}}-1
+}}}}}}}
+}
+$|; 
+
+$key = q/B;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ B$|; 
+
+$key = q/{ensuremath{{2theta}}}_{max}={ensuremath{{2theta}}}_0+MB;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ {\ensuremath{{2\theta}}}_{max}={\ensuremath{{2\theta}}}_0+MB$|; 
+
+$key = q/displaystylehat{B}_ell,quadKR_ell,quadKsigma_{R_ell};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \hat{B}_\ell, \quad KR_\ell, \quad K\sigma_{R_\ell}
+$|; 
+
+$key = q/E_t=E_0slash2;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ E_t=E_0/2$|; 
+
+$key = q/displaystylesigma_{C_0}=sqrt{langlen^2rangle-langlenrangle^2}=sqrt{C_0};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \sigma_{C_0}=\sqrt{\langle n^2\rangle-\langle n\rangle^2}=\sqrt{C_0}
+$|; 
+
+$key = q/epsilon_lambda;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \epsilon_\lambda$|; 
+
+$key = q/displaystyle{I_0}DeltatDeltaOmega{ensuremath{displaystyle{frac{{ensuremath{displ}}}}{{ensuremath{displaystyle{{ensuremath{mathrm{d}{},}}Omega}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle {I_0}\Delta t \Delta\Omega{\ensuremath{\displaystyle{\frac{{\ensu...
+...ma}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}  }}\Omega}}}}}}}
+$|; 
+
+$key = q/displaystyleqquad{ensuremath{left|{b_{k,j}capB_ell}right|}}>0.;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \qquad {\ensuremath{\left\vert{ b_{k,j}\cap B_\ell }\right\vert}} > 0.
+$|; 
+
+$key = q/displaystyle{ensuremath{displaystyle{frac{{ensuremath{displaystyle{p}}}}{{ensuremath{displaystyle{R_m}}}}}}};;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{p}}}}{{\ensuremath{\displaystyle{R_m}}}}}}};$|; 
+
 $key = q/Updownarrow;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ \Updownarrow$|; 
 
 $key = q/includegraphics[width=textwidth]{imagesslashgated_acquisition.eps};AAT/;
 $cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/gated_acquisition.eps}|; 
 
-$key = q/Rightarrow;MSF=1.6;AAT/;
+$key = q/displaystyleD_m;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ \Rightarrow$|; 
+ WIDTH="30" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img61.png"
+ ALT="$\displaystyle D_m$">|; 
 
-$key = q/cdot;MSF=1.6;AAT/;
+$key = q/epsilon_lambda=sqrt{lambdaslashN}slashlambda=1slashsqrt{Nlambda};MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ \cdot$|; 
+ WIDTH="179" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img198.png"
+ ALT="$ \epsilon_\lambda=\sqrt{\lambda/N}/\lambda=1/\sqrt{N\lambda}$">|; 
 
-$key = q/d;MSF=1.6;AAT/;
+$key = q/{langlexrangle_{!mathrm{w(1)}}}:;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ d$|; 
+ WIDTH="64" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img208.png"
+ ALT="$ {\langle x \rangle_{\!\mathrm{w(1)}}} :$">|; 
 
-$key = q/includegraphics[width=textwidth]{imagesslashFFSetup};AAT/;
+$key = q/displaystylehat{B}_ell={ensuremath{{2theta}}}_0+(ell-1slash2)B,;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/FFSetup}|; 
+ WIDTH="166" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img91.png"
+ ALT="$\displaystyle \hat{B}_\ell={\ensuremath{{2\theta}}}_0+(\ell-1/2)B,$">|; 
 
-$key = q/includegraphics[width=textwidth]{imagesslashthr_scan_fluo};AAT/;
+$key = q/DeltaOmegaproptoDelta{ensuremath{{2theta}}};MSF=1.6;AAT/;
 $cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/thr_scan_fluo}|; 
+ WIDTH="80" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="|."$dir".q|img71.png"
+ ALT="$ \Delta\Omega\propto \Delta {\ensuremath{{2\theta}}}$">|; 
 
-$key = q/includegraphics[width=textwidth]{imagesslashthr_scan_expl};AAT/;
+$key = q/displaystyleR_m;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/thr_scan_expl}|; 
+ WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img59.png"
+ ALT="$\displaystyle R_m$">|; 
 
-$key = q/includegraphics[width=textwidth]{imagesslashsample_with_fluorescence};AAT/;
+$key = q/displaystyleY_ell={ensuremath{displaystyle{frac{{ensuremath{displaystyle{{ensureh{displaystyle{|b|^2m^2}}}}{{ensuremath{displaystyle{e^2(C+1)}}}}}}};MSF=1.6;AAT/;
 $cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/sample_with_fluorescence}|; 
+ WIDTH="344" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img122.png"
+ ALT="$\displaystyle Y_\ell={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyl...
+...\displaystyle{\vert b\vert^2m^2}}}}{{\ensuremath{\displaystyle{e^2(C+1)}}}}}}}
+$">|; 
 
-$key = q/includegraphics[width=textwidth]{imagesslashsettings};AAT/;
+$key = q/displaystyle{ensuremath{left|{b_{k,j}}right|}}={ensuremath{{2theta}}}_{k,j}^{+}-{ensuremath{{2theta}}}_{k,j}^{-};MSF=1.6;AAT/;
 $cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/settings}|; 
-
-$key = q/includegraphics[width=textwidth]{imagesslashnoise_thresholdscanuntrimmed};AAT/;
-$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/noise_thresholdscanuntrimmed}|; 
+ WIDTH="145" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
+ SRC="|."$dir".q|img79.png"
+ ALT="$\displaystyle {\ensuremath{\left\vert{b_{k,j}}\right\vert}}={\ensuremath{{2\theta}}}_{k,j}^{+}-{\ensuremath{{2\theta}}}_{k,j}^{-}
+$">|; 
 
 $key = q/E_t>E_f+3;MSF=1.6;AAT/;
 $cached_env_img{$key} = q|$ E_t>E_f+3$|; 
 
+$key = q/displaystyleb_{k,j};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle b_{k,j}$|; 
+
+$key = q/displaystylelanglenrangle=mathop{sum}_{n=0}^{+infty}nP(n)=C_0;;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \langle n\rangle=\mathop{\sum}_{n=0}^{+\infty}
+nP(n)=C_0 ;
+$|; 
+
+$key = q/displaystyleE{ensuremath{left({{ensuremath{displaystyle{frac{{ensuremath{displaye}}}^{-2lambda}}}}}{{ensuremath{displaystyle{4lambda^2}}}}}}}%{n!m!};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle E{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremat...
+...hrm{e}}}^{-2\lambda}}}}}{{\ensuremath{\displaystyle{4\lambda^2}}}}}}}
+%{n!m!}
+$|; 
+
+$key = q/mu;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \mu$|; 
+
+$key = q/alpha_{jm};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \alpha_{jm}$|; 
+
+$key = q/E_t;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ E_t$|; 
+
+$key = q/displaystylewidehat{P}(eta)={ensuremath{displaystyle{frac{{ensuremath{displaystyght)}}^2}}}}}{{ensuremath{displaystyle{sigma_{eta_0}sqrt{2pi}}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \widehat{P}(\eta)={\ensuremath{\displaystyle{\frac{{\ensuremath{\...
+...ght)}}^2
+}
+}}}}{{\ensuremath{\displaystyle{
+\sigma_{\eta_0}\sqrt{2\pi}
+}}}}}}}
+$|; 
+
+$key = q/{ensuremath{{2theta}}}_0;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ {\ensuremath{{2\theta}}}_0$|; 
+
+$key = q/displaystyle{ensuremath{displaystyle{frac{{ensuremath{displaystyle{sigma_X}}}}{{{sigma_{eta_0}}}}}{{ensuremath{displaystyle{eta_0}}}}}}}}right)}}^2};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sigm...
+...yle{\sigma_{\eta_0}}}}}{{\ensuremath{\displaystyle{\eta_0}}}}}}}}\right)}}^2
+}
+$|; 
+
+$key = q/sqrt{C_0};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \sqrt{C_0}$|; 
+
+$key = q/includegraphics[width=textwidth]{imagesslashtrimbitplot};AAT/;
+$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/trimbitplot}|; 
+
+$key = q/P;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ P$|; 
+
+$key = q/includegraphics[width=textwidth]{imagesslashbad_ff_col};AAT/;
+$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/bad_ff_col}|; 
+
+$key = q/{langlexrangle_{!mathrm{w(2)}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ {\langle x \rangle_{\!\mathrm{w(2)}}}$|; 
+
+$key = q/displaystylelangleX^2rangle=mathop{sum}_{n=0}^{+infty}eta_0^2n^2P(n)=eta_0^2(C_0^2+C_0)=X_0^2+eta_0X_0;;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \langle X^2\rangle=\mathop{\sum}_{n=0}^{+\infty}
+\eta_0^2 n^2 P(n)=\eta_0^2(C_0^2+C_0)=X_0^2+\eta_0 X_0 ;
+$|; 
+
+$key = q/displaystyleb_{k,j}={ensuremath{left[{{ensuremath{{2theta}}}_{k,j}^{-},{ensuremath{{2theta}}}_{k,j}^{+}}right]}},qquadj=1,ldots,N_k;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle b_{k,j}={\ensuremath{\left[{{\ensuremath{{2\theta}}}_{k,j}^{-},{\ensuremath{{2\theta}}}_{k,j}^{+}}\right]}},\qquad j=1,\ldots,N_k
+$|; 
+
+$key = q/sigma_j^2=C_j;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \sigma_j^2=C_j$|; 
+
+$key = q/pm;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \pm$|; 
+
+$key = q/xi_lambda=;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \xi_\lambda = $|; 
+
+$key = q/k,j;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ k,j$|; 
+
+$key = q/m_{k,j};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ m_{k,j}$|; 
+
+$key = q/lambda<100;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \lambda<100$|; 
+
+$key = q/displaystyleE{ensuremath{left({langlexrangle}right)}}=mathop{sum}_{m,n=0}^{+inft{mathrm{e}}}^{-lambda}}}}}{{ensuremath{displaystyle{n!}}}}}}}=lambda;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle E{\ensuremath{\left({\langle x \rangle}\right)}} = \mathop{\sum}_...
+...ath{\mathrm{e}}}^{-\lambda}}}}}{{\ensuremath{\displaystyle{n!}}}}}}}
+=\lambda
+$|; 
+
+$key = q/e_lambdaslashepsilon_lambda;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ e_\lambda/\epsilon_\lambda$|; 
+
+$key = q/includegraphics[width=textwidth]{imagesslashtrigger_acquisition.eps};AAT/;
+$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/trigger_acquisition.eps}|; 
+
+$key = q/displaystylec_m;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle c_m$|; 
+
+$key = q/k=0ldotss;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ k=0\ldots s$|; 
+
+$key = q/k_m;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ k_m$|; 
+
+$key = q/E_lambda;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ E_\lambda$|; 
+
+$key = q/includegraphics[width=textwidth]{imagesslashnormal_acquisition.eps};AAT/;
+$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/normal_acquisition.eps}|; 
+
+$key = q/displaystylemathop{sum}_{ell=1}^M{ensuremath{displaystyle{frac{{ensuremath{displlaystyle{R_ell}}}}{{ensuremath{displaystyle{sigma_{R_ell}^2}}}}}}}=M;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \mathop{\sum}_{\ell=1}^M{\ensuremath{\displaystyle{\frac{{\ensure...
+...\displaystyle{R_\ell}}}}{{\ensuremath{\displaystyle{\sigma_{R_\ell}^2}}}}}}}=M
+$|; 
+
+$key = q/displaystylelangleOrangle={ensuremath{displaystyle{frac{{ensuremath{displaystylemath{displaystyle{mathop{sum}_{n=1}^{N_E}nu_nsigma_{O_n}^{-2}}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \langle O\rangle ={\ensuremath{\displaystyle{\frac{{\ensuremath{\...
+...remath{\displaystyle{
+\mathop{\sum}_{n=1}^{N_E}\nu_n
+\sigma_{O_n}^{-2}
+}}}}}}}
+$|; 
+
+$key = q/Omega;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \Omega$|; 
+
+$key = q/displaystylechi_{(1)}^2=mathop{sum}_{j=1}^{N_{mathrm{obs}}}{ensuremath{displaystght)}}}right)}}}right)}}^2}}}}{{ensuremath{displaystyle{C_j+1}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \chi_{(1)}^2 = \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}
+{\ensuremat...
+...\right)}}}\right)}}}\right)}}^2
+}}}}{{\ensuremath{\displaystyle{
+C_j+1
+}}}}}}}
+$|; 
+
+$key = q/displaystylemathsf{GoF}_{(1)}=sqrt{{ensuremath{displaystyle{frac{{ensuremath{disremath{left({langlexrangle^*-langlexrangle_{!mathrm{w(1)}}}right)}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \mathsf{GoF}_{(1)}=
+\sqrt{
+{\ensuremath{\displaystyle{\frac{{\ens...
+...th{\left({
+\langle x\rangle^*-\langle x \rangle_{\!\mathrm{w(1)}}
+}\right)}}
+}
+$|; 
+
+$key = q/displaystylealpha_{jm}=Phi_m-{ensuremath{left({{ensuremath{displaystyle{frac{{endisplaystyle{D_m-pj}}}}{{ensuremath{displaystyle{R_m}}}}}}}}right)}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \alpha_{jm}=\Phi_m-{\ensuremath{\left({{\ensuremath{\displaystyle...
+...remath{\displaystyle{D_m-pj}}}}{{\ensuremath{\displaystyle{R_m}}}}}}}}\right)}}$|; 
+
+$key = q/nu_n;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \nu_n$|; 
+
+$key = q/C_0;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ C_0$|; 
+
+$key = q/langlexrangle;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \langle x \rangle$|; 
+
+$key = q/includegraphics[width=textwidth]{imagesslasheffiSiHardXRays2};AAT/;
+$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/effiSiHardXRays2}|; 
+
+$key = q/B_ell;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ B_\ell$|; 
+
+$key = q/displaystylelangleXrangle=int_{-infty}^{+infty}{ensuremath{mathrm{d}{eta},}}math+infty}{ensuremath{mathrm{d}{eta},}}widehat{P}(eta)eta=eta_0C_0=X_0;;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \langle X\rangle=\int_{-\infty}^{+\infty}{\ensuremath{\mathrm{d}{...
+...}{\ensuremath{\mathrm{d}{\eta}  }} \widehat{P}(\eta)\eta
+=
+\eta_0 C_0=X_0 ;
+$|; 
+
+$key = q/displaystyle{ensuremath{displaystyle{frac{{ensuremath{displaystyle{{ensuremath{m}}}}{{ensuremath{displaystyle{{ensuremath{mathrm{d}{},}}Omega}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ens...
+...ma}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}  }}\Omega}}}}}}}
+$|; 
+
+$key = q/sigma_j;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \sigma_j$|; 
+
+$key = q/includegraphics[width=textwidth]{imagesslashFFSetup};AAT/;
+$cached_env_img{$key} = q|\includegraphics[width=\textwidth]{images/FFSetup}|; 
+
+$key = q/cdot;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ \cdot$|; 
+
+$key = q/Y_ell=0;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ Y_\ell=0$|; 
+
+$key = q/displaystyleepsilon_x={ensuremath{displaystyle{frac{{ensuremath{displaystyle{sigma_x}}}}{{ensuremath{displaystyle{x}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \epsilon_x = {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sigma_x}}}}{{\ensuremath{\displaystyle{x}}}}}}}
+$|; 
+
+$key = q/n;MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$ n$|; 
+
+$key = q/displaystylechi^2=mathop{sum}_{j=1}^{N_{mathrm{obs}}}{ensuremath{displaystyle{frleft({x-O_j}right)}}^2}}}}{{ensuremath{displaystyle{sigma_j^2}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \chi^2 = \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}
+{\ensuremath{\dis...
+...h{\left({x-O_j}\right)}}^2
+}}}}{{\ensuremath{\displaystyle{
+\sigma_j^2
+}}}}}}}
+$|; 
+
+$key = q/displaystyleP'(X)=P(Xslasheta_0)=P(n)qquadBiggl|Biggr.qquadfrac{X}{eta_0}equivninmathbb{Z};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle P'(X)=P(X/\eta_0)=P(n)\qquad\Biggl\vert\Biggr.\qquad \frac{X}{\eta_0}\equiv n\in\mathbb{Z}
+$|; 
+
+$key = q/displaystylehat{b}_{k,j}={ensuremath{displaystyle{frac{{ensuremath{displaystyle{nsuremath{{2theta}}}_{k,j}^{-}}}}}{{ensuremath{displaystyle{2}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \hat{b}_{k,j}={\ensuremath{\displaystyle{\frac{{\ensuremath{\disp...
+...{+}+{\ensuremath{{2\theta}}}_{k,j}^{-}}}}}{{\ensuremath{\displaystyle{2}}}}}}}
+$|; 
+
+$key = q/displaystylesqrt{{ensuremath{displaystyle{frac{{ensuremath{displaystyle{B}}}}{{ensuremath{displaystyle{{ensuremath{left|{bcapB_ell}right|}}}}}}}}}};MSF=1.6;AAT/;
+$cached_env_img{$key} = q|$\displaystyle \sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle...
+...ath{\displaystyle{{\ensuremath{\left\vert{ b\cap B_\ell }\right\vert}}}}}}}}}}
+$|; 
+
 1;
 
diff --git a/manual/docs/html/slsDetectors-FAQ/images.tex b/manual/docs/html/slsDetectors-FAQ/images.tex
index b756e3d51..267e7c444 100644
--- a/manual/docs/html/slsDetectors-FAQ/images.tex
+++ b/manual/docs/html/slsDetectors-FAQ/images.tex
@@ -228,11 +228,17 @@
 
 % !!! IMAGES START HERE !!!
 
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline7641}%
+$ \chi ^2$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
 \stepcounter{chapter}
 \stepcounter{section}
 \stepcounter{section}
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2621}%
+\lthtmlpictureA{tex2html_wrap7721}%
 \includegraphics[width=\textwidth]{multi_detector}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
@@ -240,7 +246,7 @@
 \stepcounter{subsection}
 \stepcounter{section}
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2627}%
+\lthtmlpictureA{tex2html_wrap7727}%
 \includegraphics[width=\textwidth]{data_receiver}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
@@ -251,26 +257,26 @@
 \stepcounter{section}
 \stepcounter{section}
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2637}%
+\lthtmlinlinemathA{tex2html_wrap_inline7737}%
 $ d$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
 
 \stepcounter{section}
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2640}%
+\lthtmlinlinemathA{tex2html_wrap_inline7740}%
 $ \Updownarrow$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2642}%
+\lthtmlinlinemathA{tex2html_wrap_inline7742}%
 $ \Rightarrow$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmldisplayA{displaymath2644}%
+\lthtmldisplayA{displaymath7744}%
 \begin{displaymath}\textrm{\textbf{MEASUREMENTS}} \\
  \left\Updownarrow \,
     \begin{array}{l} \\
@@ -346,25 +352,25 @@ $ \Rightarrow$%
 
 \stepcounter{section}
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2667}%
+\lthtmlpictureA{tex2html_wrap7767}%
 \includegraphics[width=\textwidth]{images/normal_acquisition.eps}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2671}%
+\lthtmlpictureA{tex2html_wrap7771}%
 \includegraphics[width=\textwidth]{images/gated_acquisition.eps}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2675}%
+\lthtmlpictureA{tex2html_wrap7775}%
 \includegraphics[width=\textwidth]{images/trigger_acquisition.eps}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2679}%
+\lthtmlpictureA{tex2html_wrap7779}%
 \includegraphics[width=\textwidth]{images/ro_trigger_acquisition.eps}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
@@ -374,13 +380,13 @@ $ \Rightarrow$%
 \stepcounter{section}
 \stepcounter{subsection}
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2690}%
+\lthtmlinlinemathA{tex2html_wrap_inline7790}%
 $ (108602\&0xFFFFFFFE)>>1 = 54301$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2692}%
+\lthtmlinlinemathA{tex2html_wrap_inline7792}%
 $ (108602\&0x1) =0$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
@@ -391,80 +397,103 @@ $ (108602\&0x1) =0$%
 \stepcounter{section}
 \stepcounter{subsection}
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2698}%
+\lthtmlpictureA{tex2html_wrap7801}%
+\includegraphics[width=\textwidth]{images/effiSiHardXRays2}%
+\lthtmlpictureZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline7803}%
+$ \mu$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlpictureA{tex2html_wrap7807}%
+\includegraphics[width=\textwidth]{images/effiThinkBackplanes}%
+\lthtmlpictureZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{subsection}
+{\newpage\clearpage
+\lthtmlpictureA{tex2html_wrap7812}%
 \includegraphics[width=\textwidth]{images/settings}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
 
+\stepcounter{section}
+\stepcounter{chapter}
+\stepcounter{section}
+\stepcounter{subsection}
 \stepcounter{section}
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2703}%
+\lthtmlpictureA{tex2html_wrap7822}%
 \includegraphics[width=\textwidth]{images/thr_scan_expl}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2707}%
+\lthtmlpictureA{tex2html_wrap7826}%
 \includegraphics[width=\textwidth]{images/thr_scan_fluo}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2712}%
+\lthtmlinlinemathA{tex2html_wrap_inline7831}%
 $ E_0$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2716}%
+\lthtmlinlinemathA{tex2html_wrap_inline7835}%
 $ E_t=E_0/2$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2720}%
+\lthtmlinlinemathA{tex2html_wrap_inline7839}%
 $ E_f$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2724}%
+\lthtmlinlinemathA{tex2html_wrap_inline7843}%
 $ E_t$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2738}%
+\lthtmlinlinemathA{tex2html_wrap_inline7857}%
 $ E_fE_f+3$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2744}%
+\lthtmlinlinemathA{tex2html_wrap_inline7863}%
 $ E_t4$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2767}%
+\lthtmlpictureA{tex2html_wrap7886}%
 \includegraphics[width=\textwidth]{images/sample_with_fluorescence}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
@@ -472,14 +501,14 @@ $ E_t>4$%
 \stepcounter{section}
 \stepcounter{subsection}
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2773}%
+\lthtmlpictureA{tex2html_wrap7892}%
 \includegraphics[width=\textwidth]{images/bad_ff_col}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
 
 \stepcounter{subsection}
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2778}%
+\lthtmlpictureA{tex2html_wrap7897}%
 \includegraphics[width=\textwidth]{images/FFSetup}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
@@ -487,49 +516,49 @@ $ E_t>4$%
 \stepcounter{section}
 \stepcounter{subsection}
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2785}%
+\lthtmlinlinemathA{tex2html_wrap_inline7904}%
 $ Vthreshold=7$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2787}%
+\lthtmlinlinemathA{tex2html_wrap_inline7906}%
 $ Counts=500$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2789}%
+\lthtmlinlinemathA{tex2html_wrap_inline7908}%
 $ Resolution=4$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2791}%
+\lthtmlinlinemathA{tex2html_wrap_inline7910}%
 $ \pm$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2792}%
+\lthtmlpictureA{tex2html_wrap7911}%
 \includegraphics[width=\textwidth]{images/noise_thresholdscanuntrimmed}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2796}%
+\lthtmlpictureA{tex2html_wrap7915}%
 \includegraphics[width=\textwidth]{images/trimbitdistribution}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2800}%
+\lthtmlpictureA{tex2html_wrap7919}%
 \includegraphics[width=\textwidth]{images/trimbitplot}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
 
 {\newpage\clearpage
-\lthtmlpictureA{tex2html_wrap2804}%
+\lthtmlpictureA{tex2html_wrap7923}%
 \includegraphics[width=\textwidth]{images/noise_thresholdscantrimmed}%
 \lthtmlpictureZ
 \lthtmlcheckvsize\clearpage}
@@ -537,7 +566,7 @@ $ \pm$%
 \stepcounter{section}
 \stepcounter{subsection}
 {\newpage\clearpage
-\lthtmlinlinemathA{tex2html_wrap_inline2813}%
+\lthtmlinlinemathA{tex2html_wrap_inline7932}%
 $ \cdot$%
 \lthtmlinlinemathZ
 \lthtmlcheckvsize\clearpage}
@@ -545,5 +574,1460 @@ $ \cdot$%
 \stepcounter{section}
 \stepcounter{section}
 \stepcounter{subsection}
+\stepcounter{chapter}
+\stepcounter{section}
+\stepcounter{section}
+\stepcounter{section}
+\stepcounter{section}
+\stepcounter{chapter}
+\stepcounter{section}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline7946}%
+$ \alpha_{jm}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline7948}%
+$ R_m$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline7950}%
+$ \Phi_m$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline7952}%
+$ D_m$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline7954}%
+$ c_m$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline7956}%
+$ o_m$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline7958}%
+$ k_m$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay7960}%
+$\displaystyle \alpha_{jm}=\Phi_m-{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{180}}}}{{\ensuremath{\displaystyle{\pi}}}}}}}}\right)}}\arctan{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{D_m-pj}}}}{{\ensuremath{\displaystyle{R_m}}}}}}}}\right)}}$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay7962}%
+$\displaystyle \alpha_{jm}=o_m+{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{180}}}}{{\ensuremath{\displaystyle{\pi}}}}}}}}\right)}}c_mk_m+{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{180}}}}{{\ensuremath{\displaystyle{\pi}}}}}}}}\right)}}\arctan{\ensuremath{\left[{{\ensuremath{\left({j-c_m}\right)}}k_m}\right]}}$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay7965}%
+$\displaystyle c_m$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay7967}%
+$\displaystyle =$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay7969}%
+$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{D_m}}}}{{\ensuremath{\displaystyle{p}}}}}}};$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay7971}%
+$\displaystyle k_m$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay7975}%
+$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{p}}}}{{\ensuremath{\displaystyle{R_m}}}}}}};$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay7977}%
+$\displaystyle o_m$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay7981}%
+$\displaystyle \Phi_m-{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{180}}}}{{\ensuremath{\displaystyle{\pi}}}}}}}{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{D_m}}}}{{\ensuremath{\displaystyle{R_m}}}}}}}.$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay7984}%
+$\displaystyle \Phi_m$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay7988}%
+$\displaystyle o_m+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{180}}}}{{\ensuremath{\displaystyle{\pi}}}}}}}c_mk_m;$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay7990}%
+$\displaystyle R_m$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay7994}%
+$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{p}}}}{{\ensuremath{\displaystyle{k_m}}}}}}};$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay7996}%
+$\displaystyle D_m$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8000}%
+$\displaystyle c_m p.$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{section}
+\stepcounter{subsection}
+\stepcounter{subsubsection}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8005}%
+$ {\ensuremath{{2\theta}}}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8007}%
+$ 2\theta$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{subsubsection}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8010}%
+$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\bf {\sigma}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\Omega}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8012}%
+$ \Omega$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8014}%
+$\displaystyle {I_0}\Delta t \Delta\Omega{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\bf {\sigma}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\Omega}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8016}%
+$ \Delta t$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8018}%
+$ \Delta\Omega$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8020}%
+$ I_0$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8024}%
+$ \Delta\Omega\propto \Delta {\ensuremath{{2\theta}}}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{subsection}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8035}%
+$ P$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8037}%
+$ k$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8039}%
+$ k=1,\ldots,P$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8041}%
+$ N_k$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8043}%
+$ 2\theta\equiv{\ensuremath{{2\theta}}}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8045}%
+$\displaystyle b_{k,j}={\ensuremath{\left[{{\ensuremath{{2\theta}}}_{k,j}^{-},{\ensuremath{{2\theta}}}_{k,j}^{+}}\right]}},\qquad j=1,\ldots,N_k
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8047}%
+$\displaystyle \hat{b}_{k,j}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{{2\theta}}}_{k,j}^{+}+{\ensuremath{{2\theta}}}_{k,j}^{-}}}}}{{\ensuremath{\displaystyle{2}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8049}%
+$\displaystyle {\ensuremath{\left|{b_{k,j}}\right|}}={\ensuremath{{2\theta}}}_{k,j}^{+}-{\ensuremath{{2\theta}}}_{k,j}^{-}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8051}%
+$ C_{k,j}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8053}%
+$ e_{k,j}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8055}%
+$ m_{k,j}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8057}%
+$ b_{k,j}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8059}%
+$\displaystyle I_{k,j}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{e_{k,j}}}}}{{\ensuremath{\displaystyle{m_{k,j}}}}}}}}{\ensuremath{\left({C_{k,j}+\min{\ensuremath{\left({1,C_{k,j}}\right)}}}\right)}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8061}%
+$\displaystyle \sigma_{I_{k,j}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{e_{k,j}}}}}{{\ensuremath{\displaystyle{m_{k,j}}}}}}}}\sqrt{{\ensuremath{\left({C_{k,j}+1}\right)}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8063}%
+$\displaystyle r_{k,j}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{I_{k,j}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\left|{b_{k,j}}\right|}}}}}}}}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{e_{k,j}}}}}{{\ensuremath{\displaystyle{m_{k,j}{\ensuremath{\left|{b_{k,j}}\right|}}}}}}}}}{\ensuremath{\left({C_{k,j}+\min{\ensuremath{\left({1,C_{k,j}}\right)}}}\right)}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8065}%
+$\displaystyle \sigma_{r_{k,j}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sigma_{I_{k,j}}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\left|{b_{k,j}}\right|}}}}}}}}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{e_{k,j}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\left|{b_{k,j}}\right|}}m_{k,j}}}}}}}}\sqrt{{\ensuremath{\left({C_{k,j}+1}\right)}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8067}%
+$ M$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8069}%
+$\displaystyle B_\ell=[{\ensuremath{{2\theta}}}_0+(\ell-1)B, {\ensuremath{{2\theta}}}_0+\ell B],\qquad \ell=1,\ldots,M
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8071}%
+$\displaystyle {\ensuremath{\left|{B_\ell}\right|}}=B$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8073}%
+$\displaystyle \hat{B}_\ell={\ensuremath{{2\theta}}}_0+(\ell-1/2)B,$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8075}%
+$ {\ensuremath{{2\theta}}}_0$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8077}%
+$ {\ensuremath{{2\theta}}}_{max}={\ensuremath{{2\theta}}}_0+MB$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8079}%
+$ \ell$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8081}%
+$\displaystyle b_{k,j}$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8082}%
+$\displaystyle \qquad {\ensuremath{\left|{ b_{k,j}\cap B_\ell }\right|}} > 0.
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8085}%
+$\displaystyle \qquad \hat{b}_{k,j}\in B_\ell .
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8089}%
+$ B_\ell$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8091}%
+$ N_E$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8093}%
+$ O_n$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8095}%
+$ O$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8097}%
+$ \sigma_{O_n}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8099}%
+$ \nu_n$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8101}%
+$\displaystyle \langle O\rangle ={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+\mathop{\sum}_{n=1}^{N_E}\nu_n
+O_n\sigma_{O_n}^{-2}
+}}}}{{\ensuremath{\displaystyle{
+\mathop{\sum}_{n=1}^{N_E}\nu_n
+\sigma_{O_n}^{-2}
+}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8103}%
+$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b_{k,j}\cap B_\ell }\right|}}}}}}{{\ensuremath{\displaystyle{B}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8105}%
+$ k,j$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8109}%
+$\displaystyle X_\ell=\mathop{\sum_{k,j}}_{ {\ensuremath{\left|{ b_{k,j}\cap B_\ell }\right|}} > 0}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b_{k,j}\cap B_\ell }\right|}}}}}}{{\ensuremath{\displaystyle{B}}}}}}}\   r_{k,j}\  {\ensuremath{\left({\sigma_{r_{k,j}}}\right)}}^{-2}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8111}%
+$\displaystyle Y_\ell=\mathop{\sum_{k,j}}_{ {\ensuremath{\left|{ b_{k,j}\cap B_\ell }\right|}} > 0}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b_{k,j}\cap B_\ell }\right|}}}}}}{{\ensuremath{\displaystyle{B}}}}}}}\   {\ensuremath{\left({\sigma_{r_{k,j}}}\right)}}^{-2}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8113}%
+$\displaystyle R_\ell={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{X_\ell}}}}{{\ensuremath{\displaystyle{Y_\ell}}}}}}};
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8115}%
+$\displaystyle \sigma_{R_\ell}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{\sqrt{Y_\ell}}}}}}}}.
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8117}%
+$ R_\ell$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8119}%
+$ \sigma_{R_\ell}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8121}%
+$ B$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8123}%
+$ K$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8127}%
+$\displaystyle \mathop{\sum}_{\ell=1}^M{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{KR_\ell}}}}{{\ensuremath{\displaystyle{K^2\sigma_{R_\ell}^2}}}}}}}=
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{K}}}}}}}
+\mathop{\sum}_{\ell=1}^M{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{R_\ell}}}}{{\ensuremath{\displaystyle{\sigma_{R_\ell}^2}}}}}}}=M
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8131}%
+$\displaystyle K={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+1
+}}}}{{\ensuremath{\displaystyle{
+M
+}}}}}}}\mathop{\sum}_{\ell=1}^M{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{R_\ell}}}}{{\ensuremath{\displaystyle{\sigma_{R_\ell}^2}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8133}%
+$\displaystyle \hat{B}_\ell, \quad KR_\ell, \quad K\sigma_{R_\ell}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{subsubsection}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8144}%
+$ X_\ell=0$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8146}%
+$ Y_\ell=0$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8148}%
+$ b$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8152}%
+$\displaystyle X_\ell={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b\cap B_\ell }\right|}}}}}}{{\ensuremath{\displaystyle{B}}}}}}}\   
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{e(C+1)}}}}{{\ensuremath{\displaystyle{m|b|}}}}}}}\  
+{\ensuremath{\left({
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{|b|m}}}}{{\ensuremath{\displaystyle{e\sqrt{C+1}}}}}}}}
+}\right)}}^{2}
+={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b\cap B_\ell }\right|}}}}}}{{\ensuremath{\displaystyle{B}}}}}}}{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{|b|m}}}}{{\ensuremath{\displaystyle{e}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8154}%
+$\displaystyle Y_\ell={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b\cap B_\ell }\right|}}}}}}{{\ensuremath{\displaystyle{B}}}}}}}\   
+{\ensuremath{\left({
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{|b|m}}}}{{\ensuremath{\displaystyle{e\sqrt{C+1}}}}}}}}
+}\right)}}^{2}
+={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b\cap B_\ell }\right|}}}}}}{{\ensuremath{\displaystyle{B}}}}}}}{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{|b|^2m^2}}}}{{\ensuremath{\displaystyle{e^2(C+1)}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8156}%
+$\displaystyle R_\ell={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{X_\ell}}}}{{\ensuremath{\displaystyle{Y_\ell}}}}}}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{e(C+1)}}}}{{\ensuremath{\displaystyle{m|b|}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8160}%
+$\displaystyle \sigma_{R_\ell}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{\sqrt{Y_\ell}}}}}}}}=
+\sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{B}}}}{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b\cap B_\ell }\right|}}}}}}}}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{e\sqrt{(C+1)}}}}}{{\ensuremath{\displaystyle{|b|m}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8164}%
+$\displaystyle \sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{B}}}}{{\ensuremath{\displaystyle{{\ensuremath{\left|{ b\cap B_\ell }\right|}}}}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{subsection}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8167}%
+$ \hat{b}_{j,k}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8169}%
+$ \hat{B}_\ell$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{subsection}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8172}%
+$ C_0$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8176}%
+$ \sqrt{C_0}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8178}%
+$ n$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8180}%
+$\displaystyle P(n)={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{C_0^n{\ensuremath{\mathrm{e}}}^{-C_0}
+}}}}{{\ensuremath{\displaystyle{
+n!}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8182}%
+$\displaystyle \mathop{\sum}_{n=0}^{+\infty}
+P(n)=1\  ;
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8184}%
+$\displaystyle \langle n\rangle=\mathop{\sum}_{n=0}^{+\infty}
+nP(n)=C_0\  ;
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8186}%
+$\displaystyle \langle n^2\rangle=\mathop{\sum}_{n=0}^{+\infty}
+n^2 P(n)=C_0^2+C_0\  ;
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8188}%
+$\displaystyle \sigma_{C_0}=\sqrt{\langle n^2\rangle-\langle n\rangle^2}=\sqrt{C_0}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8192}%
+$\displaystyle \chi^2 = \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left({F_j-O_j}\right)}}^2
+}}}}{{\ensuremath{\displaystyle{
+\sigma_j^2
+}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8194}%
+$ O_j$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8196}%
+$ F_j$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8198}%
+$ \sigma_j$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8200}%
+$\displaystyle \chi_{(0)}^2 = \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left({F_j-C_j}\right)}}^2
+}}}}{{\ensuremath{\displaystyle{
+C_j
+}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8202}%
+$\displaystyle \chi_{(1)}^2 = \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left({F_j-{\ensuremath{\left({C_j+\min{\ensuremath{\left({1,C_j}\right)}}}\right)}}}\right)}}^2
+}}}}{{\ensuremath{\displaystyle{
+C_j+1
+}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{subsection}
+\stepcounter{subsubsection}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8208}%
+$ N_{\mathrm{obs}}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8210}%
+$ C_j,\quad j=1\ldots N_{\mathrm{obs}}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8212}%
+$ x$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8216}%
+$\displaystyle x=\langle x\rangle={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{ N_{\mathrm{obs}}}}}}}}}
+ \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}C_j\  .
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8218}%
+$\displaystyle \sigma_x=\sqrt{\langle x^2\rangle-\langle x\rangle^2}=\sqrt{
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{ N_{\mathrm{obs}}}}}}}}}
+ \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}C_j^2-{\ensuremath{\left({
+ {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{ N_{\mathrm{obs}}}}}}}}}
+ \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}C_j
+ }\right)}}
+ }
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8220}%
+$\displaystyle \sigma_x={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{ N_{\mathrm{obs}}}}}}}}}\sqrt{  \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}C_j }
+=\sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\langle x\rangle}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}}}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{subsubsection}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8223}%
+$ C_j=0$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8225}%
+$ N_{\mathrm{obs}}^*$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8227}%
+$\displaystyle x=\langle x\rangle^*={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{ N_{\mathrm{obs}}^*}}}}}}}
+ \mathop{\sum}_ {\stackrel{1\leqslant j\leqslant N_{\mathrm{obs}}}{{C_j>0}}}
+ C_j={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{ N_{\mathrm{obs}}^*}}}}}}}
+ \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}C_j = {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{N_{\mathrm{obs}}}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}^*}}}}}}}\langle x\rangle
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8229}%
+$\displaystyle \sigma_{x^*}= {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{N_{\mathrm{obs}}}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}^*}}}}}}}\sigma_x = \sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{N_{\mathrm{obs}}}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}^*}}}}}}}}
+\sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\langle x\rangle}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}^*}}}}}}}}=\sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\langle x\rangle^*}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}^*}}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8231}%
+$ C_j$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{subsubsection}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8238}%
+$\displaystyle \chi^2 = \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\left({x-O_j}\right)}}^2
+}}}}{{\ensuremath{\displaystyle{
+\sigma_j^2
+}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8240}%
+$\displaystyle x= \langle x \rangle_{\!\mathrm{w}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+\mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{O_j
+}}}}{{\ensuremath{\displaystyle{
+\sigma_j^2
+}}}}}}}
+}}}}{{\ensuremath{\displaystyle{
+\mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1
+}}}}{{\ensuremath{\displaystyle{
+\sigma_j^2
+}}}}}}}
+}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8244}%
+$\displaystyle \sigma_{\langle x \rangle_{\!\mathrm{w}}} = {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+1
+}}}}{{\ensuremath{\displaystyle{\sqrt{
+\mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1
+}}}}{{\ensuremath{\displaystyle{
+\sigma_j^2
+}}}}}}}
+}}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8246}%
+$\displaystyle \mathsf{GoF}=
+\sqrt{
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+\mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{O_j^2
+}}}}{{\ensuremath{\displaystyle{
+\sigma_j^2
+}}}}}}}
+-{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+{\ensuremath{\left[{
+\mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{O_j
+}}}}{{\ensuremath{\displaystyle{
+\sigma_j^2
+}}}}}}}
+}\right]}}^2
+}}}}{{\ensuremath{\displaystyle{ \mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1
+}}}}{{\ensuremath{\displaystyle{
+\sigma_j^2
+}}}}}}} }}}}}}}
+}}}}{{\ensuremath{\displaystyle{
+N_{\mathrm{obs}}-1
+}}}}}}}
+}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8248}%
+$\displaystyle {\sigma}_{\langle x \rangle_{\!\mathrm{w}}}^{\mathrm{corrected}} = \mathsf{GoF}\  \sigma_{\langle x \rangle_{\!\mathrm{w}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{subsubsection}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8251}%
+$ O_j=C_j$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8253}%
+$ \sigma_j^2=C_j$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8255}%
+$\displaystyle \langle x \rangle_{\!\mathrm{w(1)}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+{N_{\mathrm{obs}}}
+}}}}{{\ensuremath{\displaystyle{
+\mathop{\sum}_{j=1}^{N_{\mathrm{obs}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1
+}}}}{{\ensuremath{\displaystyle{
+C_j
+}}}}}}}
+}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8263}%
+$\displaystyle \sigma_{\langle x \rangle_{\!\mathrm{w(1)}}} = {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+1
+}}}}{{\ensuremath{\displaystyle{\sqrt{
+\mathop{\sum}_{\stackrel{1\leqslant j\leqslant N_{\mathrm{obs}}}{{C_j>0}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1
+}}}}{{\ensuremath{\displaystyle{
+C_j
+}}}}}}}
+}}}}}}}}=\sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\langle x \rangle_{\!\mathrm{w(1)}}}}}}{{\ensuremath{\displaystyle{
+N_{\mathrm{obs}}^*
+}}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8265}%
+$\displaystyle \mathsf{GoF}_{(1)}=
+\sqrt{
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+\mathop{\sum}_{\stackrel{1\leqslant j\leqslant N_{\mathrm{obs}}}{{C_j>0}}}
+\!\!\!\!C_j
+-{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+{\ensuremath{\left[{
+N_{\mathrm{obs}}^*
+}\right]}}^2
+}}}}{{\ensuremath{\displaystyle{ \mathop{\sum}_{\stackrel{1\leqslant j\leqslant N_{\mathrm{obs}}}{{C_j>0}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1
+}}}}{{\ensuremath{\displaystyle{
+C_j
+}}}}}}} }}}}}}}
+}}}}{{\ensuremath{\displaystyle{
+N_{\mathrm{obs}}^*-1
+}}}}}}}
+}
+=\sqrt{
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{N_{\mathrm{obs}}^*}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}^*-1}}}}}}}
+{\ensuremath{\left({
+\langle x\rangle^*-\langle x \rangle_{\!\mathrm{w(1)}}
+}\right)}}
+}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8267}%
+$ \langle x\rangle^*$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8269}%
+$\displaystyle {\sigma}_{\langle x \rangle_{\!\mathrm{w(1)}}}^{\mathrm{corrected}} = \mathsf{GoF}_{(1)}\  \sigma_{\langle x \rangle_{\!\mathrm{w(1)}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{subsubsection}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8272}%
+$ O_j=C_j+\min{\ensuremath{\left({1,C_j}\right)}}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8274}%
+$ \sigma_j^2=C_j+1$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8276}%
+$\displaystyle \langle x \rangle_{\!\mathrm{w(2)}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+{N_{\mathrm{obs}}^*}
+}}}}{{\ensuremath{\displaystyle{
+\mathop{\sum}_{\stackrel{1\leqslant j\leqslant N_{\mathrm{obs}}}{{C_j>0}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1
+}}}}{{\ensuremath{\displaystyle{
+C_j+1
+}}}}}}}
+}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8278}%
+$\displaystyle \sigma_{\langle x \rangle_{\!\mathrm{w(2)}}} = {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+1
+}}}}{{\ensuremath{\displaystyle{\sqrt{
+\mathop{\sum}_{\stackrel{1\leqslant j\leqslant N_{\mathrm{obs}}}{{C_j>0}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1
+}}}}{{\ensuremath{\displaystyle{
+C_j+1
+}}}}}}}
+}}}}}}}}=\sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\langle x \rangle_{\!\mathrm{w(2)}}}}}}{{\ensuremath{\displaystyle{
+N_{\mathrm{obs}}^*
+}}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8280}%
+$\displaystyle \mathsf{GoF}_{(2)}=
+\sqrt{
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+\mathop{\sum}_{\stackrel{1\leqslant j\leqslant N_{\mathrm{obs}}}{{C_j>0}}}
+\!\!\!\!C_j+N_{\mathrm{obs}}^*
+-{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+{\ensuremath{\left[{
+N_{\mathrm{obs}}^*
+}\right]}}^2
+}}}}{{\ensuremath{\displaystyle{ \mathop{\sum}_{\stackrel{1\leqslant j\leqslant N_{\mathrm{obs}}}{{C_j>0}}}
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1
+}}}}{{\ensuremath{\displaystyle{
+C_j+1
+}}}}}}} }}}}}}}
+}}}}{{\ensuremath{\displaystyle{
+N_{\mathrm{obs}}^*-1
+}}}}}}}
+}
+=\sqrt{
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{N_{\mathrm{obs}}^*}}}}{{\ensuremath{\displaystyle{N_{\mathrm{obs}}^*-1}}}}}}}
+{\ensuremath{\left({
+\langle x\rangle^*-\langle x \rangle_{\!\mathrm{w(2)}}+1
+}\right)}}
+}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8284}%
+$\displaystyle {\sigma}_{\langle x \rangle_{\!\mathrm{w(2)}}}^{\mathrm{corrected}} = \mathsf{GoF}_{(2)}\  \sigma_{\langle x \rangle_{\!\mathrm{w(2)}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{subsubsection}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8291}%
+$\displaystyle \epsilon_x = {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sigma_x}}}}{{\ensuremath{\displaystyle{x}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8295}%
+$ O(\epsilon_x^2)$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8299}%
+$ \propto\epsilon_x$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8303}%
+$ O(\epsilon_x^3)$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{subsubsection}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8306}%
+$ N_{\mathrm{obs}}=2$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8308}%
+$ C_1$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8310}%
+$ C_2$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8312}%
+$\displaystyle \langle x \rangle={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{C_1+C_2}}}}{{\ensuremath{\displaystyle{2}}}}}}}; \qquad \sigma_x={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sqrt{C_1+C_2}}}}}{{\ensuremath{\displaystyle{2}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8314}%
+$\displaystyle \langle x \rangle_{\mathrm{w(2)}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{2(C_1+1)(C_2+1)}}}}{{\ensuremath{\displaystyle{C_1+C_2+2}}}}}}}; \qquad 
+\sigma_{\langle x \rangle_{\mathrm{w(2)}}}=\sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{(C_1+1)(C_2+1)}}}}{{\ensuremath{\displaystyle{C_1+C_2+2}}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8316}%
+$ C_1,C_2$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8318}%
+$ \lambda$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8320}%
+$\displaystyle E{\ensuremath{\left({\langle x \rangle}\right)}} = \mathop{\sum}_{m,n=0}^{+\infty}
+ {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{n+m}}}}{{\ensuremath{\displaystyle{2}}}}}}}P(n)P(m)=\mathop{\sum}_{m=0}^{+\infty}
+ {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{m}}}}{{\ensuremath{\displaystyle{2}}}}}}}{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\lambda^m{\ensuremath{\mathrm{e}}}^{-\lambda}}}}}{{\ensuremath{\displaystyle{m!}}}}}}}
+ +\mathop{\sum}_{n=0}^{+\infty}
+ {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{n}}}}{{\ensuremath{\displaystyle{2}}}}}}}{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\lambda^n{\ensuremath{\mathrm{e}}}^{-\lambda}}}}}{{\ensuremath{\displaystyle{n!}}}}}}}
+ =\lambda
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8322}%
+$\displaystyle E{\ensuremath{\left({\sigma_x^2}\right)}} = \mathop{\sum}_{m,n=0}^{+\infty}
+ {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{n+m}}}}{{\ensuremath{\displaystyle{4}}}}}}}P(n)P(m)={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+ \lambda}}}}{{\ensuremath{\displaystyle{2}}}}}}};\qquad E{\ensuremath{\left({\sigma_x}\right)}} =\sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\lambda}}}}{{\ensuremath{\displaystyle{2}}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8324}%
+$\displaystyle \langle x \rangle_{\mathrm{w(2)}}=\langle x \rangle + 1 -{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{(C_1-C_2)^2}}}}{{\ensuremath{\displaystyle{4(\langle x \rangle+1)}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8326}%
+$\displaystyle E{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{(C_1-C_2)^2}}}}{{\ensuremath{\displaystyle{4(\langle x \rangle+1)}}}}}}}}\right)}} = 
+ \mathop{\sum}_{m,n=0}^{+\infty}
+ {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{(n-m)^2}}}}{{\ensuremath{\displaystyle{2(n+m+2) }}}}}}}P(n)P(m)={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{e}}}^{-2\lambda}}}}}{{\ensuremath{\displaystyle{2}}}}}}}
+ \mathop{\sum}_{m,n=0}^{+\infty}
+ {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{(n-m)^2}}}}{{\ensuremath{\displaystyle{(n+m+2) }}}}}}}{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\lambda^{n+m}}}}}{{\ensuremath{\displaystyle{n!m!}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8328}%
+$ s=n+m$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8330}%
+$ s=0\ldots +\infty$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8332}%
+$ n-m=s-2k$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8334}%
+$ k=0\ldots s$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8336}%
+$\displaystyle E{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{(C_1-C_2)^2}}}}{{\ensuremath{\displaystyle{4(\langle x \rangle+1)}}}}}}}}\right)}} = 
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{e}}}^{-2\lambda}}}}}{{\ensuremath{\displaystyle{2}}}}}}}
+ \mathop{\sum}_{s=0}^{+\infty}
+  \mathop{\sum}_{k=0}^{s}
+ {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{(s-2k)^2(s+1)}}}}{{\ensuremath{\displaystyle{(s+2)! }}}}}}}{\lambda^{s}}
+ \binom{s}{k}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{2}}}}}}}-{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{2\lambda}}}}}}}+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1-{\ensuremath{\mathrm{e}}}^{-2\lambda}}}}}{{\ensuremath{\displaystyle{4\lambda^2}}}}}}}
+ %{n!m!}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8338}%
+$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{E{\ensuremath{\left({\langle x \rangle_{\mathrm{w(2)}}-\langle x \rangle}\right)}}}}}}{{\ensuremath{\displaystyle{E{\ensuremath{\left({\langle x \rangle}\right)}}}}}}}}}=
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{2\lambda}}}}}}}+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{2\lambda^2}}}}}}}-{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1-{\ensuremath{\mathrm{e}}}^{-2\lambda}}}}}{{\ensuremath{\displaystyle{4\lambda^3}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8340}%
+$ \langle x \rangle$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8342}%
+$\displaystyle \epsilon = {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sigma_x}}}}{{\ensuremath{\displaystyle{\langle x \rangle}}}}}}} = 
+{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\lambda^{1/2}}}}}{{\ensuremath{\displaystyle{\sqrt{2} \lambda}}}}}}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{1}}}}{{\ensuremath{\displaystyle{\sqrt{2\lambda}}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8344}%
+$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{E{\ensuremath{\left({\langle x \rangle_{\mathrm{w(2)}}-\langle x \rangle}\right)}}}}}}{{\ensuremath{\displaystyle{E{\ensuremath{\left({\langle x \rangle}\right)}}}}}}}}}=
+O(\epsilon^2)
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{subsubsection}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8349}%
+$ \lambda=1,10,100,\ldots,1000000$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8353}%
+$ N=10^8$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8359}%
+$ \xi_\lambda=\sqrt{\lambda/N}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8361}%
+$ \epsilon_\lambda=\sqrt{\lambda/N}/\lambda=1/\sqrt{N\lambda}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8363}%
+$ E_\lambda$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8367}%
+$ e_\lambda=E_\lambda/\lambda$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8369}%
+$ e_\lambda/\epsilon_\lambda$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8371}%
+$ \lambda =$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8373}%
+$ \xi_\lambda = $%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8375}%
+$ \epsilon_\lambda$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8377}%
+$ {\langle x \rangle_{\!\mathrm{w(1)}}}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8379}%
+$ {\langle x \rangle_{\!\mathrm{w(2)}}}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8387}%
+$ e_\lambda$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8731}%
+$ {\langle x \rangle_{\!\mathrm{w(1)}}}\  :$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8735}%
+$ {\langle x \rangle^*}\  $%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8737}%
+$ \lambda<100$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8739}%
+$ {\langle x \rangle}\ $%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{subsection}
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8764}%
+$\displaystyle X_0=\eta_0 C_0
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8766}%
+$ \eta_0$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8768}%
+$ X$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8770}%
+$\displaystyle P'(X)=P(X/\eta_0)=P(n)\qquad\Biggl|\Biggr.\qquad \frac{X}{\eta_0}\equiv n\in\mathbb{Z}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8774}%
+$\displaystyle \langle X\rangle=\mathop{\sum}_{n=0}^{+\infty}
+\eta_0 nP(n)=\eta_0 C_0=X_0\  ;
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8776}%
+$\displaystyle \langle X^2\rangle=\mathop{\sum}_{n=0}^{+\infty}
+\eta_0^2 n^2 P(n)=\eta_0^2(C_0^2+C_0)=X_0^2+\eta_0 X_0\  ;
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8778}%
+$\displaystyle \sigma_X=\sqrt{\langle X^2\rangle-\langle X\rangle^2}=\sqrt{\eta_0 X_0}=\eta_0\sqrt{C_0}=\sqrt{\eta_0}\sqrt{X_0}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8780}%
+$ \sigma_X=\sqrt{\langle X\rangle}=\sqrt{X_0}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8782}%
+$\displaystyle \sigma_X=\sqrt{\eta_0}\sqrt{X_0}=\eta_0\sqrt{C_0}=\eta_0\sigma_{C_0}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_inline8786}%
+$ \sigma_{\eta_0}$%
+\lthtmlinlinemathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8788}%
+$\displaystyle \widehat{P}(\eta)={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{
+{\ensuremath{\mathrm{e}}}^{
+-\frac{1}{2}
+{\ensuremath{\left({
+\frac{\eta-\eta_0}{\sigma_{\eta_0}}
+}\right)}}^2
+}
+}}}}{{\ensuremath{\displaystyle{
+\sigma_{\eta_0}\sqrt{2\pi}
+}}}}}}}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8790}%
+$\displaystyle \int_{-\infty}^{+\infty}{\ensuremath{\mathrm{d}{\eta}\, }}\mathop{\sum}_{n=0}^{+\infty}
+P(n)\widehat{P}(\eta)=1\  ;
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8792}%
+$\displaystyle \langle X\rangle=\int_{-\infty}^{+\infty}{\ensuremath{\mathrm{d}{\eta}\, }}\mathop{\sum}_{n=0}^{+\infty}
+\widehat{P}(\eta)\eta nP(n)=
+\mathop{\sum}_{n=0}^{+\infty}
+ nP(n)
+\int_{-\infty}^{+\infty}{\ensuremath{\mathrm{d}{\eta}\, }} \widehat{P}(\eta)\eta
+ =
+\eta_0 C_0=X_0\  ;
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8794}%
+$\displaystyle \langle X^2\rangle=\int_{-\infty}^{+\infty}{\ensuremath{\mathrm{d}{\eta}\, }}\mathop{\sum}_{n=0}^{+\infty}
+\widehat{P}(\eta)\eta^2 n^2 P(n)=
+\int_{-\infty}^{+\infty}{\ensuremath{\mathrm{d}{\eta}\, }}\widehat{P}(\eta)\eta^2
+\mathop{\sum}_{n=0}^{+\infty}
+ n^2 P(n)
+=
+(\eta_0^2+\sigma_{\eta_0}^2)(C_0^2+C_0)\  ;
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+{\newpage\clearpage
+\lthtmlinlinemathA{tex2html_wrap_indisplay8796}%
+$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sigma_X}}}}{{\ensuremath{\displaystyle{\langle X\rangle}}}}}}}={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sqrt{\langle X^2\rangle-\langle X\rangle^2}}}}}{{\ensuremath{\displaystyle{\langle X\rangle}}}}}}}
+={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sqrt{
+\eta_0^2 C_0+\sigma_{\eta_0}^2C_0^2+\sigma_{\eta_0}^2 C_0
+}}}}}{{\ensuremath{\displaystyle{\eta_0C_0}}}}}}}=
+\sqrt{
+{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{ \sigma_{C_0}}}}}{{\ensuremath{\displaystyle{C_0}}}}}}}}\right)}}^2
++{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sigma_{\eta_0}}}}}{{\ensuremath{\displaystyle{\eta_0}}}}}}}}\right)}}^2+{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sigma_{\eta_0}}}}}{{\ensuremath{\displaystyle{\eta_0}}}}}}}{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sigma_{C_0}}}}}{{\ensuremath{\displaystyle{C_0}}}}}}}}\right)}}^2
+}\approx\sqrt{
+{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{ \sigma_{C_0}}}}}{{\ensuremath{\displaystyle{C_0}}}}}}}}\right)}}^2
++{\ensuremath{\left({{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{\sigma_{\eta_0}}}}}{{\ensuremath{\displaystyle{\eta_0}}}}}}}}\right)}}^2
+}
+$%
+\lthtmlindisplaymathZ
+\lthtmlcheckvsize\clearpage}
+
+\stepcounter{section}
 
 \end{document}
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diff --git a/manual/docs/html/slsDetectors-FAQ/index.html b/manual/docs/html/slsDetectors-FAQ/index.html
index c73dfec23..e773fb4e3 100644
--- a/manual/docs/html/slsDetectors-FAQ/index.html
+++ b/manual/docs/html/slsDetectors-FAQ/index.html
@@ -25,7 +25,7 @@ Frequently Asked Questions">
 
 
 
-
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@@ -33,14 +33,14 @@ Frequently Asked Questions">
  SRC="file:/usr/share/latex2html/icons/up_g.png"> 
 previous 
-
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- Next:  Next: Contents
-       Contents 
 

 

@@ -53,7 +53,7 @@ Frequently Asked Questions">
 Frequently Asked Questions
 
Anna Bergamaschi
 

-
Date: August 22, 2017

+
Date: August 23, 2017

 
 

 
@@ -62,102 +62,189 @@ Frequently Asked Questions
 
 
 
 
 

 

 Thattil Dhanya
-2017-08-22
+2017-08-23
 

 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node10.html b/manual/docs/html/slsDetectors-FAQ/node10.html
index 3db2c7c28..24131ab6c 100644
--- a/manual/docs/html/slsDetectors-FAQ/node10.html
+++ b/manual/docs/html/slsDetectors-FAQ/node10.html
@@ -26,30 +26,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
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-
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- Next:  Next: How can several controllers
- Up:  Up: SLS Detectors Software
- Previous:  Previous: Which is the sequence
-       Contents 
 

 

@@ -106,7 +106,7 @@ Auto timing: the detection time is defined by the exposure time and the period b
 

 \includegraphics[width=\textwidth]{images/normal_acquisition.eps}
 
 

@@ -123,7 +123,7 @@ Gating mode: the detector acquires for a number of gates define by the  user (in
 

 \includegraphics[width=\textwidth]{images/gated_acquisition.eps}
 
 

@@ -140,7 +140,7 @@ Trigger mode: the external trigger signal defines the start of the beginning of
 

 \includegraphics[width=\textwidth]{images/trigger_acquisition.eps}
 
 

@@ -157,7 +157,7 @@ Read Out Trigger mode: the external trigger signal defines the beginning of the
 

 \includegraphics[width=\textwidth]{images/ro_trigger_acquisition.eps}
 
 

@@ -167,35 +167,35 @@ Read Out Trigger mode: the external trigger signal defines the beginning of the
 

 

 
-
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-
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- Next:  Next: How can several controllers
- Up:  Up: SLS Detectors Software
- Previous:  Previous: Which is the sequence
-       Contents 
 
 

 Thattil Dhanya
-2017-08-22
+2017-08-23
 

 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node11.html b/manual/docs/html/slsDetectors-FAQ/node11.html
index 31a82a217..d097051b4 100644
--- a/manual/docs/html/slsDetectors-FAQ/node11.html
+++ b/manual/docs/html/slsDetectors-FAQ/node11.html
@@ -26,30 +26,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
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- Next:  Next: How can the detector
- Up:  Up: SLS Detectors Software
- Previous:  Previous: How can I synchronize
-       Contents 
 

 

@@ -75,35 +75,35 @@ After the configuration, the synchronization of the controllers will be complete
 

 

 
-
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- Next:  Next: How can the detector
- Up:  Up: SLS Detectors Software
- Previous:  Previous: How can I synchronize
-       Contents 
 
 

 Thattil Dhanya
-2017-08-22
+2017-08-23
 

 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node12.html b/manual/docs/html/slsDetectors-FAQ/node12.html
index 981a4d31e..0bf9c0765 100644
--- a/manual/docs/html/slsDetectors-FAQ/node12.html
+++ b/manual/docs/html/slsDetectors-FAQ/node12.html
@@ -26,30 +26,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
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-
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-
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-
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- Next:  Next: In which data format
- Up:  Up: SLS Detectors Software
- Previous:  Previous: How can several controllers
-       Contents 
 

 

@@ -75,35 +75,35 @@ A simple high-level solution in case you need to maintain the software for sever
 

 

 
-
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- Next:  Next: In which data format
- Up:  Up: SLS Detectors Software
- Previous:  Previous: How can several controllers
-       Contents 
 
 

 Thattil Dhanya
-2017-08-22
+2017-08-23
 

 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node13.html b/manual/docs/html/slsDetectors-FAQ/node13.html
index 9fc22f332..2875cfba8 100644
--- a/manual/docs/html/slsDetectors-FAQ/node13.html
+++ b/manual/docs/html/slsDetectors-FAQ/node13.html
@@ -25,30 +25,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
 next 
-
 up 
-
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-
 contents  
 

- Next: Single photon counting detectors
- Up:  Next: General questions about detectors
+ Up: SLS Detectors Software
- Previous:  Previous: How can the detector
-       Contents 
 

 

@@ -57,11 +57,11 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 Subsections
 
 
 
@@ -100,7 +100,7 @@ Then this 
 $ (108602\&0xFFFFFFFE)>>1 = 54301$
  is the frame number
 and  
 $ (108602\&0x1) =0$
  is the packet number.
 

@@ -159,35 +159,35 @@ JUNGFRAU
 

 

 
-
 next 
-
 up 
-
 previous 
-
 contents  
 

- Next: Single photon counting detectors
- Up:  Next: General questions about detectors
+ Up: SLS Detectors Software
- Previous:  Previous: How can the detector
-       Contents 
 
 

 Thattil Dhanya
-2017-08-22
+2017-08-23
 

 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node14.html b/manual/docs/html/slsDetectors-FAQ/node14.html
index f137ab431..4a8c34bfd 100644
--- a/manual/docs/html/slsDetectors-FAQ/node14.html
+++ b/manual/docs/html/slsDetectors-FAQ/node14.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 
 
-Single photon counting detectors
-
+General questions about detectors
+
 
 
 
@@ -18,7 +18,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
+
 
 
 
@@ -26,37 +26,37 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
 next 
-
 up 
-
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-
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- Next: Which detector settings should
- Up:  Next: In which X-ray energy
+ Up: SLS Detectors Frequently Asked
- Previous:  Previous: In which data format
-       Contents 
 

 

 
 
 

-Single photon counting detectors
+General questions about detectors
 

 
 

@@ -65,51 +65,23 @@ Single photon counting detectors
 Subsections
 
 

 
 

 

 Thattil Dhanya
-2017-08-22
+2017-08-23
 

 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node15.html b/manual/docs/html/slsDetectors-FAQ/node15.html
index 808b9963e..1538f78d2 100644
--- a/manual/docs/html/slsDetectors-FAQ/node15.html
+++ b/manual/docs/html/slsDetectors-FAQ/node15.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 
 
-Which detector settings should I choose?
-
+In which X-ray energy range can I use the detector?
+
 
 
 
@@ -26,30 +26,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
 next 
-
 up 
-
 previous 
-
 contents  
 

- Next: How do I chose
- Up: Single photon counting detectors
- Previous: Single photon counting detectors
-      Next: What limits the maximum
+ Up: General questions about detectors
+ Previous: General questions about detectors
+     Contents 
 

 

@@ -58,95 +58,152 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 Subsections
 
 
 
 

 
 

-Which detector settings should I choose?
+In which X-ray energy range can I use the detector?
 

-
-

-The choice of the operation settings is very important in order to obtain good quality data. 
-

-Normally slower settings will reduce the electronics noise and therefore it is possible to work at lower energies, but will saturate for high photon fluxes.
-

-On the other hand, faster settings will allow to work with higher photon intensities without pileup, but not to access lower energies because of an higher electronics noise.
-

-Therefore it is extremely important to chose adequate settings for the detector depending on the X-ray energy and expected maximum count rate.
-In the following is a description of the energy and intensity range coverd by the different settings for each detector.
+What limits the energy range in which the detector can be used is defined both by the sensors characteristics and the readout electronics.
 
 

 
 

-MYTHEN
+Sensors
+

+Most of the SLS detectors make use of silicon sensors.
+
+

+Since silicon is a relatively light for hard X-rays the only limitation at high energies is the acceptable absorption efficiency that can be achieved in the sensors thickness.
+

+Figure 2.1 shows the absorption efficiency as a function of the X-ray energy and detector thickness. Normally it is possible to use sensors up to 1 mm thick, while to achieve larger absorption thicknesses it is necessary tu assemble and control telescopic systems (possible up to a few mms).
+

+To achieve larger absorption thicknesses, the sensors can be oriented in edge-on configuration (in particular strip sensors). However in this case one should take into consideration the dead entrance window due to the cutting distance from the strips, which is normally several hundreds micron, or even up to mms and reduces the absorption efficiency at lower energies.
+
+

+
+

+
+
+
+
Figure 2.1:
+Efficiency of a silicon sensor as a function of the sensors thickness and X-ray energy.
\includegraphics[width=\textwidth]{images/effiSiHardXRays2}

+

+
+

+In standard face-on orientation, the backplane of the sensor acts as the entrance window. It presents a think n+ doped layer, which is unsensitive to radiation and causes a loss of efficiency at low energies.
+Figure 2.2 shows the absorption efficiency of the sensors for different backplane thicknesses at low energies.
+

+The exact thickness of the backplane for standard SLS sensors is not exactly known but should be about 1-2 $ \mu$
+m.
+
+

+
+

+
+
+
+
Figure 2.2:
+Efficiency of a silicon sensor as a function of the X-ray energy for different thicknesses of the backplane.
\includegraphics[width=\textwidth]{images/effiThinkBackplanes}

+

+
+

+However for lower energies, the main limitation is normally given by the noise of the frontend electronics (if single photon resolution is required).
+

+For higher energies it is also possible to use different sesnor materials as CdTe or Ge, although up to now they cannot provide the same signal quality as silicon.
+
+

+
+

+Frontend electronics
 

 
 

-Normally the user can follow these rules:
+The limitations on the energy range arising from the readout electronics come from the noise and from saturation. 
+The electronic noise  limits the minimum detectable energy for single photons, while saturation limits the maximum detectable signal either for single photons or in total.
 
-
    
-
  1. If the X-ray energy is lower than 8 keV the High gain setting should be used. Since it is a slow mode of operation it is necessary to take care that the maximum count rate is lower than 100 kcounts/s for all channels (use filters to reduce the beam intensisty).
-
    2. 
-
  2. For energies higher than 8 keV, the Standard setting is normally fine if the count rate can be kept lower than 300 kcounts/s for all channels (use filters to reduce the beam intensisty). 
+
      
+
    • In single photon counting detectors, the minimum threshold  cannot be set lower than 3-5 times the electronic noise.
+If the threshold is set at approximately half of the X-ray energy (see specific documentation about single photon counting detectors), the minimu detectable energy will be about 6-10 times the noise.
+
      
+In order to reduce the noise of the frontend electronics different settings can be chosen, but this puts a limit on the maximum incoming flux that can be detected without incurring in pileup (see specific documentation about single photon counting detectors). Figure 2.3 shows an example of the settings used for the MYTHEN detector for different energy ranges and fluxes.
+
      
+For state of the art single photon counting detectors, the minimum thrshold can be about 2-3 keV (details depend on the detector and can be further reduced using special settings).
+
+
      
+Concerning saturation, this imposes a maximum value for the comparator threshold. Normally photons of higher energies can still be detected, but without resolution concerning the threshold energy and eventually losing spatial resolution.
+By changing the settings it is possible to increase the maximum threshold value (normally also noise increases in this case).
 
 
      
 
      • 
-
    • In case a larger count rate is required in order to keep the acquisition time shorter, the Fast setting must be selected. However the maximum count rate should never exceed 1 Mcounts/s   for all channels.
+
    • For charge integrating detectors the electronics noise puts a limit on the minimum detectable signal. Therefore if single photon resolution is required, the minimum detectable energy is defined as for single photon counting detectors at about 6-10 times the electronic noise. In case no single photon resolution is required, the electronic noise will put a limit on the sensitivity of the detector i.e. the total accumulated signal needs to be larger than 6-10 times the noise in order to be detected (also about 2-3 keV depending on the detector). It is important to point out that the acquisition time of charge integrating detectors is limited by the leakage current of the sesnors and the noise quadratically sums out. Therefore the signal for low energy photons should be strong enough to be acquired during single frames.
+
+
      
+Concerning saturation, this sets a limit on the total number of photons acquired during the acquistion slot and is normally much larger than the energy released by single X-rays. Dynamic gain switching can strongly increase the dynamic range of the detector up to 10E+4 12 keV photons. 
+
+
      
 
      • 
-

+
 
 

 
-

+

 
-
-
+ SRC="img17.png"
+ ALT="\includegraphics[width=\textwidth]{images/settings}">
Figure 2.1:
-Plot indicating the reccomended choice of detector settings as a function of the X-ray energy and maximum count rate per channel..

-

-Figure 2.3:
+Settings to be chosen for the MYTHEN detector as a function of the X-ray energy and radiation intensity.
+
\includegraphics[width=\textwidth]{images/settings}
-
-

 

 

 
 

 

 
-
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-
 up 
-
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-
 contents  
 

- Next: How do I chose
- Up: Single photon counting detectors
- Previous: Single photon counting detectors
-      Next: What limits the maximum
+ Up: General questions about detectors
+ Previous: General questions about detectors
+     Contents 
 
 

 Thattil Dhanya
-2017-08-22
+2017-08-23
 

 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node16.html b/manual/docs/html/slsDetectors-FAQ/node16.html
index 54a82ef1b..aa460d167 100644
--- a/manual/docs/html/slsDetectors-FAQ/node16.html
+++ b/manual/docs/html/slsDetectors-FAQ/node16.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 
 
-How do I chose the comparator threshold?
-
+What limits the maximum frame rate?
+
 
 
 
@@ -18,7 +18,6 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
 
 
 
@@ -26,286 +25,87 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
 next 
-
 up 
-
 previous 
-
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- Next: How does the flat
- Up: Single photon counting detectors
- Previous: Which detector settings should
-      Next: Single photon counting detectors
+ Up: General questions about detectors
+ Previous: In which X-ray energy
+     Contents 
 

 

 
 
 

-How do I chose the comparator threshold?
+What limits the maximum frame rate?
 

 
 

+In order to acquired the data, they should be:
 
-

-
-
-
-
Figure 2.2:
-Number of counts as a function of the threshold detected in an ideal case.

-

-\includegraphics[width=\textwidth]{images/thr_scan_expl}
-
-

-

-
-

-
-

-
-
-
-
Figure 2.3:
-Number of counts as a function of the threshold detected in presence of fluorescent radiation

-

-\includegraphics[width=\textwidth]{images/thr_scan_fluo}
-
-

-

-
-

-Once selected the settings, the threshold should be selected.
-Figure 2.2 shows the number of counts as a function of the threshold value in the ideal case of monoenergetix X-rays of energy $ E_0$
-=10 keV.
-For thresholds larger than the X-ray energy the detector should always count 0 and for lower thresholds it should always count all the photons. However the curve is smoothed around $ E_0$
- because of the electronic noise (ENC) and is not perfectly flat for lower energies because the photons absorbed in the region between two strips distribute their energy between them and it is not flully collected by a single channel (charge sharing).
+
    
+
  • Transferred from readout electronics to readout board memory. This readou time is very dependent on the detector and on the dynamic range chose (for single photon counting detectors if configurable) and can range from hundreds or tens to few us. 
 
    
-In order to count once al X-rays the threshold should be set at half of the X-ray energy $ E_t=E_0/2$
-: if the threshold would be higher some photons would not be counted, leading to a loss of efficiency, while if it would be lower some photons would be counted twice leading to a loss of spatial resolution. 
+In case the board has some memory that can be accessed by the hardware, this is the only limitation on the maximum frame rate as long as the memory is not filled (burst mode). Frame rates as high as a few tens of kHz can be achieved for photon countign detectors (EIGER) or up to 1 MHz for charge integrating (GOTTHARD).
 
 
    
-Since the detector threshold can't be precisely set at the same value for all channels but there will always be some spread of the order of 200 eV (threshold dispersion) there will always be some fluctuations on the number of counts between channels, which however should be corrected by the flat field correction.
+
    • 
+
  • Transferred from readout board to client PC or file server. In this case the main bottleneck is normally given by the data transfer rate on the network and on the performances of the receiver PC. This limits the frame rate in continous mode. However also the data writing capabilities and amount of data which are being acquired should be taken into consideration when setting up very fast acquisitions.
 
 
    
-The choice of the threshold should also depend from  considerations regarding the emission of fluorescent radiation from the sample.
-
    
-Figure 2.3 shows  how the curve of the counts would look like for monochromatic X-rays of energy $ E_0$
- in presence of radiation of energy $ E_f$
- emitted by the sample. The curve would show a second step at $ E_f$
-. 
-
-
    
-Since the fluorecence emission is not present in the flat field data, the difference of counts between the channels due to the fluorescent radiation cannot be corrected and the threshold $ E_t$
- should be set at an energy larger than $ E_f$
-. This also helps to cut down the background.
-
    
-The difference of counts between the channels will be particularly large if the threshold is set in some ``steep'' part of the curve i.e. close to $ E_f$
- or to $ E_0$
- (but in this case it would be corrected by the flat field, at cost of loss of efficiency).
-Because of the presence of the electronic noise, $ E_t$
- should be at least 3 keV larger than $ E_f$
-.
-
-
    
-Here is a short list of rules to select the appropriate working threshold in order of importance (and eventually modify the X-ray energy):
-
-
      
-
    1. List the fluorescent emission lines $ E_f$
- that you expect from your sample. 
 
      2. 
-
    2. If there is no fluorescent emission ($ E_f<E_0$
-) $ E_t=E_0/2$
-
-
      3. 
-
    3. If there is fluorescent emission 
-
-
        
-
      1. $ E_t>E_f+3$
- keV
-
        2. 
-
      2. $ E_t<E_0-3$
- keV 
-
        3. 
-
      
-If the range where both requirements are satisfied is large, try to increase the distance of $ E_t$
- from $ E_f$
- up to 5 keV and then set $ E_t$
- as close as possible to the ideal value $ E_t=E_0/2$
-
-
      4. 
-
    4. If it is not possible to satisfy the previous minimal requirements:
-
-
        
-
      1. If you need high quality data and you can sacrifice detector efficiency (a lot!)  $ E_t>E_f+3$
- keV
-
        2. 
-
      2. If you need fast measurments and you can sacrifice detector uniformity (difficult to say how much) and increase the background $ E_t<E_f-3$
- keV. Remember that $ E_t$
- is klimited by the electronic noise $ E_t>4$
- keV (3 keV for High gain settings).
-
        3. 
-
      3. Consider to change $ E_0$
- to values lower than $ E_f$
- or at least 6-8 keV larger than $ E_f$
-
-
        4. 
-
      
-
      5. 
-
    
-
-
    
-
-
    
-
-
-
-
    Figure 2.4:
-Example of data from a sample emitting fluorescent light and detector threshold set at a value close to the emission line. The background data cannot be properly flat field corrected.
    
-
    
-\includegraphics[width=\textwidth]{images/sample_with_fluorescence}
-
-
    
-
    
+

 
 

 

 
-
 next 
-
 up 
-
 previous 
-
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- Next: How does the flat
- Up: Single photon counting detectors
- Previous: Which detector settings should
-      Next: Single photon counting detectors
+ Up: General questions about detectors
+ Previous: In which X-ray energy
+     Contents 
 
 

 Thattil Dhanya
-2017-08-22
+2017-08-23
 

 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node17.html b/manual/docs/html/slsDetectors-FAQ/node17.html
index da506b2b9..454c83b96 100644
--- a/manual/docs/html/slsDetectors-FAQ/node17.html
+++ b/manual/docs/html/slsDetectors-FAQ/node17.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 
 
-How does the flat field correction work?
-
+Single photon counting detectors
+
 
 
 
@@ -18,160 +18,98 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
-
-
+
+
+
 
 
 
 
 
-
 next 
-
+
 up 
-
 previous 
-
 contents  
 

- Next: What happens when I
- Up: Single photon counting detectors
- Previous: How do I chose
-      Next: Which detector settings should
+ Up: SLS Detectors Frequently Asked
+ Previous: What limits the maximum
+     Contents 
 

 

 
+
+

+Single photon counting detectors
+

+
+

+

 
 Subsections
 
 
-
-

-
-

-How does the flat field correction work?
-

-
-

-
-

-Why isn't my flat-field flat?
-

-
-

-The main reasons of a non flat flat-field can be:
-
+
  • Which detector settings should I choose?
 
      
-
    • The scattering from the glass rod is not uniform over the angular range. In this case you should take the flat field dynamically i.e. scanning the detector in front of the cylinder with the small window, as we do at the SLS. In this case when you shift the detector, the shape of the illumination remains in the same angular position (and shifts in channel number). Of course it depends a lot on the energy and on the geometry of the flat field acquisition.
-
-
      
-
-
-
-
      Figure 2.5:
-Example of a very bad flat field data set with highlights of some of the reasons which can cause the non-flat behavior for the MYTHEN detector. Similar effects can be visible also in 2D.
      
-
      
-\includegraphics[width=\textwidth]{images/bad_ff_col}
-
-
      
-
      
-
-
      
-
      • 
-
    • The entrance window for the X-rays is deformed (we also have this problem at the SLS). In this case when you move the detector the "mountain" moves with it in angle (And remains still in channel number). However this should correct without problems with the flat field correction, even in case of fluorescent emission. Should appear at all energies.
-
      • 
-
    • Differences of efficiency between the modules i.e. mainly bad energy calibration. You normally see really steps at the transition between modules. Sometimes you have some groups of strips withing a module that are not properly trimmed and look as smallish peaks or valleys in the flat field. When you move the detector, these steps or peaks move in angle and remain still in channel number.
-These differences can slightly change as a function of the energy (probably more evident at lower energies) but should normally always be there for the same settings.
-These differences get much worse in presence of fluorescent emission, but normally correct properly with flat field correction.
-
      • 
+
    • MYTHEN
 
    
-
-
    
-
-
    
-Dynamic acquisition of the flat field
-
    
-
-
    
-In case it is not possible to uniformely illuminate the detector due to its large dimensions, one of the solutions is to scan it in front of an illuminated are with a uniform speed such that the integrated number of counts during the exposure time is the same for all channels.
 
    
-
    
-To do that, at the SLS we have optimized the dynamic acquisition of the flat fiel with the MYTHEN detector using a setup similar to the one sketched in figure 2.6.
-It is important that the scanning range of the detector is chose such that the detector is not illuminated both at the beginning and at the end of the acquisition. Moreover the movement of the detector should be as uniform as possible. To avoid this kind of systematic errors we normally sum two flat field images taken in the two opposite directions of translation.
+
  • How do I chose the comparator threshold?
+
  • How does the flat field correction work?
+
 
    
-
    
-Also take care that your sample does not emit fluorescent light at the chosen energy (e.g. a glass rod works at all energies, but heavier materials can be chosen to increase the efficiency at higher energies taking care that the fluorescence emission is negligible).
-
-
    
-
-
    
-
-
-
-
    Figure 2.6:
-Sketch of the experimental setup for a dynamic acquisition of the flat field.
    
-
    
-\includegraphics[width=\textwidth]{images/FFSetup}
-
-
    
-
    
-
-
    
-
    
-
-
-next 
-
-up 
-
-previous 
-
-contents  
+
  • What happens when I trim the detector?
+
 
    
- Next: What happens when I
- Up: Single photon counting detectors
- Previous: How do I chose
-     Contents 
-
+
  • In what consists the energy calibration of the detector?
+
+
    
+
  • Why should I change the dynamic range of the counters?
+
  • When should I enable rate correction
+
+
+
    
 
    
 Thattil Dhanya
-2017-08-22
+2017-08-23
 
    
 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node18.html b/manual/docs/html/slsDetectors-FAQ/node18.html
index 499a3508d..eea6add94 100644
--- a/manual/docs/html/slsDetectors-FAQ/node18.html
+++ b/manual/docs/html/slsDetectors-FAQ/node18.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 
 
-What happens when I trim the detector?
-
+Which detector settings should I choose?
+
 
 
 
@@ -20,36 +20,36 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
+
 
 
 
 
 
-
 next 
-
+
 up 
-
 previous 
-
 contents  
 
    
- Next: In what consists the
- Up: Single photon counting detectors
- Previous: How does the flat
-      Next: How do I chose
+ Up: Single photon counting detectors
+ Previous: Single photon counting detectors
+     Contents 
 
    
 
    
@@ -58,207 +58,95 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 Subsections
 
 
 
 
    
 
-
    
-What happens when I trim the detector?
+
    
+Which detector settings should I choose?
 
    
 
 
    
-General remarks about trimming.
+The choice of the operation settings is very important in order to obtain good quality data. 
+
    
+Normally slower settings will reduce the electronics noise and therefore it is possible to work at lower energies, but will saturate for high photon fluxes.
+
    
+On the other hand, faster settings will allow to work with higher photon intensities without pileup, but not to access lower energies because of an higher electronics noise.
+
    
+Therefore it is extremely important to chose adequate settings for the detector depending on the X-ray energy and expected maximum count rate.
+In the following is a description of the energy and intensity range coverd by the different settings for each detector.
 
 
    
 
-
    
+
    
 MYTHEN
 
    
 
 
    
-Trimming with noise 
-
    
-
    
-The first step in the trimming procedure is to trim with noise (this is often sufficient). This has to be done for all the settings which are foreseen to be used (highgain, standard and fast).
-
    
-The procedure for the noise trimming is as follows:
+Normally the user can follow these rules:
 
 
      
-
    1. In the Initialization tab click on the settings for which you want to trim (e.g. standard)
+
    2. If the X-ray energy is lower than 8 keV the High gain setting should be used. Since it is a slow mode of operation it is necessary to take care that the maximum count rate is lower than 100 kcounts/s for all channels (use filters to reduce the beam intensisty).
 
      3. 
-
    3. In the Initialization tab click on the advanced radio button to make the trimming accessible.
+
    4. For energies higher than 8 keV, the Standard setting is normally fine if the count rate can be kept lower than 300 kcounts/s for all channels (use filters to reduce the beam intensisty). 
+
+
      
 
      5. 
-
    5. In the Acquisition tab set the acquisition time to 100 ms, the repetion to 1 and the delay between frames to 0.
-
      6. 
-
    6. For noise trimming usually the default parameters 
-$ Vthreshold=7$
-, 
-$ Counts=500$
-, 
-$ Resolution=4$
- work.
-
      
-However, to verify the threshold setting it is best to make a threshold scan. To do this go to the Data tab, in the Data display section select the 2D color and type advanced option. In the Acquisition tab select your data directory. Set the number of positions to 0. Select Scan, Type threshold. Typical values for the range are 500 to 900 with a step size of 10. Then click on the start button to perform the threshold scan. After the threhold scan has finished an image similar to the one in 2.7 should be shown. Depending on the system the number of modules may vary. If the plot is similar to the one in 2.10 the noise trim files did already exist and have been loaded when selecting the settings. In this case you don't need to trim with noise again.
-
      
-Set the parameter Vthreshold in the Trimming box (Initialization tab) 10-30 DAC units below the onset of the noise for the module with the lowest threshold offset. Since the modules have differences in the offset and gain the onset of the noise varies. 
-
      
-You can usually leave the remaining parameters unchanged (Counts/pixel=500; Resolution=4).
-
      7. 
-
    7. Select the directory where the noise trim files should be written and the filename, to wich will be attached the extension given by the module serial number (.snxxx). If you want the trimfiles to be loaded authomatically when the global settings are selected, select the default directory specified in the config file (or in the ``trimbits/beamline'' directory for the older software versions). 
-Click on Trim to start the noise trimming process. After the trimming has finished look at the plot and the distribution of the trim bits. The distribution should be around 32$ \pm$
-5 and should look gaussian. An example distribution is shown in figure 2.8 and an example plot in 2.9. If the distribution is too much off center change the counts/pixel, if it is too narrow reduce the resolution (set it to 3), if it is too wide increase it (set it to 5). Make sure not too many channels have a trim value of 0 or 63.
-
      8. 
-
    8. Execute the treshold scan again to verify the trimming was done properly. A plot similar tho the one in figure 2.10 should appear.
+
    9. In case a larger count rate is required in order to keep the acquisition time shorter, the Fast setting must be selected. However the maximum count rate should never exceed 1 Mcounts/s   for all channels.
 
      10. 
 
    
 
 
    
 
-
    
+
    
 
-
+
    Figure 2.7:
-The untrimmed threshold scan.Figure 3.1:
+Plot indicating the reccomended choice of detector settings as a function of the X-ray energy and maximum count rate per channel..
 
    
 
    
 \includegraphics[width=\textwidth]{images/noise_thresholdscanuntrimmed}
+ WIDTH="555" HEIGHT="284" ALIGN="BOTTOM" BORDER="0"
+ SRC="img17.png"
+ ALT="\includegraphics[width=\textwidth]{images/settings}">
 
 
    
 
    
 
    
 
-
    
-
-
    
-
-
-
-
    Figure 2.8:
-The distribution of the trimbits.
    
-
    
-\includegraphics[width=\textwidth]{images/trimbitdistribution}
-
-
    
-
    
-
-
    
-
-
    
-
-
-
-
    Figure 2.9:
-The trimbits for all the channels.
    
-
    
-\includegraphics[width=\textwidth]{images/trimbitplot}
-
-
    
-
    
-
-
    
-
-
    
-
-
-
-
    Figure 2.10:
-The trimmed threshold scan.
    
-
    
-\includegraphics[width=\textwidth]{images/noise_thresholdscantrimmed}
-
-
    
-
    
-
-
    
-Improve the trimming using X-rays
-
    
-
    
-The improvement of the trimming acquired with noise is not essential: at 12 keV an untrimmed module has a threshold dispersion which is about 1.4 keV and is already reduced to 200 eV at 12 keV by the noise trimming. At lower energies the noise trimming will be more effective, while the threshold dispesion will be still larger at higher energies. The trimming improvement reduces the threshold dispersion to 140 eV at 12 keV and is expected to be almost constant at all energies. For this reason it is suggested to perform the trimming improvement only when a small threshold dispersion is really important (e.g. to avoid flat field corrections or in presence of fluorescent lines close to the threshold value) and it will probably be not worthy at lower energies (i.e. threshold lower than 6 keV and X-ray energy lower than 12 keV). 
-The procedure for the trimming improvement is as follows:
-
-
      
-
    1. Select the settings of the detector and load the noise trimming file
-
      2. 
-
    2. Set the threshold at half of the X-ray energy (better if the detector has already been calibrated in energy like explained in 2.5)
-
      3. 
-
    3. Illuminate the detector with a flat field. This is very important to obtain a good trimming. 
-
      4. 
-
    4. Select the acquisition time in the acquisition tab so that there are at least 1000 counts/strip per frame (the more counts, the better trimming). Set the repetions to 1 and the delay between frames to 0.
-
      5. 
-
    5. Go to expert mode by clicking on advanced in the initialization tab, settings box
-
      6. 
-
    6. In the trimming box  select the directory where the noise trim files should be written and the filename, to wich will be attached the extension given by the module serial number (.snxxx).
-
      7. 
-
    7. Select the improve method
-Start the trimming
-
      8. 
-
    
-If the trimming is correctly performed and the illumination is flat enough, the same trimming can be used every time you will measure at this same energy.
-The authomatic loading of energy-specific trim files is not yet implemented.
-
 
    
 
    
 
-
 next 
-
+
 up 
-
 previous 
-
 contents  
 
    
- Next: In what consists the
- Up: Single photon counting detectors
- Previous: How does the flat
-      Next: How do I chose
+ Up: Single photon counting detectors
+ Previous: Single photon counting detectors
+     Contents 
 
 
    
 Thattil Dhanya
-2017-08-22
+2017-08-23
 
    
 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node19.html b/manual/docs/html/slsDetectors-FAQ/node19.html
index 14f36488a..55b9de60b 100644
--- a/manual/docs/html/slsDetectors-FAQ/node19.html
+++ b/manual/docs/html/slsDetectors-FAQ/node19.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 
 
-In what consists the energy calibration of the detector?
-
+How do I chose the comparator threshold?
+
 
 
 
@@ -20,166 +20,292 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
+
 
 
 
 
 
-
 next 
-
+
 up 
-
 previous 
-
 contents  
 
    
- Next: Why should I change
- Up: Single photon counting detectors
- Previous: What happens when I
-      Next: How does the flat
+ Up: Single photon counting detectors
+ Previous: Which detector settings should
+     Contents 
 
    
 
    
 
-
-Subsections
 
-
-
-
    
-
-
    
-
    
-In what consists the energy calibration of the detector?
+
    
+How do I chose the comparator threshold?
 
    
 
 
    
-General remarks about DAC to energy conversion
+
+
    
+
+
+
+
    Figure 3.2:
+Number of counts as a function of the threshold detected in an ideal case.
    
+
    
+\includegraphics[width=\textwidth]{images/thr_scan_expl}
+
+
    
+
    
 
 
    
 
-
    
-MYTHEN
-
    
+
    
+
+
+
+
    Figure 3.3:
+Number of counts as a function of the threshold detected in presence of fluorescent radiation
    
+
    
+\includegraphics[width=\textwidth]{images/thr_scan_fluo}
+
+
    
+
    
 
 
    
-Since the conversion between the threshold DAC units and energy depends on the gain and offset of the channels the energy calibration has to be done for all settings (high gain, standard and fast). For each setting follow this procedure:
-
-
      
-
    • Select the setting in the Initialization tab.
-
      • 
-
    • Enter in expert mode by clicking the Advanced radiobutton in the Global settings box in the Initialization tab.
-
      • 
-
    • If the trimfiles are in the correct location and with the correct name, they should be loaded by default every time you select the corresponding settings in the global settings box in the initialization tab 2.1.
-If the trim files do not yet exist generate them as explained in section 2.4.1.
-
      • 
-
    • Execute a threshold scan of the detector with at least three different energies. The more monochromatic are the X-rays, the better the calibration will be (i.e. scattered X-rays are better than the fluorescent emission). 
+Once selected the settings, the threshold should be selected.
+Figure 3.2 shows the number of counts as a function of the threshold value in the ideal case of monoenergetix X-rays of energy $ E_0$
+=10 keV.
+For thresholds larger than the X-ray energy the detector should always count 0 and for lower thresholds it should always count all the photons. However the curve is smoothed around $ E_0$
+ because of the electronic noise (ENC) and is not perfectly flat for lower energies because the photons absorbed in the region between two strips distribute their energy between them and it is not flully collected by a single channel (charge sharing).
 
      
-The scan should range from where all modules count 0 (estimate 850-20$ \cdot$
-energy(keV) DAcu) and where all modules start having a lot of noise (usually 800 DACu) with a step of 1 or 2 DACu. The acquisition time should be chosen so that there are at least 1000 counts per strip on the plateau.
-
      • 
-
    • Open the file root/CalAllModules.C for editing. Change the value of the following global variables according to your needs:
+In order to count once al X-rays the threshold should be set at half of the X-ray energy $ E_t=E_0/2$
+: if the threshold would be higher some photons would not be counted, leading to a loss of efficiency, while if it would be lower some photons would be counted twice leading to a loss of spatial resolution. 
 
-
        
-
      • nmod is the number of modules of your system.
+
        
+Since the detector threshold can't be precisely set at the same value for all channels but there will always be some spread of the order of 200 eV (threshold dispersion) there will always be some fluctuations on the number of counts between channels, which however should be corrected by the flat field correction.
+
+
        
+The choice of the threshold should also depend from  considerations regarding the emission of fluorescent radiation from the sample.
+
        
+Figure 3.3 shows  how the curve of the counts would look like for monochromatic X-rays of energy $ E_0$
+ in presence of radiation of energy $ E_f$
+ emitted by the sample. The curve would show a second step at $ E_f$
+. 
+
+
        
+Since the fluorecence emission is not present in the flat field data, the difference of counts between the channels due to the fluorescent radiation cannot be corrected and the threshold $ E_t$
+ should be set at an energy larger than $ E_f$
+. This also helps to cut down the background.
+
        
+The difference of counts between the channels will be particularly large if the threshold is set in some ``steep'' part of the curve i.e. close to $ E_f$
+ or to $ E_0$
+ (but in this case it would be corrected by the flat field, at cost of loss of efficiency).
+Because of the presence of the electronic noise, $ E_t$
+ should be at least 3 keV larger than $ E_f$
+.
+
+
        
+Here is a short list of rules to select the appropriate working threshold in order of importance (and eventually modify the X-ray energy):
+
+
          
+
        1. List the fluorescent emission lines $ E_f$
+ that you expect from your sample. 
 
          2. 
-
        2. nscan is the number of different threshold scans you acquired.
+
        3. If there is no fluorescent emission ($ E_f<E_0$
+) $ E_t=E_0/2$
+
 
          4. 
-
        4. en is the array with the energies at which you acquired the scans, in keV.
+
        5. If there is fluorescent emission 
+
+
            
+
          1. $ E_t>E_f+3$
+ keV
 
            2. 
-
          2. een is the array with the errors on the energies at which you acquired the scans, in keV. It is usually small, but can be some hundreds eV in case of dirty fluorescent samples.
+
          3. $ E_t<E_0-3$
+ keV 
 
            4. 
-
          4. fn is the array containing the location and root file name of your data.
+
          
+If the range where both requirements are satisfied is large, try to increase the distance of $ E_t$
+ from $ E_f$
+ up to 5 keV and then set $ E_t$
+ as close as possible to the ideal value $ E_t=E_0/2$
+
 
          6. 
-
        6. run is the array containing the run index of your data.
+
        7. If it is not possible to satisfy the previous minimal requirements:
+
+
            
+
          1. If you need high quality data and you can sacrifice detector efficiency (a lot!)  $ E_t>E_f+3$
+ keV
 
            2. 
-
          2. startscan is the array containing the threshold value at which you started the scans.
+
          3. If you need fast measurments and you can sacrifice detector uniformity (difficult to say how much) and increase the background $ E_t<E_f-3$
+ keV. Remember that $ E_t$
+ is klimited by the electronic noise $ E_t>4$
+ keV (3 keV for High gain settings).
 
            4. 
-
          4. stopscan is the array containing the threshold value at which you finished the scans.
+
          5. Consider to change $ E_0$
+ to values lower than $ E_f$
+ or at least 6-8 keV larger than $ E_f$
+
 
            6. 
-
          6. stepscan is the array containing the threshold step of the scans.
+
          
 
          8. 
-
        8. ave is the array containing the average number of counts per strip on the plateau (it must not be too precise).
-
          9. 
-
        9. sn is the array containing the list of the serial number of the modules to be calibrated. It is important that the list is in the right order, so that the optput calibration files have the extension .snxxx corresponding to the right module.
-
          10. 
-
        10. of is the location and root file name of the calibration file. The directory should already exist and the extension .snxxx will be attached to the output file.  
-
          11. 
-
      
-
      • 
-
    • Launch root, which you should have already installed on your linux PC
-
      • 
-
    • Execute the following commands in order to load the macros needed for the calibration:
-
      -root$ .L root/NewMythenMacros.C++
-root$ .L root/CalAllModules.C++
-
      
-You should get a lot of warnings, but no errors.
-
      • 
-
    • Execute the following command in order to run the calibration:
-
      -root$ EnCalModules()
-root$
-
      
-Reading and analyzing the data takes some time, but, after a while, a canvas should open where the plots of the median of the counts of every module as a function of the threshold should be shown for each energy, fitted with a modified erf function in order to find the inflextion point. The last plot of the canvas should represent the inflexion points as a function of the energies, and by fitting it with a straight line it is possible to calculate the offset and gain for each module i.e. calibrate it as a function of the energy. Please check that this automated fitting procedure succeeds. In case you see many fitting errors you should try to check wether the variable you edited in  root/CalAllModules.C are all correct or try to edit the fitting procedures in the two root macro files (sorry!).
-
      • 
-
    • Copy the calibration file you obtained to calibration/settings.snxxx 2.2 By doing this the correct threshold for each module will be calculated every time you change the threhsold energy in the global settings box in the initialization tab, you have loaded some default settings and you are not in expert mode.  
-
      • 
-
    
+
+
+
    
+
+
    
+
+
+
+
    Figure 3.4:
+Example of data from a sample emitting fluorescent light and detector threshold set at a value close to the emission line. The background data cannot be properly flat field corrected.
    
+
    
+\includegraphics[width=\textwidth]{images/sample_with_fluorescence}
+
+
    
+
    
 
 
    
 
    
 
-
 next 
-
+
 up 
-
 previous 
-
 contents  
 
    
- Next: Why should I change
- Up: Single photon counting detectors
- Previous: What happens when I
-      Next: How does the flat
+ Up: Single photon counting detectors
+ Previous: Which detector settings should
+     Contents 
 
 
    
 Thattil Dhanya
-2017-08-22
+2017-08-23
 
    
 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node2.html b/manual/docs/html/slsDetectors-FAQ/node2.html
index dc8788743..db855efae 100644
--- a/manual/docs/html/slsDetectors-FAQ/node2.html
+++ b/manual/docs/html/slsDetectors-FAQ/node2.html
@@ -26,30 +26,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
 next 
-
 up 
-
 previous 
-
 contents  
 
    
- Next:  Next: Which programs can I
- Up:  Up: SLS Detectors Frequently Asked
- Previous:  Previous: Contents
-       Contents 
 
    
 
    
@@ -65,53 +65,53 @@ SLS Detectors Software
 Subsections
 
 
 
 
    
 
    
 Thattil Dhanya
-2017-08-22
+2017-08-23
 
    
 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node20.html b/manual/docs/html/slsDetectors-FAQ/node20.html
index e9484edf3..bdec53e65 100644
--- a/manual/docs/html/slsDetectors-FAQ/node20.html
+++ b/manual/docs/html/slsDetectors-FAQ/node20.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 
 
-Why should I change the dynamic range of the counters?
-
+How does the flat field correction work?
+
 
 
 
@@ -20,50 +20,158 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
+
 
 
 
 
 
-
 next 
-
+
 up 
-
 previous 
-
 contents  
 
    
- Next: When should I enable
- Up: Single photon counting detectors
- Previous: In what consists the
-      Next: What happens when I
+ Up: Single photon counting detectors
+ Previous: How do I chose
+     Contents 
 
    
 
    
 
+
+Subsections
 
-
    
-Why should I change the dynamic range of the counters?
+
+
+
    
+
+
    
+How does the flat field correction work?
 
    
 
 
    
-
    
+
+
    
+Why isn't my flat-field flat?
+
    
+
+
    
+The main reasons of a non flat flat-field can be:
+
+
      
+
    • The scattering from the glass rod is not uniform over the angular range. In this case you should take the flat field dynamically i.e. scanning the detector in front of the cylinder with the small window, as we do at the SLS. In this case when you shift the detector, the shape of the illumination remains in the same angular position (and shifts in channel number). Of course it depends a lot on the energy and on the geometry of the flat field acquisition.
+
+
      
+
+
+
+
      Figure 3.5:
+Example of a very bad flat field data set with highlights of some of the reasons which can cause the non-flat behavior for the MYTHEN detector. Similar effects can be visible also in 2D.
      
+
      
+\includegraphics[width=\textwidth]{images/bad_ff_col}
+
+
      
+
      
+
+
      
+
      • 
+
    • The entrance window for the X-rays is deformed (we also have this problem at the SLS). In this case when you move the detector the "mountain" moves with it in angle (And remains still in channel number). However this should correct without problems with the flat field correction, even in case of fluorescent emission. Should appear at all energies.
+
      • 
+
    • Differences of efficiency between the modules i.e. mainly bad energy calibration. You normally see really steps at the transition between modules. Sometimes you have some groups of strips withing a module that are not properly trimmed and look as smallish peaks or valleys in the flat field. When you move the detector, these steps or peaks move in angle and remain still in channel number.
+These differences can slightly change as a function of the energy (probably more evident at lower energies) but should normally always be there for the same settings.
+These differences get much worse in presence of fluorescent emission, but normally correct properly with flat field correction.
+
      • 
+
    
+
+
    
+
+
    
+Dynamic acquisition of the flat field
+
    
+
+
    
+In case it is not possible to uniformely illuminate the detector due to its large dimensions, one of the solutions is to scan it in front of an illuminated are with a uniform speed such that the integrated number of counts during the exposure time is the same for all channels.
+
    
+
    
+To do that, at the SLS we have optimized the dynamic acquisition of the flat fiel with the MYTHEN detector using a setup similar to the one sketched in figure 3.6.
+It is important that the scanning range of the detector is chose such that the detector is not illuminated both at the beginning and at the end of the acquisition. Moreover the movement of the detector should be as uniform as possible. To avoid this kind of systematic errors we normally sum two flat field images taken in the two opposite directions of translation.
+
    
+
    
+Also take care that your sample does not emit fluorescent light at the chosen energy (e.g. a glass rod works at all energies, but heavier materials can be chosen to increase the efficiency at higher energies taking care that the fluorescence emission is negligible).
+
+
    
+
+
    
+
+
+
+
    Figure 3.6:
+Sketch of the experimental setup for a dynamic acquisition of the flat field.
    
+
    
+\includegraphics[width=\textwidth]{images/FFSetup}
+
+
    
+
    
+
+
    
+
    
+
+
+next 
+
+up 
+
+previous 
+
+contents  
+
    
+ Next: What happens when I
+ Up: Single photon counting detectors
+ Previous: How do I chose
+     Contents 
+
 
    
 Thattil Dhanya
-2017-08-22
+2017-08-23
 
    
 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node21.html b/manual/docs/html/slsDetectors-FAQ/node21.html
index f66e4ffa4..6c82df9e0 100644
--- a/manual/docs/html/slsDetectors-FAQ/node21.html
+++ b/manual/docs/html/slsDetectors-FAQ/node21.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 
 
-When should I enable rate correction
-
+What happens when I trim the detector?
+
 
 
 
@@ -18,37 +18,38 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
+
 
-
+
 
 
 
 
 
-
 next 
-
+
 up 
-
 previous 
-
 contents  
 
    
- Next: About this document ...
- Up: Single photon counting detectors
- Previous: Why should I change
-      Next: In what consists the
+ Up: Single photon counting detectors
+ Previous: How does the flat
+     Contents 
 
    
 
    
@@ -57,25 +58,207 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 Subsections
 
 
 
 
    
 
-
    
-When should I enable rate correction
+
    
+What happens when I trim the detector?
 
    
 
-
    
-How can I choose the dead time?
+
    
+General remarks about trimming.
+
+
    
+
+
    
+MYTHEN
 
    
 
 
    
-
    
+Trimming with noise 
+
    
+
    
+The first step in the trimming procedure is to trim with noise (this is often sufficient). This has to be done for all the settings which are foreseen to be used (highgain, standard and fast).
+
    
+The procedure for the noise trimming is as follows:
+
+
      
+
    1. In the Initialization tab click on the settings for which you want to trim (e.g. standard)
+
      2. 
+
    2. In the Initialization tab click on the advanced radio button to make the trimming accessible.
+
      3. 
+
    3. In the Acquisition tab set the acquisition time to 100 ms, the repetion to 1 and the delay between frames to 0.
+
      4. 
+
    4. For noise trimming usually the default parameters 
+$ Vthreshold=7$
+, 
+$ Counts=500$
+, 
+$ Resolution=4$
+ work.
+
      
+However, to verify the threshold setting it is best to make a threshold scan. To do this go to the Data tab, in the Data display section select the 2D color and type advanced option. In the Acquisition tab select your data directory. Set the number of positions to 0. Select Scan, Type threshold. Typical values for the range are 500 to 900 with a step size of 10. Then click on the start button to perform the threshold scan. After the threhold scan has finished an image similar to the one in 3.7 should be shown. Depending on the system the number of modules may vary. If the plot is similar to the one in 3.10 the noise trim files did already exist and have been loaded when selecting the settings. In this case you don't need to trim with noise again.
+
      
+Set the parameter Vthreshold in the Trimming box (Initialization tab) 10-30 DAC units below the onset of the noise for the module with the lowest threshold offset. Since the modules have differences in the offset and gain the onset of the noise varies. 
+
      
+You can usually leave the remaining parameters unchanged (Counts/pixel=500; Resolution=4).
+
      5. 
+
    5. Select the directory where the noise trim files should be written and the filename, to wich will be attached the extension given by the module serial number (.snxxx). If you want the trimfiles to be loaded authomatically when the global settings are selected, select the default directory specified in the config file (or in the ``trimbits/beamline'' directory for the older software versions). 
+Click on Trim to start the noise trimming process. After the trimming has finished look at the plot and the distribution of the trim bits. The distribution should be around 32$ \pm$
+5 and should look gaussian. An example distribution is shown in figure 3.8 and an example plot in 3.9. If the distribution is too much off center change the counts/pixel, if it is too narrow reduce the resolution (set it to 3), if it is too wide increase it (set it to 5). Make sure not too many channels have a trim value of 0 or 63.
+
      6. 
+
    6. Execute the treshold scan again to verify the trimming was done properly. A plot similar tho the one in figure 3.10 should appear.
+
      7. 
+
    
+
+
    
+
+
    
+
+
+
+
    Figure 3.7:
+The untrimmed threshold scan.
    
+
    
+\includegraphics[width=\textwidth]{images/noise_thresholdscanuntrimmed}
+
+
    
+
    
+
+
    
+
+
    
+
+
+
+
    Figure 3.8:
+The distribution of the trimbits.
    
+
    
+\includegraphics[width=\textwidth]{images/trimbitdistribution}
+
+
    
+
    
+
+
    
+
+
    
+
+
+
+
    Figure 3.9:
+The trimbits for all the channels.
    
+
    
+\includegraphics[width=\textwidth]{images/trimbitplot}
+
+
    
+
    
+
+
    
+
+
    
+
+
+
+
    Figure 3.10:
+The trimmed threshold scan.
    
+
    
+\includegraphics[width=\textwidth]{images/noise_thresholdscantrimmed}
+
+
    
+
    
+
+
    
+Improve the trimming using X-rays
+
    
+
    
+The improvement of the trimming acquired with noise is not essential: at 12 keV an untrimmed module has a threshold dispersion which is about 1.4 keV and is already reduced to 200 eV at 12 keV by the noise trimming. At lower energies the noise trimming will be more effective, while the threshold dispesion will be still larger at higher energies. The trimming improvement reduces the threshold dispersion to 140 eV at 12 keV and is expected to be almost constant at all energies. For this reason it is suggested to perform the trimming improvement only when a small threshold dispersion is really important (e.g. to avoid flat field corrections or in presence of fluorescent lines close to the threshold value) and it will probably be not worthy at lower energies (i.e. threshold lower than 6 keV and X-ray energy lower than 12 keV). 
+The procedure for the trimming improvement is as follows:
+
+
      
+
    1. Select the settings of the detector and load the noise trimming file
+
      2. 
+
    2. Set the threshold at half of the X-ray energy (better if the detector has already been calibrated in energy like explained in 3.5)
+
      3. 
+
    3. Illuminate the detector with a flat field. This is very important to obtain a good trimming. 
+
      4. 
+
    4. Select the acquisition time in the acquisition tab so that there are at least 1000 counts/strip per frame (the more counts, the better trimming). Set the repetions to 1 and the delay between frames to 0.
+
      5. 
+
    5. Go to expert mode by clicking on advanced in the initialization tab, settings box
+
      6. 
+
    6. In the trimming box  select the directory where the noise trim files should be written and the filename, to wich will be attached the extension given by the module serial number (.snxxx).
+
      7. 
+
    7. Select the improve method
+Start the trimming
+
      8. 
+
    
+If the trimming is correctly performed and the illumination is flat enough, the same trimming can be used every time you will measure at this same energy.
+The authomatic loading of energy-specific trim files is not yet implemented.
+
+
    
+
    
+
+
+next 
+
+up 
+
+previous 
+
+contents  
+
    
+ Next: In what consists the
+ Up: Single photon counting detectors
+ Previous: How does the flat
+     Contents 
+
 
    
 Thattil Dhanya
-2017-08-22
+2017-08-23
 
    
 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node22.html b/manual/docs/html/slsDetectors-FAQ/node22.html
index 1c0bcabc3..3f8ba8aaa 100644
--- a/manual/docs/html/slsDetectors-FAQ/node22.html
+++ b/manual/docs/html/slsDetectors-FAQ/node22.html
@@ -7,8 +7,8 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
   Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
 
 
-About this document ...
-
+In what consists the energy calibration of the detector?
+
 
 
 
@@ -18,62 +18,168 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
-
+
+
+
+
 
 
 
 
+
 next 
-
+ SRC="file:/usr/share/latex2html/icons/next.png"> 
+
 up 
-
 previous 
-
 contents  
 
    
- Up: SLS Detectors Frequently Asked
- Previous: When should I enable
-      Next: Why should I change
+ Up: Single photon counting detectors
+ Previous: What happens when I
+     Contents 
 
    
 
    
 
+
+Subsections
 
-
    
-About this document ...
+
+
+
    
+
+
    
+
    
+In what consists the energy calibration of the detector?
 
    
- SLS Detectors
+
+
    
+General remarks about DAC to energy conversion
+
+
    
+
+
    
+MYTHEN
+
    
+
+
    
+Since the conversion between the threshold DAC units and energy depends on the gain and offset of the channels the energy calibration has to be done for all settings (high gain, standard and fast). For each setting follow this procedure:
+
+
      
+
    • Select the setting in the Initialization tab.
+
      • 
+
    • Enter in expert mode by clicking the Advanced radiobutton in the Global settings box in the Initialization tab.
+
      • 
+
    • If the trimfiles are in the correct location and with the correct name, they should be loaded by default every time you select the corresponding settings in the global settings box in the initialization tab 3.1.
+If the trim files do not yet exist generate them as explained in section 3.4.1.
+
      • 
+
    • Execute a threshold scan of the detector with at least three different energies. The more monochromatic are the X-rays, the better the calibration will be (i.e. scattered X-rays are better than the fluorescent emission). 
 
      
-Frequently Asked Questions
      
-This document was generated using the
-LaTeX2HTML translator Version 2008 (1.71)
+The scan should range from where all modules count 0 (estimate 850-20$ \cdot$
+energy(keV) DAcu) and where all modules start having a lot of noise (usually 800 DACu) with a step of 1 or 2 DACu. The acquisition time should be chosen so that there are at least 1000 counts per strip on the plateau.
+
      • 
+
    • Open the file root/CalAllModules.C for editing. Change the value of the following global variables according to your needs:
+
+
        
+
      • nmod is the number of modules of your system.
+
        • 
+
      • nscan is the number of different threshold scans you acquired.
+
        • 
+
      • en is the array with the energies at which you acquired the scans, in keV.
+
        • 
+
      • een is the array with the errors on the energies at which you acquired the scans, in keV. It is usually small, but can be some hundreds eV in case of dirty fluorescent samples.
+
        • 
+
      • fn is the array containing the location and root file name of your data.
+
        • 
+
      • run is the array containing the run index of your data.
+
        • 
+
      • startscan is the array containing the threshold value at which you started the scans.
+
        • 
+
      • stopscan is the array containing the threshold value at which you finished the scans.
+
        • 
+
      • stepscan is the array containing the threshold step of the scans.
+
        • 
+
      • ave is the array containing the average number of counts per strip on the plateau (it must not be too precise).
+
        • 
+
      • sn is the array containing the list of the serial number of the modules to be calibrated. It is important that the list is in the right order, so that the optput calibration files have the extension .snxxx corresponding to the right module.
+
        • 
+
      • of is the location and root file name of the calibration file. The directory should already exist and the extension .snxxx will be attached to the output file.  
+
        • 
+
      
+
      • 
+
    • Launch root, which you should have already installed on your linux PC
+
      • 
+
    • Execute the following commands in order to load the macros needed for the calibration:
+
      +root$ .L root/NewMythenMacros.C++
+root$ .L root/CalAllModules.C++
+
      
+You should get a lot of warnings, but no errors.
+
      • 
+
    • Execute the following command in order to run the calibration:
+
      +root$ EnCalModules()
+root$
+
      
+Reading and analyzing the data takes some time, but, after a while, a canvas should open where the plots of the median of the counts of every module as a function of the threshold should be shown for each energy, fitted with a modified erf function in order to find the inflextion point. The last plot of the canvas should represent the inflexion points as a function of the energies, and by fitting it with a straight line it is possible to calculate the offset and gain for each module i.e. calibrate it as a function of the energy. Please check that this automated fitting procedure succeeds. In case you see many fitting errors you should try to check wether the variable you edited in  root/CalAllModules.C are all correct or try to edit the fitting procedures in the two root macro files (sorry!).
+
      • 
+
    • Copy the calibration file you obtained to calibration/settings.snxxx 3.2 By doing this the correct threshold for each module will be calculated every time you change the threhsold energy in the global settings box in the initialization tab, you have loaded some default settings and you are not in expert mode.  
+
      • 
+
    
+
 
    
-Copyright © 1993, 1994, 1995, 1996,
-Nikos Drakos, 
-Computer Based Learning Unit, University of Leeds.
+
    
+
+
+next 
+
+up 
+
+previous 
+
+contents  
 
    
-Copyright © 1997, 1998, 1999,
-Ross Moore, 
-Mathematics Department, Macquarie University, Sydney.
-
    
-The command line arguments were: 
    
- latex2html -split 4 slsDetectors-FAQ.tex
-
    
-The translation was initiated by Thattil Dhanya on 2017-08-22
-
    
+ Next: Why should I change
+ Up: Single photon counting detectors
+ Previous: What happens when I
+     Contents 
+
 
    
 Thattil Dhanya
-2017-08-22
+2017-08-23
 
    
 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node3.html b/manual/docs/html/slsDetectors-FAQ/node3.html
index 118eb82c3..2e1ea4e41 100644
--- a/manual/docs/html/slsDetectors-FAQ/node3.html
+++ b/manual/docs/html/slsDetectors-FAQ/node3.html
@@ -26,30 +26,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
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-
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-
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-
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- Next:  Next: How can I control
- Up:  Up: SLS Detectors Software
- Previous:  Previous: SLS Detectors Software
-       Contents 
 
    
 
    
@@ -82,35 +82,35 @@ The class slsDetectorUsers can be used as API from your acquisition software (se
 
    
 
    
 
-
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-
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-
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-
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- Next:  Next: How can I control
- Up:  Up: SLS Detectors Software
- Previous:  Previous: SLS Detectors Software
-       Contents 
 
 
    
 Thattil Dhanya
-2017-08-22
+2017-08-23
 
    
 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node4.html b/manual/docs/html/slsDetectors-FAQ/node4.html
index 2c07018fb..58907ce3b 100644
--- a/manual/docs/html/slsDetectors-FAQ/node4.html
+++ b/manual/docs/html/slsDetectors-FAQ/node4.html
@@ -26,30 +26,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
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-
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-
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-
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- Next:  Next: How can I configure
- Up:  Up: SLS Detectors Software
- Previous:  Previous: Which programs can I
-       Contents 
 
    
 
    
@@ -58,7 +58,7 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 Subsections
 
 
 
@@ -104,7 +104,7 @@ Finally each module within a controller has an internal index. However in genera
 Scketch of a possible complex system architecture composed of several detector, each consisting in many controllers eventually controlling several modules.
 \includegraphics[width=\textwidth]{multi_detector}
 
 
    
@@ -130,35 +130,35 @@ You will need to configure more than one detector, only in case you want to oper
 
    
 
    
 
-
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-
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-
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-
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- Next:  Next: How can I configure
- Up:  Up: SLS Detectors Software
- Previous:  Previous: Which programs can I
-       Contents 
 
 
    
 Thattil Dhanya
-2017-08-22
+2017-08-23
 
    
 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node5.html b/manual/docs/html/slsDetectors-FAQ/node5.html
index 532d9feeb..753f918f7 100644
--- a/manual/docs/html/slsDetectors-FAQ/node5.html
+++ b/manual/docs/html/slsDetectors-FAQ/node5.html
@@ -26,30 +26,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
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-
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-
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-
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- Next:  Next: What are settings and
- Up:  Up: SLS Detectors Software
- Previous:  Previous: How can I control
-       Contents 
 
    
 
    
@@ -75,7 +75,7 @@ The data receiver can run on any machine (e.g. a file server) accessible by both
 Scketch of the communication between the control PC, the detector and the data receiver.
 \includegraphics[width=\textwidth]{data_receiver}
 
 
    • 
@@ -105,35 +105,35 @@ The client will take care of communicating with the data receiver and the detect
 
    
 
    
 
-
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-
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-
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-
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- Next:  Next: What are settings and
- Up:  Up: SLS Detectors Software
- Previous:  Previous: How can I control
-       Contents 
 
 
    
 Thattil Dhanya
-2017-08-22
+2017-08-23
 
    
 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node6.html b/manual/docs/html/slsDetectors-FAQ/node6.html
index fd8cda925..51cd4af1c 100644
--- a/manual/docs/html/slsDetectors-FAQ/node6.html
+++ b/manual/docs/html/slsDetectors-FAQ/node6.html
@@ -26,30 +26,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
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-
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-
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-
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- Next:  Next: How should a configuration
- Up:  Up: SLS Detectors Software
- Previous:  Previous: How can I configure
-       Contents 
 
    
 
    
@@ -58,9 +58,9 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 Subsections
 
 
 
@@ -115,35 +115,35 @@ It must contain the subdirectories dynamicgain, gain1,
 
    
 
    
 
-
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-
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-
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-
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- Next:  Next: How should a configuration
- Up:  Up: SLS Detectors Software
- Previous:  Previous: How can I configure
-       Contents 
 
 
    
 Thattil Dhanya
-2017-08-22
+2017-08-23
 
    
 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node7.html b/manual/docs/html/slsDetectors-FAQ/node7.html
index a85e85c6d..b430ce8f3 100644
--- a/manual/docs/html/slsDetectors-FAQ/node7.html
+++ b/manual/docs/html/slsDetectors-FAQ/node7.html
@@ -26,30 +26,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
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-
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-
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-
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- Next:  Next: What is the meaning
- Up:  Up: SLS Detectors Software
- Previous:  Previous: What are settings and
-       Contents 
 
    
 
    
@@ -71,7 +71,7 @@ The configuration files look different for the different detector types. Example
 
    
 
    
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-2017-08-22
+2017-08-23
 
    
 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node8.html b/manual/docs/html/slsDetectors-FAQ/node8.html
index 4918c0fc3..3d3bf8e82 100644
--- a/manual/docs/html/slsDetectors-FAQ/node8.html
+++ b/manual/docs/html/slsDetectors-FAQ/node8.html
@@ -26,30 +26,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
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-
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-
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-
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- Next:  Next: Which is the sequence
- Up:  Up: SLS Detectors Software
- Previous:  Previous: How should a configuration
-       Contents 
 
    
 
    
@@ -61,7 +61,7 @@ What is the meaning of the file name?
 The final file name will be: 
 
    outdir/prefix[_d$ d$
 ][_Sv0][_sv1][_pp][_ff]_i.ext
 
    
@@ -80,7 +80,7 @@ where:
 
    
 
    
 Thattil Dhanya
-2017-08-22
+2017-08-23
 
    
 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/node9.html b/manual/docs/html/slsDetectors-FAQ/node9.html
index 769d3a41e..3b63fad7c 100644
--- a/manual/docs/html/slsDetectors-FAQ/node9.html
+++ b/manual/docs/html/slsDetectors-FAQ/node9.html
@@ -26,30 +26,30 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
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-
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-
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-
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- Next:  Next: How can I synchronize
- Up:  Up: SLS Detectors Software
- Previous:  Previous: What is the meaning
-       Contents 
 
    
 
    
@@ -69,14 +69,14 @@ Figure 1.7 shows in which sequence the various sc
  -->
 $ \Updownarrow$
  symbol, while the scripts using the  
 $ \Rightarrow$
 .
 
@@ -158,7 +158,7 @@ Figure 1.7 shows in which sequence the various sc
 
    
 \begin{displaymath}\textrm{\textbf{MEASUREMENTS}} \\
 \left\Updownarrow \,
 \be...
@@ -309,35 +309,35 @@ where i si the <I>file index</I> and p is the <I>stop script parameter</I>.
 <P>
 <HR>
 <!--Navigation Panel-->
-<A NAME=
 next 
-
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-
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-
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- Next:  Next: How can I synchronize
- Up:  Up: SLS Detectors Software
- Previous:  Previous: What is the meaning
-       Contents 
 
 
    
 Thattil Dhanya
-2017-08-22
+2017-08-23
 
    
 
 
diff --git a/manual/docs/html/slsDetectors-FAQ/slsDetectors-FAQ.html b/manual/docs/html/slsDetectors-FAQ/slsDetectors-FAQ.html
index c73dfec23..e773fb4e3 100644
--- a/manual/docs/html/slsDetectors-FAQ/slsDetectors-FAQ.html
+++ b/manual/docs/html/slsDetectors-FAQ/slsDetectors-FAQ.html
@@ -25,7 +25,7 @@ Frequently Asked Questions">
 
 
 
-
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@@ -33,14 +33,14 @@ Frequently Asked Questions">
  SRC="file:/usr/share/latex2html/icons/up_g.png"> 
 previous 
-
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- Next:  Next: Contents
-       Contents 
 
    
 
    
@@ -53,7 +53,7 @@ Frequently Asked Questions">
 Frequently Asked Questions
 
    Anna Bergamaschi
 
    
-
    Date: August 22, 2017
    
+
    Date: August 23, 2017
    
 
 
    
 
@@ -62,102 +62,189 @@ Frequently Asked Questions
 
 
 
      
-
    • Contents
-
    • SLS Detectors Software
 
 
      
-
    • Single photon counting detectors
-
        
-
      • Which detector settings should I choose?
-
 
      • How do I chose the comparator threshold?
+  HREF="node14.html">General questions about detectors
+
 
 
        
 
        
 Thattil Dhanya
-2017-08-22
+2017-08-23
 
        
 
 
diff --git a/manual/docs/pdf/slsDetectorInstall.pdf b/manual/docs/pdf/slsDetectorInstall.pdf
index c72b93cd3..ba2e2ad29 100644
Binary files a/manual/docs/pdf/slsDetectorInstall.pdf and b/manual/docs/pdf/slsDetectorInstall.pdf differ
diff --git a/manual/docs/pdf/slsDetectors-FAQ.pdf b/manual/docs/pdf/slsDetectors-FAQ.pdf
index b28427d9a..73c62f1cf 100644
Binary files a/manual/docs/pdf/slsDetectors-FAQ.pdf and b/manual/docs/pdf/slsDetectors-FAQ.pdf differ
diff --git a/manual/manual-main/Makefile b/manual/manual-main/Makefile
index 5e19a02ea..a87cf09e1 100644
--- a/manual/manual-main/Makefile
+++ b/manual/manual-main/Makefile
@@ -4,7 +4,7 @@ DESTDIR=../docs
 TEX=latex
 
 
-MAINTEXS= slsDetectors-FAQ.tex slsDetectorInstall.tex 
+MAINTEXS= slsDetectorInstall.tex slsDetectors-FAQ.tex 
 
 TEXS=slsDetector-softFAQ.tex singlePhotonCounting-FAQ.tex angConv-FAQ.tex generalDet-FAQ.tex 
 
@@ -32,9 +32,10 @@ $(HTMLS): $(TEXS) $(MAINTEXS)
 	$(shell test -d $(DESTDIR) || mkdir -p $(DESTDIR))
 	$(shell test -d $(DESTDIR)/html || mkdir -p $(DESTDIR)/html)
 	$(shell test -d $(DESTDIR)/html/$@ && rm -fr $(DESTDIR)/html/$@)
+	echo "*****************************  $@"
 	latex $@.tex
 	latex2html -split 4 $@.tex	
-	mv $(HTMLS) $(DESTDIR)/html
+	mv $@ $(DESTDIR)/html
 
 
 %.dvi : %.tex $(TEXS)
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new file mode 100755
index 000000000..c242bf8d1
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+%%EndData
+showpage
+%%Trailer
+end
+%%EOF
diff --git a/manual/manual-main/slsDetectorInstall.tex b/manual/manual-main/slsDetectorInstall.tex
index 28a5135c5..4b73977ec 100644
--- a/manual/manual-main/slsDetectorInstall.tex
+++ b/manual/manual-main/slsDetectorInstall.tex
@@ -333,7 +333,7 @@ You will need to configure more than one detector, only in case you want to oper
 
 \subsection{MYTHEN}
 In order to be able to properly operate your detector you need a directory where the trimbit files (needed to set the detector settings and eventually equalize the individual channel thresholds) which in the following will be named \textit{settingsdir} and a directory where the calibration files (needed to convert the threshold energy in DAC units) are stored which in the following will be named \textit{caldir}. \\
-\textit{settingsdirdir} and \textit{caldir} can even be the same directory, and an example of it is given in the software package by the example directory \verb=trimdir=. 
+\textit{settingsdir} and \textit{caldir} can even be the same directory, and an example of it is given in the software package by the example directory \verb=trimdir=. 
 Since these directories are customized by producing trimbit files and calibration for each detector, make sure not to overwrite yours every time you upgrade the software.
 
 \textit{settingsdir} should contain three subdirectories \verb=standard=,  \verb=fast= and  \verb=highgain= containing respectively the trimfiles \verb=standard.trim=,  \verb=fast.trim= and  \verb=highgain.trim= which contain the correct voltage settings for the detector although all the individual channel thresholds set to 0. The original files contained in the package should be used, infact in case of error the detector would not recognize the correct settings.\\
diff --git a/manual/manual-main/slsDetectors-FAQ.tex b/manual/manual-main/slsDetectors-FAQ.tex
index 8bb86955e..a0f0ef40a 100644
--- a/manual/manual-main/slsDetectors-FAQ.tex
+++ b/manual/manual-main/slsDetectors-FAQ.tex
@@ -98,7 +98,6 @@
 
 
 
-
 
 
 \begin{document}
@@ -112,23 +111,23 @@
 \chapter{SLS Detectors Software}
 \input{slsDetector-softFAQ}
 
-\begin{comment}
+%\begin{comment}
 \chapter{General questions about detectors}
 \input{generalDet-FAQ}
-\end{comment}
+%	\end{comment}
 
 \chapter{Single photon counting detectors}
 \input{singlePhotonCounting-FAQ}
 
 
 
-\begin{comment}
+%\begin{comment}
 \chapter{Charge Integrating detectors}
 \input{chargeInt-FAQ}
 
 
 \chapter{Angular conversion}
 \input{angConv-FAQ}
-\end{comment}
+%\end{comment}
 
 \end{document}