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slsDetectorPackage/manual/docs/html/slsDetectors-FAQ/images.pl

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# LaTeX2HTML 2008 (1.71)
# Associate images original text with physical files.
$key = q/includegraphics[width=textwidth]{imagesslashtrimbitdistribution};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="554" HEIGHT="275" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img37.png"
ALT="\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|<IMG
WIDTH="380" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img121.png"
ALT="$\displaystyle X_\ell={\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyl...
...nsuremath{\displaystyle{\vert b\vert m}}}}{{\ensuremath{\displaystyle{e}}}}}}}
$">|;
$key = q/E_f<E_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="65" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img24.png"
ALT="$ E_f&lt;E_0$">|;
$key = q/E_t<E_f-3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="91" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img27.png"
ALT="$ E_t&lt;E_f-3$">|;
$key = q/lambda=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="31" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img202.png"
ALT="$ \lambda =$">|;
$key = q/N_{mathrm{obs}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="37" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img142.png"
ALT="$ N_{\mathrm{obs}}$">|;
$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|<IMG
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/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|<IMG
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|<IMG
WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img75.png"
ALT="$ N_k$">|;
$key = q/E_t>4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="51" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img28.png"
ALT="$ E_t&gt;4$">|;
$key = q/displaystylePhi_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img57.png"
ALT="$\displaystyle \Phi_m$">|;
$key = q/DeltaOmega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="29" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img69.png"
ALT="$ \Delta\Omega$">|;
$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|<IMG
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|<IMG
WIDTH="98" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img187.png"
ALT="$ 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|<IMG
WIDTH="698" HEIGHT="637" BORDER="0"
SRC="|."$dir".q|img7.png"
ALT="\begin{displaymath}\textrm{\textbf{MEASUREMENTS}} \\\\
\left\Updownarrow
\be...
...
\\\\
\end{array}
% \right. \\\\
\\\\
\end{array}
\right.
\end{displaymath}">|;
$key = q/X;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img214.png"
ALT="$ X$">|;
$key = q/N_{mathrm{obs}}^*;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
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|<IMG
WIDTH="154" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img157.png"
ALT="$\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|<IMG
WIDTH="254" HEIGHT="87" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img108.png"
ALT="$\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|<IMG
WIDTH="152" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img123.png"
ALT="$\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|<IMG
WIDTH="23" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img127.png"
ALT="$ \hat{B}_\ell$">|;
$key = q/n-m=s-2k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="112" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img188.png"
ALT="$ 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|<IMG
WIDTH="232" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img84.png"
ALT="$\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|<IMG
WIDTH="111" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img34.png"
ALT="$ Resolution=4$">|;
$key = q/E_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img20.png"
ALT="$ E_0$">|;
$key = q/displaystylex=langlexrangle^*={ensuremath{displaystyle{frac{{ensuremath{displays}}}}}{{ensuremath{displaystyle{N_{mathrm{obs}}^*}}}}}}}langlexrangle;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
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/sigma_{eta_0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="27" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img221.png"
ALT="$ \sigma_{\eta_0}$">|;
$key = q/displaystyle{ensuremath{left|{B_ell}right|}}=B;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
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/{ensuremath{{2theta}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
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|<IMG
WIDTH="379" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img218.png"
ALT="$\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|<IMG
WIDTH="109" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img56.png"
ALT="$\displaystyle \Phi_m-{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyl...
...\frac{{\ensuremath{\displaystyle{D_m}}}}{{\ensuremath{\displaystyle{R_m}}}}}}}.$">|;
$key = q/E_t<E_0-3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="89" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img26.png"
ALT="$ E_t&lt;E_0-3$">|;
$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|<IMG
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/C_j,quadj=1ldotsN_{mathrm{obs}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
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|<IMG
WIDTH="169" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img193.png"
ALT="$\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|<IMG
WIDTH="244" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img220.png"
ALT="$\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|<IMG
WIDTH="63" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img196.png"
ALT="$ N=10^8$">|;
$key = q/D_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="30" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img44.png"
ALT="$ 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|<IMG
WIDTH="77" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img105.png"
ALT="$\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|<IMG
WIDTH="53" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img118.png"
ALT="$ X_\ell=0$">|;
$key = q/C_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img176.png"
ALT="$ C_1$">|;
$key = q/e_lambda=E_lambdaslashlambda;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="79" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img200.png"
ALT="$ e_\lambda=E_\lambda/\lambda$">|;
$key = q/sigma_{R_ell};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="30" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img112.png"
ALT="$ \sigma_{R_\ell}$">|;
$key = q/F_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img138.png"
ALT="$ F_j$">|;
$key = q/includegraphics[width=textwidth]{imagesslashnoise_thresholdscantrimmed};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="554" HEIGHT="275" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img39.png"
ALT="\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|<IMG
WIDTH="185" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img170.png"
ALT="$\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|<IMG
WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img53.png"
ALT="$\displaystyle k_m$">|;
$key = q/b_{k,j};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img83.png"
ALT="$ b_{k,j}$">|;
$key = q/Rightarrow;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="20" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img6.png"
ALT="$ \Rightarrow$">|;
$key = q/d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img4.png"
ALT="$ d$">|;
$key = q/Phi_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img43.png"
ALT="$ \Phi_m$">|;
$key = q/2thetaequiv{ensuremath{{2theta}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="57" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img76.png"
ALT="$ 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|<IMG
WIDTH="351" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img89.png"
ALT="$\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|<IMG
WIDTH="556" HEIGHT="539" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img18.png"
ALT="\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|<IMG
WIDTH="38" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img52.png"
ALT="$\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|<IMG
WIDTH="33" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img80.png"
ALT="$ 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|<IMG
WIDTH="180" HEIGHT="117" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img167.png"
ALT="$\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|<IMG
WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img207.png"
ALT="$ e_\lambda$">|;
$key = q/displaystyleX_0=eta_0C_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="80" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img212.png"
ALT="$\displaystyle X_0=\eta_0 C_0
$">|;
$key = q/includegraphics[width=textwidth]{imagesslashsample_with_fluorescence};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="556" HEIGHT="539" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img29.png"
ALT="\includegraphics[width=\textwidth]{images/sample_with_fluorescence}">|;
$key = q/xi_lambda=sqrt{lambdaslashN};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="88" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img197.png"
ALT="$ \xi_\lambda=\sqrt{\lambda/N}$">|;
$key = q/includegraphics[width=textwidth]{imagesslashnoise_thresholdscanuntrimmed};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="554" HEIGHT="275" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img36.png"
ALT="\includegraphics[width=\textwidth]{images/noise_thresholdscanuntrimmed}">|;
$key = q/C_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img177.png"
ALT="$ 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|<IMG
WIDTH="202" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img223.png"
ALT="$\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|<IMG
WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img111.png"
ALT="$ 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|<IMG
WIDTH="184" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img194.png"
ALT="$\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|<IMG
WIDTH="49" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img180.png"
ALT="$ C_1,C_2$">|;
$key = q/N_{mathrm{obs}}=2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="66" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img175.png"
ALT="$ 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|<IMG
WIDTH="185" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img164.png"
ALT="$\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|<IMG
WIDTH="448" HEIGHT="71" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img179.png"
ALT="$\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|<IMG
WIDTH="269" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img87.png"
ALT="$\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|<IMG
WIDTH="114" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img32.png"
ALT="$ 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|<IMG
WIDTH="258" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img124.png"
ALT="$\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|<IMG
WIDTH="258" HEIGHT="141" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img161.png"
ALT="$\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|<IMG
WIDTH="221" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img134.png"
ALT="$\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|<IMG
WIDTH="90" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img74.png"
ALT="$ k=1,\ldots,P$">|;
$key = q/proptoepsilon_x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="36" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img173.png"
ALT="$ \propto\epsilon_x$">|;
$key = q/o_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img46.png"
ALT="$ 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|<IMG
WIDTH="323" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img86.png"
ALT="$\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|<IMG
WIDTH="394" HEIGHT="87" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img146.png"
ALT="$\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|<IMG
WIDTH="188" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img195.png"
ALT="$ \lambda=1,10,100,\ldots,1000000$">|;
$key = q/langlexrangle^*;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img163.png"
ALT="$ \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|<IMG
WIDTH="115" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img58.png"
ALT="$\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|<IMG
WIDTH="173" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img145.png"
ALT="$\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|<IMG
WIDTH="157" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img165.png"
ALT="$ 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|<IMG
WIDTH="44" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img172.png"
ALT="$ 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|<IMG
WIDTH="244" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img216.png"
ALT="$\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|<IMG
WIDTH="551" HEIGHT="293" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img3.png"
ALT="\includegraphics[width=\textwidth]{data_receiver}">|;
$key = q/chi^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="22" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img1.png"
ALT="$ \chi ^2$">|;
$key = q/includegraphics[width=textwidth]{imagesslasheffiThinkBackplanes};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="554" HEIGHT="538" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img16.png"
ALT="\includegraphics[width=\textwidth]{images/effiThinkBackplanes}">|;
$key = q/M;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="22" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img88.png"
ALT="$ M$">|;
$key = q/K;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img114.png"
ALT="$ 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|<IMG
WIDTH="141" HEIGHT="126" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img154.png"
ALT="$\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|<IMG
WIDTH="391" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img49.png"
ALT="$\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|<IMG
WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img22.png"
ALT="$ 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|<IMG
WIDTH="72" HEIGHT="53" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img109.png"
ALT="$\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|<IMG
WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img81.png"
ALT="$ e_{k,j}$">|;
$key = q/I_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img70.png"
ALT="$ 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|<IMG
WIDTH="216" HEIGHT="78" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img147.png"
ALT="$\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|<IMG
WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img213.png"
ALT="$ \eta_0$">|;
$key = q/s=n+m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="76" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img186.png"
ALT="$ s=n+m$">|;
$key = q/b;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="11" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img120.png"
ALT="$ b$">|;
$key = q/x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img144.png"
ALT="$ x$">|;
$key = q/C_j=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="52" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img148.png"
ALT="$ C_j=0$">|;
$key = q/c_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img45.png"
ALT="$ c_m$">|;
$key = q/R_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img42.png"
ALT="$ R_m$">|;
$key = q/{langlexrangle};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="31" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img211.png"
ALT="$ {\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|<IMG
WIDTH="118" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img131.png"
ALT="$\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|<IMG
WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img152.png"
ALT="$ C_j$">|;
$key = q/includegraphics[width=textwidth]{imagesslashthr_scan_fluo};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="556" HEIGHT="539" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img19.png"
ALT="\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|<IMG
WIDTH="151" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img136.png"
ALT="$\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|<IMG
WIDTH="36" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img62.png"
ALT="$\displaystyle c_m p.$">|;
$key = q/O_j=C_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="63" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img158.png"
ALT="$ O_j=C_j$">|;
$key = q/includegraphics[width=textwidth]{imagesslashsettings};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="555" HEIGHT="284" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img17.png"
ALT="\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|<IMG
WIDTH="397" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img183.png"
ALT="$\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|<IMG
WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img99.png"
ALT="$ N_E$">|;
$key = q/displaystyle{ensuremath{displaystyle{frac{{ensuremath{displaystyle{p}}}}{{ensuremath{displaystyle{k_m}}}}}}};;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="33" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img60.png"
ALT="$\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|<IMG
WIDTH="104" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img132.png"
ALT="$\displaystyle \mathop{\sum}_{n=0}^{+\infty}
P(n)=1 ;
$">|;
$key = q/hat{b}_{j,k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="28" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img126.png"
ALT="$ \hat{b}_{j,k}$">|;
$key = q/(108602&0xFFFFFFFE)>>1=54301;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="296" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img12.png"
ALT="$ (108602\&amp;0xFFFFFFFE)&#187;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|<IMG
WIDTH="222" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img184.png"
ALT="$\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|<IMG
WIDTH="14" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img181.png"
ALT="$ \lambda$">|;
$key = q/includegraphics[width=textwidth]{multi_detector};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="554" HEIGHT="139" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img2.png"
ALT="\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|<IMG
WIDTH="130" HEIGHT="122" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img155.png"
ALT="$\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|<IMG
WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img64.png"
ALT="$ 2\theta$">|;
$key = q/O;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img101.png"
ALT="$ O$">|;
$key = q/includegraphics[width=textwidth]{imagesslashro_trigger_acquisition.eps};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="555" HEIGHT="161" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img11.png"
ALT="\includegraphics[width=\textwidth]{images/ro_trigger_acquisition.eps}">|;
$key = q/O_n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img100.png"
ALT="$ O_n$">|;
$key = q/displaystyleo_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img55.png"
ALT="$\displaystyle o_m$">|;
$key = q/(108602&0x1)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="131" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img13.png"
ALT="$ (108602\&amp;0x1) =0$">|;
$key = q/ell;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="11" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img94.png"
ALT="$ \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|<IMG
WIDTH="300" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img151.png"
ALT="$\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|<IMG
WIDTH="44" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img174.png"
ALT="$ O(\epsilon_x^3)$">|;
$key = q/k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img73.png"
ALT="$ 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|<IMG
WIDTH="90" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img110.png"
ALT="$\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|<IMG
WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img51.png"
ALT="$\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|<IMG
WIDTH="286" HEIGHT="141" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img168.png"
ALT="$\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|<IMG
WIDTH="103" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img97.png"
ALT="$\displaystyle \qquad \hat{b}_{k,j}\in B_\ell .
$">|;
$key = q/{langlexrangle_{!mathrm{w(1)}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="50" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img205.png"
ALT="$ {\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|<IMG
WIDTH="631" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img225.png"
ALT="$\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|<IMG
WIDTH="32" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img102.png"
ALT="$ \sigma_{O_n}$">|;
$key = q/{langlexrangle^*};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="39" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img209.png"
ALT="$ {\langle x \rangle^*} $">|;
$key = q/Counts=500;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="102" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img33.png"
ALT="$ 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|<IMG
WIDTH="177" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img85.png"
ALT="$\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|<IMG
WIDTH="24" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img68.png"
ALT="$ \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|<IMG
WIDTH="126" HEIGHT="110" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img160.png"
ALT="$\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|<IMG
WIDTH="288" HEIGHT="87" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img107.png"
ALT="$\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|<IMG
WIDTH="119" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img116.png"
ALT="$\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|<IMG
WIDTH="144" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img219.png"
ALT="$ \sigma_X=\sqrt{\langle X\rangle}=\sqrt{X_0}$">|;
$key = q/O_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img137.png"
ALT="$ O_j$">|;
$key = q/sigma_j^2=C_j+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="88" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img166.png"
ALT="$ \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|<IMG
WIDTH="579" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img185.png"
ALT="$\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|<IMG
WIDTH="230" HEIGHT="267" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img156.png"
ALT="$\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|<IMG
WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img113.png"
ALT="$ B$">|;
$key = q/{ensuremath{{2theta}}}_{max}={ensuremath{{2theta}}}_0+MB;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="140" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img93.png"
ALT="$ {\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|<IMG
WIDTH="141" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img117.png"
ALT="$\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|<IMG
WIDTH="78" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img21.png"
ALT="$ 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|<IMG
WIDTH="200" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img135.png"
ALT="$\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|<IMG
WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img204.png"
ALT="$ \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|<IMG
WIDTH="89" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img67.png"
ALT="$\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|<IMG
WIDTH="139" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img96.png"
ALT="$\displaystyle \qquad {\ensuremath{\left\vert{ b_{k,j}\cap B_\ell }\right\vert}} &gt; 0.
$">|;
$key = q/displaystyle{ensuremath{displaystyle{frac{{ensuremath{displaystyle{p}}}}{{ensuremath{displaystyle{R_m}}}}}}};;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="37" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img54.png"
ALT="$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{p}}}}{{\ensuremath{\displaystyle{R_m}}}}}}};$">|;
$key = q/Updownarrow;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="14" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img5.png"
ALT="$ \Updownarrow$">|;
$key = q/includegraphics[width=textwidth]{imagesslashgated_acquisition.eps};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="555" HEIGHT="194" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img9.png"
ALT="\includegraphics[width=\textwidth]{images/gated_acquisition.eps}">|;
$key = q/displaystyleD_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="30" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img61.png"
ALT="$\displaystyle D_m$">|;
$key = q/epsilon_lambda=sqrt{lambdaslashN}slashlambda=1slashsqrt{Nlambda};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
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/{langlexrangle_{!mathrm{w(1)}}}:;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="64" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img208.png"
ALT="$ {\langle x \rangle_{\!\mathrm{w(1)}}} :$">|;
$key = q/displaystylehat{B}_ell={ensuremath{{2theta}}}_0+(ell-1slash2)B,;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
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/DeltaOmegaproptoDelta{ensuremath{{2theta}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="80" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img71.png"
ALT="$ \Delta\Omega\propto \Delta {\ensuremath{{2\theta}}}$">|;
$key = q/displaystyleR_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img59.png"
ALT="$\displaystyle R_m$">|;
$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|<IMG
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/displaystyle{ensuremath{left|{b_{k,j}}right|}}={ensuremath{{2theta}}}_{k,j}^{+}-{ensuremath{{2theta}}}_{k,j}^{-};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
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|<IMG
WIDTH="91" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img25.png"
ALT="$ E_t&gt;E_f+3$">|;
$key = q/displaystyleb_{k,j};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img95.png"
ALT="$\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|<IMG
WIDTH="168" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img133.png"
ALT="$\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|<IMG
WIDTH="550" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img190.png"
ALT="$\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|<IMG
WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img15.png"
ALT="$ \mu$">|;
$key = q/alpha_{jm};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="33" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img41.png"
ALT="$ \alpha_{jm}$">|;
$key = q/E_t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img23.png"
ALT="$ 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|<IMG
WIDTH="142" HEIGHT="77" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img222.png"
ALT="$\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|<IMG
WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img92.png"
ALT="$ {\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|<IMG
WIDTH="812" HEIGHT="79" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img226.png"
ALT="$\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|<IMG
WIDTH="36" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img129.png"
ALT="$ \sqrt{C_0}$">|;
$key = q/includegraphics[width=textwidth]{imagesslashtrimbitplot};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="554" HEIGHT="275" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img38.png"
ALT="\includegraphics[width=\textwidth]{images/trimbitplot}">|;
$key = q/P;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img72.png"
ALT="$ P$">|;
$key = q/includegraphics[width=textwidth]{imagesslashbad_ff_col};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="554" HEIGHT="538" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img30.png"
ALT="\includegraphics[width=\textwidth]{images/bad_ff_col}">|;
$key = q/{langlexrangle_{!mathrm{w(2)}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="50" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img206.png"
ALT="$ {\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|<IMG
WIDTH="367" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img217.png"
ALT="$\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|<IMG
WIDTH="270" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img77.png"
ALT="$\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|<IMG
WIDTH="61" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img159.png"
ALT="$ \sigma_j^2=C_j$">|;
$key = q/pm;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="17" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img35.png"
ALT="$ \pm$">|;
$key = q/xi_lambda=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="37" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img203.png"
ALT="$ \xi_\lambda = $">|;
$key = q/k,j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img106.png"
ALT="$ k,j$">|;
$key = q/m_{k,j};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="36" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img82.png"
ALT="$ m_{k,j}$">|;
$key = q/lambda<100;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="59" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img210.png"
ALT="$ \lambda&lt;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|<IMG
WIDTH="491" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img182.png"
ALT="$\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|<IMG
WIDTH="43" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img201.png"
ALT="$ e_\lambda/\epsilon_\lambda$">|;
$key = q/includegraphics[width=textwidth]{imagesslashtrigger_acquisition.eps};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="555" HEIGHT="199" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img10.png"
ALT="\includegraphics[width=\textwidth]{images/trigger_acquisition.eps}">|;
$key = q/displaystylec_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img50.png"
ALT="$\displaystyle c_m$">|;
$key = q/k=0ldotss;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="74" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img189.png"
ALT="$ k=0\ldots s$">|;
$key = q/k_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img47.png"
ALT="$ k_m$">|;
$key = q/E_lambda;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="25" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img199.png"
ALT="$ E_\lambda$">|;
$key = q/includegraphics[width=textwidth]{imagesslashnormal_acquisition.eps};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="555" HEIGHT="159" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img8.png"
ALT="\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|<IMG
WIDTH="216" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img115.png"
ALT="$\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|<IMG
WIDTH="146" HEIGHT="121" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img104.png"
ALT="$\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|<IMG
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img66.png"
ALT="$ \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|<IMG
WIDTH="266" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img141.png"
ALT="$\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|<IMG
WIDTH="463" HEIGHT="189" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img162.png"
ALT="$\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|<IMG
WIDTH="285" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img48.png"
ALT="$\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|<IMG
WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img103.png"
ALT="$ \nu_n$">|;
$key = q/C_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img128.png"
ALT="$ C_0$">|;
$key = q/langlexrangle;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img192.png"
ALT="$ \langle x \rangle$">|;
$key = q/includegraphics[width=textwidth]{imagesslasheffiSiHardXRays2};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="556" HEIGHT="537" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img14.png"
ALT="\includegraphics[width=\textwidth]{images/effiSiHardXRays2}">|;
$key = q/B_ell;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img98.png"
ALT="$ 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|<IMG
WIDTH="533" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img224.png"
ALT="$\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|<IMG
WIDTH="31" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img65.png"
ALT="$\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|<IMG
WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img139.png"
ALT="$ \sigma_j$">|;
$key = q/includegraphics[width=textwidth]{imagesslashFFSetup};AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="555" HEIGHT="396" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img31.png"
ALT="\includegraphics[width=\textwidth]{images/FFSetup}">|;
$key = q/cdot;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="9" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img40.png"
ALT="$ \cdot$">|;
$key = q/Y_ell=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
WIDTH="49" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img119.png"
ALT="$ 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|<IMG
WIDTH="61" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img171.png"
ALT="$\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|<IMG
WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="|."$dir".q|img130.png"
ALT="$ 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|<IMG
WIDTH="143" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img153.png"
ALT="$\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|<IMG
WIDTH="335" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img215.png"
ALT="$\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|<IMG
WIDTH="140" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img78.png"
ALT="$\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|<IMG
WIDTH="76" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
SRC="|."$dir".q|img125.png"
ALT="$\displaystyle \sqrt{{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle...
...ath{\displaystyle{{\ensuremath{\left\vert{ b\cap B_\ell }\right\vert}}}}}}}}}}
$">|;
1;
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