mirror of
https://github.com/slsdetectorgroup/slsDetectorPackage.git
synced 2025-04-28 17:10:03 +02:00
180 lines
5.9 KiB
HTML
180 lines
5.9 KiB
HTML
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
|
|
|
|
<!--Converted with LaTeX2HTML 2012 (1.2)
|
|
original version by: Nikos Drakos, CBLU, University of Leeds
|
|
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
|
* with significant contributions from:
|
|
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
|
|
<HTML>
|
|
<HEAD>
|
|
<TITLE>Observables</TITLE>
|
|
<META NAME="description" CONTENT="Observables">
|
|
<META NAME="keywords" CONTENT="slsDetectors-FAQ">
|
|
<META NAME="resource-type" CONTENT="document">
|
|
<META NAME="distribution" CONTENT="global">
|
|
|
|
<META NAME="Generator" CONTENT="LaTeX2HTML v2012">
|
|
<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
|
|
|
|
<LINK REL="STYLESHEET" HREF="slsDetectors-FAQ.css">
|
|
|
|
<LINK REL="previous" HREF="node48.html">
|
|
<LINK REL="up" HREF="node47.html">
|
|
<LINK REL="next" HREF="node50.html">
|
|
</HEAD>
|
|
|
|
<BODY >
|
|
<!--Navigation Panel-->
|
|
<A NAME="tex2html794"
|
|
HREF="node50.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="file:/usr/share/latex2html/icons/next.png"></A>
|
|
<A NAME="tex2html790"
|
|
HREF="node47.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="file:/usr/share/latex2html/icons/up.png"></A>
|
|
<A NAME="tex2html786"
|
|
HREF="node48.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="file:/usr/share/latex2html/icons/prev.png"></A>
|
|
<A NAME="tex2html792"
|
|
HREF="node1.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="file:/usr/share/latex2html/icons/contents.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A NAME="tex2html795"
|
|
HREF="node50.html">Basic binning</A>
|
|
<B> Up:</B> <A NAME="tex2html791"
|
|
HREF="node47.html">Introduction</A>
|
|
<B> Previous:</B> <A NAME="tex2html787"
|
|
HREF="node48.html">Notation</A>
|
|
<B> <A NAME="tex2html793"
|
|
HREF="node1.html">Contents</A></B>
|
|
<BR>
|
|
<BR>
|
|
<!--End of Navigation Panel-->
|
|
|
|
<H3><A NAME="SECTION00621200000000000000">
|
|
Observables</A>
|
|
</H3>
|
|
The physical observable of interest in any scattering experiment is [1-3] the differential cross section
|
|
<P><!-- MATH
|
|
\begin{displaymath}
|
|
{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\bf {\sigma}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\Omega}}}}}}}
|
|
\end{displaymath}
|
|
-->
|
|
</P>
|
|
<DIV ALIGN="CENTER">
|
|
<IMG
|
|
WIDTH="31" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img65.png"
|
|
ALT="$\displaystyle {\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ens...
|
|
...ma}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\Omega}}}}}}}
|
|
$">
|
|
</DIV><P>
|
|
</P>
|
|
as a function of direction <IMG
|
|
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img66.png"
|
|
ALT="$ \Omega$">
|
|
.
|
|
To measure that directly we should operate with zero-width point detectors, with instant measurement and unit incident intensity.
|
|
Practically
|
|
the quantity we can actually measure - putting a detector in a position covering a certain
|
|
solid angle for a certain time with a certain incident intensity - is
|
|
<P><!-- MATH
|
|
\begin{displaymath}
|
|
{I_0}\Delta t \Delta\Omega{\ensuremath{\displaystyle{\frac{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\bf {\sigma}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\Omega}}}}}}}
|
|
\end{displaymath}
|
|
-->
|
|
</P>
|
|
<DIV ALIGN="CENTER">
|
|
<IMG
|
|
WIDTH="89" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img67.png"
|
|
ALT="$\displaystyle {I_0}\Delta t \Delta\Omega{\ensuremath{\displaystyle{\frac{{\ensu...
|
|
...ma}}}}}{{\ensuremath{\displaystyle{{\ensuremath{\mathrm{d}{}\, }}\Omega}}}}}}}
|
|
$">
|
|
</DIV><P>
|
|
</P>
|
|
If <IMG
|
|
WIDTH="24" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img68.png"
|
|
ALT="$ \Delta t$">
|
|
, <!-- MATH
|
|
$\Delta\Omega$
|
|
-->
|
|
<IMG
|
|
WIDTH="29" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img69.png"
|
|
ALT="$ \Delta\Omega$">
|
|
are small and known and <IMG
|
|
WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img70.png"
|
|
ALT="$ I_0$">
|
|
is separately monitored,
|
|
we can (have to) normalize the observations by simply dividing them out.
|
|
|
|
<P>
|
|
Specifically for the powder diffraction field, historically, this is not usually done because
|
|
- as it is normally true with anode sources and point detectors and usual procedures -
|
|
the counting times <IMG
|
|
WIDTH="24" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img68.png"
|
|
ALT="$ \Delta t$">
|
|
, the solid angle width <!-- MATH
|
|
$\Delta\Omega\propto \Delta {\ensuremath{{2\theta}}}$
|
|
-->
|
|
<IMG
|
|
WIDTH="80" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img71.png"
|
|
ALT="$ \Delta\Omega\propto \Delta {\ensuremath{{2\theta}}}$">
|
|
|
|
and the incident intensity <IMG
|
|
WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img70.png"
|
|
ALT="$ I_0$">
|
|
are considered
|
|
constant and therefore go into some 'global scaling' constant that is usually considered arbitrary.
|
|
|
|
<P>
|
|
However, as we have more sophisticated acquisition methods,
|
|
we may need revert to the original approach and consider the
|
|
counts divided by time and angular width as the real observable.
|
|
|
|
<P>
|
|
<HR>
|
|
<!--Navigation Panel-->
|
|
<A NAME="tex2html794"
|
|
HREF="node50.html">
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
|
SRC="file:/usr/share/latex2html/icons/next.png"></A>
|
|
<A NAME="tex2html790"
|
|
HREF="node47.html">
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
|
SRC="file:/usr/share/latex2html/icons/up.png"></A>
|
|
<A NAME="tex2html786"
|
|
HREF="node48.html">
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
|
SRC="file:/usr/share/latex2html/icons/prev.png"></A>
|
|
<A NAME="tex2html792"
|
|
HREF="node1.html">
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
|
SRC="file:/usr/share/latex2html/icons/contents.png"></A>
|
|
<BR>
|
|
<B> Next:</B> <A NAME="tex2html795"
|
|
HREF="node50.html">Basic binning</A>
|
|
<B> Up:</B> <A NAME="tex2html791"
|
|
HREF="node47.html">Introduction</A>
|
|
<B> Previous:</B> <A NAME="tex2html787"
|
|
HREF="node48.html">Notation</A>
|
|
<B> <A NAME="tex2html793"
|
|
HREF="node1.html">Contents</A></B>
|
|
<!--End of Navigation Panel-->
|
|
<ADDRESS>
|
|
Thattil Dhanya
|
|
2018-09-28
|
|
</ADDRESS>
|
|
</BODY>
|
|
</HTML>
|