<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <!--Converted with LaTeX2HTML 98.1p1 release (March 2nd, 1998) originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), 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>Discussion</TITLE> <META NAME="description" CONTENT="Discussion"> <META NAME="keywords" CONTENT="vol2"> <META NAME="resource-type" CONTENT="document"> <META NAME="distribution" CONTENT="global"> <META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1"> <LINK REL="STYLESHEET" HREF="vol2.css"> <LINK REL="next" HREF="node444.html"> <LINK REL="previous" HREF="node442.html"> <LINK REL="up" HREF="node441.html"> <LINK REL="next" HREF="node444.html"> </HEAD> <BODY > <!--Navigation Panel--> <A NAME="tex2html6978" HREF="node444.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="icons.gif/next_motif.gif"></A> <A NAME="tex2html6975" HREF="node441.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="icons.gif/up_motif.gif"></A> <A NAME="tex2html6969" HREF="node442.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="icons.gif/previous_motif.gif"></A> <A NAME="tex2html6977" HREF="node1.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="icons.gif/contents_motif.gif"></A> <BR> <B> Next:</B> <A NAME="tex2html6979" HREF="node444.html">Reduction Steps</A> <B> Up:</B> <A NAME="tex2html6976" HREF="node441.html">CCD Detectors</A> <B> Previous:</B> <A NAME="tex2html6970" HREF="node442.html">Introduction</A> <BR> <BR> <!--End of Navigation Panel--> <H2><A NAME="SECTION002512000000000000000"> Discussion</A> </H2> <P> The mean absolute error of INT_FRM(i,j) yields with ICONS = 1: <BR><P></P> <DIV ALIGN="CENTER"> <!-- MATH: \begin{equation} (\Delta I)^2 = \left({\partial I \over \partial S}\right)^2 (\Delta S)^2 + \left({\partial I \over \partial D}\right)^2 (\Delta D)^2 + \left({\partial I \over \partial F}\right)^2 (\Delta F)^2 \end{equation} --> <TABLE WIDTH="100%" ALIGN="CENTER"> <TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="ccd-7"> </A><IMG WIDTH="550" HEIGHT="62" SRC="img923.gif" ALT="\begin{displaymath}(\Delta I)^2 = \left({\partial I \over \partial S}\right)^2 (... ... + \left({\partial I \over \partial F}\right)^2 (\Delta F)^2 \end{displaymath}"></TD> <TD WIDTH=10 ALIGN="RIGHT"> (18.7)</TD></TR> </TABLE> </DIV> <BR CLEAR="ALL"><P></P>(Only the first letter is used for abbreviations.) <P> Computing the partial derivatives we get <BR><P></P> <DIV ALIGN="CENTER"> <!-- MATH: \begin{equation} (\Delta I)^2 = {(F - D)^2(\Delta S)^2 + (S - F)^2(\Delta D)^2 + (S - D)^2(\Delta F)^2 \over (F - D)^4} \end{equation} --> <TABLE WIDTH="100%" ALIGN="CENTER"> <TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="ccd-8"> </A><IMG WIDTH="584" HEIGHT="63" SRC="img924.gif" ALT="\begin{displaymath}(\Delta I)^2 = {(F - D)^2(\Delta S)^2 + (S - F)^2(\Delta D)^2 + (S - D)^2(\Delta F)^2 \over (F - D)^4} \end{displaymath}"></TD> <TD WIDTH=10 ALIGN="RIGHT"> (18.8)</TD></TR> </TABLE> </DIV> <BR CLEAR="ALL"><P></P> A small error in <IMG WIDTH="35" HEIGHT="22" ALIGN="BOTTOM" BORDER="0" SRC="img925.gif" ALT="$\Delta I$"> is obtained if <IMG WIDTH="39" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="img926.gif" ALT="$\Delta S$">, <IMG WIDTH="42" HEIGHT="22" ALIGN="BOTTOM" BORDER="0" SRC="img927.gif" ALT="$\Delta D$"> and <IMG WIDTH="42" HEIGHT="22" ALIGN="BOTTOM" BORDER="0" SRC="img928.gif" ALT="$\Delta F$"> are kept small. This is achieved by averaging Dark, Flat and Science frames. <IMG WIDTH="35" HEIGHT="22" ALIGN="BOTTOM" BORDER="0" SRC="img929.gif" ALT="$\Delta I$"> is further reduced if <I>S</I>=<I>F</I>, then Equation (<A HREF="node443.html#ccd-8">B.8</A>) simplifies to <BR><P></P> <DIV ALIGN="CENTER"> <!-- MATH: \begin{equation} (\Delta I)^2 = {(\Delta S)^2 + (\Delta F)^2 \over (F - D)^2} \end{equation} --> <TABLE WIDTH="100%" ALIGN="CENTER"> <TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="ccd-9"> </A><IMG WIDTH="234" HEIGHT="63" SRC="img930.gif" ALT="\begin{displaymath}(\Delta I)^2 = {(\Delta S)^2 + (\Delta F)^2 \over (F - D)^2} \end{displaymath}"></TD> <TD WIDTH=10 ALIGN="RIGHT"> (18.9)</TD></TR> </TABLE> </DIV> <BR CLEAR="ALL"><P></P> <P> This equation holds only at levels near the sky-background and is relevant for detection of low-brightness emission. In practice however it is difficult to get a similar exposure level for the FLAT_FRM and SCIE_FRM since the flats are usually measured inside the Dome. From this point of view it is desirable to measure the empty sky (adjacent to the object) just before or after the object observations. <BR><HR> <ADDRESS> <I>Petra Nass</I> <BR><I>1999-06-15</I> </ADDRESS> </BODY> </HTML>