<!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>Introduction</TITLE> <META NAME="description" CONTENT="Introduction"> <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="node443.html"> <LINK REL="previous" HREF="node441.html"> <LINK REL="up" HREF="node441.html"> <LINK REL="next" HREF="node443.html"> </HEAD> <BODY > <!--Navigation Panel--> <A NAME="tex2html6967" HREF="node443.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="icons.gif/next_motif.gif"></A> <A NAME="tex2html6964" HREF="node441.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="icons.gif/up_motif.gif"></A> <A NAME="tex2html6958" HREF="node441.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="icons.gif/previous_motif.gif"></A> <A NAME="tex2html6966" 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="tex2html6968" HREF="node443.html">Discussion</A> <B> Up:</B> <A NAME="tex2html6965" HREF="node441.html">CCD Detectors</A> <B> Previous:</B> <A NAME="tex2html6959" HREF="node441.html">CCD Detectors</A> <BR> <BR> <!--End of Navigation Panel--> <H2><A NAME="SECTION002511000000000000000"> </A> <A NAME="introduction1"> </A> <BR> Introduction </H2> <P> The nominal output <I>X</I><SUB><I>ij</I></SUB> of a CCD-element to a quantum of light <I>I</I><SUB><I>ij</I></SUB>can be given as <BR><P></P> <DIV ALIGN="CENTER"> <!-- MATH: \begin{equation} X_{ij} = A_{ij} + B_{ij} \times I_{ij} + \hbox{non--linear terms} + \hbox{BIAS} \end{equation} --> <TABLE WIDTH="100%" ALIGN="CENTER"> <TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="ccd-1"> </A><IMG WIDTH="466" HEIGHT="41" SRC="img915.gif" ALT="\begin{displaymath}X_{ij} = A_{ij} + B_{ij} \times I_{ij} + \hbox{non--linear terms} + \hbox{BIAS} \end{displaymath}"></TD> <TD WIDTH=10 ALIGN="RIGHT"> (18.1)</TD></TR> </TABLE> </DIV> <BR CLEAR="ALL"><P></P> This equation does not account for charge transfer inefficiencies and other effects known to exist in CCDs. <P> The dark current and the cold columns contribute to the additive term A; the quantum- and transfer-efficiency enter into the multiplicative term <IMG WIDTH="62" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="img916.gif" ALT="$B\times I$">. It is known that the response of the CCD is essentially linear so the non-linear terms are generally neglected. The Bias is normally added to the output electronically to avoid problems with digitising values near to zero. <P> The objective of the first step in reducing CCD-images is to determine the relative intensity <I>I</I><SUB><I>ij</I></SUB> of a science data frame. In order to do this, two more frames are required in addition to the science picture, namely: <UL> <LI>FLAT-frames to determine the term <I>B</I><SUB><I>ij</I></SUB>, and <LI>DARK-frames to describe the term <I>A</I><SUB><I>ij</I></SUB>. </UL>FLAT-fields are made by illuminating the CCD with a uniformly emitting source. The Flat-field then describes the sensitivity over the CCD which is not uniform. For FLAT-field exposures and SCIENCE-frames we get from Equation (<A HREF="node442.html#ccd-1">B.1</A>) <BR><P></P> <DIV ALIGN="CENTER"> <!-- MATH: \begin{equation} \rm FLAT\_FRM(i,j) = DARK(i,j) + B(i,j) \times ICONS + BIAS \end{equation} --> <TABLE WIDTH="100%" ALIGN="CENTER"> <TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="ccd-2"> </A><IMG WIDTH="544" HEIGHT="40" SRC="img918.gif" ALT="\begin{displaymath}\rm FLAT\_FRM(i,j) = DARK(i,j) + B(i,j) \times ICONS + BIAS \end{displaymath}"></TD> <TD WIDTH=10 ALIGN="RIGHT"> (18.2)</TD></TR> </TABLE> </DIV> <BR CLEAR="ALL"><P></P> <BR><P></P> <DIV ALIGN="CENTER"> <!-- MATH: \begin{equation} \rm SCIE\_FRM(i,j) = DARK(i,j)+B(i,j) \times INT\_FRM(i,j) + BIAS \end{equation} --> <TABLE WIDTH="100%" ALIGN="CENTER"> <TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="ccd-3"> </A><IMG WIDTH="604" HEIGHT="40" SRC="img919.gif" ALT="\begin{displaymath}\rm SCIE\_FRM(i,j) = DARK(i,j)+B(i,j) \times INT\_FRM(i,j) + BIAS \end{displaymath}"></TD> <TD WIDTH=10 ALIGN="RIGHT"> (18.3)</TD></TR> </TABLE> </DIV> <BR CLEAR="ALL"><P></P> where ICONS represents a flux from a uniform source, and BIAS is a constant signal which is added to the video signal of the CCD before being digitised. <P> The DARK-current is measured in the absence of any external input signal: <BR><P></P> <DIV ALIGN="CENTER"> <!-- MATH: \begin{equation} \rm DARK\_FRM(i,j) = DARK(i,j) + BIAS \end{equation} --> <TABLE WIDTH="100%" ALIGN="CENTER"> <TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="ccd-4"> </A><IMG WIDTH="374" HEIGHT="40" SRC="img920.gif" ALT="\begin{displaymath}\rm DARK\_FRM(i,j) = DARK(i,j) + BIAS \end{displaymath}"></TD> <TD WIDTH=10 ALIGN="RIGHT"> (18.4)</TD></TR> </TABLE> </DIV> <BR CLEAR="ALL"><P></P> Combining Eqs.(<A HREF="node442.html#ccd-2">B.2</A>), (<A HREF="node442.html#ccd-3">B.3</A>) and (<A HREF="node442.html#ccd-4">B.4</A>) we isolate: <BR><P></P> <DIV ALIGN="CENTER"> <!-- MATH: \begin{equation} \rm INT\_FRM(i,j) = {{SCIE\_FRM(i,j)-DARK\_FRM(i,j) \over FLAT\_FRM(i,j)-DARK\_FRM(i,j)}} \times ICONS \end{equation} --> <TABLE WIDTH="100%" ALIGN="CENTER"> <TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="ccd-5"> </A><IMG WIDTH="610" HEIGHT="61" SRC="img921.gif" ALT="\begin{displaymath}\rm INT\_FRM(i,j) = {{SCIE\_FRM(i,j)-DARK\_FRM(i,j) \over FLAT\_FRM(i,j)-DARK\_FRM(i,j)}} \times ICONS \end{displaymath}"></TD> <TD WIDTH=10 ALIGN="RIGHT"> (18.5)</TD></TR> </TABLE> </DIV> <BR CLEAR="ALL"><P></P> <P> ICONS can be any number. If set to the average signal of the dark-corrected FLAT-frame or a subimage thereof: <P> <BR><P></P> <DIV ALIGN="CENTER"> <!-- MATH: \begin{equation} \rm ICONS = \left< FLAT\_FRM-DARK\_FRM \right> \end{equation} --> <TABLE WIDTH="100%" ALIGN="CENTER"> <TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="ccd-6"> </A><IMG WIDTH="379" HEIGHT="40" SRC="img922.gif" ALT="\begin{displaymath}\rm ICONS = \left< FLAT\_FRM-DARK\_FRM \right> \end{displaymath}"></TD> <TD WIDTH=10 ALIGN="RIGHT"> (18.6)</TD></TR> </TABLE> </DIV> <BR CLEAR="ALL"><P></P> then the reduced intensity frame INT_FRM will have similar data values as the original SCIE_FRM. <P> <HR> <!--Navigation Panel--> <A NAME="tex2html6967" HREF="node443.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="icons.gif/next_motif.gif"></A> <A NAME="tex2html6964" HREF="node441.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="icons.gif/up_motif.gif"></A> <A NAME="tex2html6958" HREF="node441.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="icons.gif/previous_motif.gif"></A> <A NAME="tex2html6966" 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="tex2html6968" HREF="node443.html">Discussion</A> <B> Up:</B> <A NAME="tex2html6965" HREF="node441.html">CCD Detectors</A> <B> Previous:</B> <A NAME="tex2html6959" HREF="node441.html">CCD Detectors</A> <!--End of Navigation Panel--> <ADDRESS> <I>Petra Nass</I> <BR><I>1999-06-15</I> </ADDRESS> </BODY> </HTML>