Sophie: eso-midas-doc-15SEPpl1.0-2.mga6 armv5tl

eso-midas-doc-15SEPpl1.0-2.mga6.armv5tl.rpm

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<H2><A NAME="SECTION002511000000000000000">&#160;</A> 
<A NAME="introduction1">&#160;</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">&#160;</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&nbsp;(<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">&#160;</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">&#160;</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">&#160;</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">&#160;</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">&#160;</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>
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<ADDRESS>
<I>Petra Nass</I>
<BR><I>1999-06-15</I>
</ADDRESS>
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