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<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>
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