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<H2><A NAME="SECTION001113000000000000000">
General Description</A>
</H2>
The first problem in the reduction of echelle spectra is, of course,
the solution of the dispersion relation. That is the mapping between
the space
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wavelength, spectral order and the space
(<I>x</I>,<I>y</I>) sample <I>x</I>, line <I>y</I> in the raw image. This relation gives the
position of the orders on the raw image, and defines the wavelength
scale of the extracted spectrum. The mapping is performed in two
steps:
<UL>
<LI>A first operation (order definition), gives the position
of the orders in the raw image. In
figure <A HREF="node148.html#fig:ech-red">7.1</A>, this
operation corresponds to the step ``Find Order Position''.
The required input is an order reference frame (usually <TT>FLAT</TT>
or <TT>STD</TT>) and the output is a set of polynomial coefficients.
These coefficients are an input of the step ``Extract Orders''.
<LI>A second operation (wavelength calibration) defines the wavelength
scale of the extracted spectrum. The successive steps of this
operation are shown in the second column of
figure <A HREF="node148.html#fig:ech-red">7.1</A>.
The output is a set of dispersion coefficients required by
the step ``Sample in Wavelength''.
</UL>Sections <A HREF="node150.html#order-definition">7.2</A> and <A HREF="node158.html#wavelength-calibration">7.6</A>
describe the solution of this mapping.
<P>
The second step in the reduction, described in
Section <A HREF="node152.html#background-definition">7.4</A>, is to estimate the image background. The
background depends mainly on the characteristics of the detector, but includes
the additional components of the scattered light in the optics and
spectrograph. This operation corresponds to the step ``Subtract Background''
in fig. <A HREF="node148.html#fig:ech-red">7.1</A>.
<P>
A particular problem in the <TT>CCD</TT>-detector used by the two
echelle instruments is the appearence of interference fringes produced
within the silicon, which can be especially important in the long
wavelength range of the instrument. By processing the flat-field
(first column of fig. <A HREF="node148.html#fig:ech-red">7.1</A>), correction
frames are prepared and used for the standard star and the object
reduction. A method to correct for this effect is described in
Section <A HREF="node164.html#flat-field-correction">7.7</A>.
<P>
After the corrections for all these effects, the information in the
spectral orders is extracted using the methods described in
Section <A HREF="node157.html#order-extraction">7.5</A>. The extracted flux, used in
conjunction with the dispersion relation, gives the photometric
profiles of the spectral orders. Two instrumental effects are still
present in these profiles: first, due to the blaze effect of the
echelle grating, the efficiency of the spectrograph changes along each
order; second, the efficiency of the whole instrument is not uniform
with wavelength. In Section <A HREF="node165.html#standard-correction">7.8</A> we describe how
to correct both effects, to normalize the fluxes and, if the input
data includes calibration stars, to convert the fluxes into absolute
units.
<P>
<BLOCKQUOTE>
<DIV ALIGN="CENTER">
<B>Note</DIV>
<I>Taking a standard star exposure (STD) is a recommended observation
strategy which can make easier the order definition in the blue part of the
spectrum as well as the correction of individual orders for the
variations of grating efficiency (blaze function). </I></B></BLOCKQUOTE>
<P>
The steps summarised above comprise the <TT>STANDARD</TT> reduction.
Alternatively, it is possible to correct the variation in sensitivity
along the spectral orders using a suitable model for the blaze
function as described in Section <A HREF="node167.html#blaze-correction">7.8.2</A>.
Figure <A HREF="node148.html#fig:ech-red">7.1</A> displays the process scheme
in a typical reduction session; slanted fonts indicate optional
operations. In the rest of this Section the algorithms used in each
step of the reduction are described.
<P>
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<ADDRESS>
<I>Petra Nass</I>
<BR><I>1999-06-15</I>
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