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<title>Munipack ‒ Colour Calibration Tutorial</title>
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<h1>Colour Calibration Of An Instrumental Photometric System</h1>
<p class="abstract">
How to calibrate of an instrumental photometric system.
</p>
<h1>Open Cluster M 67</h1>
<p>
Open cluster M 67 is an old galactic cluster with a differently
evolved stars and with many kinds of spectra. The wide variability
induces variability on fluxes per filters and are the crucial
for successful calibration.
</p>
<p>
The principle of colour calibration is determining of a relation
between instrumental and standard (calibrated) fluxes.
</p>
<h2>Sample Data</h2>
<p>
A sample data are available as
<a href="ftp://munipack.physics.muni.cz/pub/munipack/munipack-data-m67.tar.gz">munipack-data-m67.tar.gz</a>. Use commands
</p>
<pre>
$ cd /tmp
$ tar zxf munipack-data-m67.tar.gz
</pre>
<p>
to unpack it to a desired directory.
We will assume that the sample data are unpacked to <samp>/tmp</samp> directory
as <samp>/tmp/munipack-data-m67</samp>.
</p>
<p>
The sample data has been acquired at MonteBoo Observatory by group
of author's students "Hrošátka". The flat-fields by ChM. Quality
of the observation is poor due to a light pollution by our urban neighbourhood.
</p>
<h2>Photometry Calibration</h2>
<p>
The main goal of photometry calibration is
to determine relations between instrumental counts
offered by our camera and expected number of
photons (derived from magnitudes in optical bands) defined
by a photometric system (with conventionally defined
transmission of filters).
</p>
<p>
General relations can by derived as an approximation
of a set of functions (instrumental filters) by another
set functions (standard filters) as a linear transformations.
A simple example is the calibration of instrumental
<i>v</i>-filter by a standard <i>V</i>-filter:
</p>
<p>
<i>
F<sub>V</sub> = c<sub>Vv</sub> F<sub>v</sub> + c<sub>Vr</sub> F<sub>r</sub><br>
F<sub>R</sub> = c<sub>Rv</sub> F<sub>v</sub> + c<sub>Rr</sub> F<sub>r</sub>
</i>
</p>
<p>
The goal is to determine coefficients <i>c<sub>ij</sub></i> by a fit
of the linear transformation. The precision and availability
depends on coverage of colour of stars and that is why we use
the evolved cluster.
</p>
<h2>Data Processing</h2>
<p>
There is an algorithm to get data for the calibration.
</p>
<ol>
<li>Prepare images for photometric corrections as describes
<a href="phcorrtut.html">Photometric Corrections Tutorial</a>.
<pre>
$ munipack dark -o d7.fits d7_*.fits
$ munipack dark -o d30.fits d30_*.fits
$ munipack flat -o fB.fits -dark d7.fits flat_*B.fits
$ munipack flat -o fV.fits -dark d7.fits flat_*V.fits
$ munipack flat -o fR.fits -dark d7.fits flat_*R.fits
$ munipack phcorr -dark d30.fits -flat fB.fits m67_*B.fits
$ munipack phcorr -dark d30.fits -flat fV.fits m67_*V.fits
$ munipack phcorr -dark d30.fits -flat fR.fits m67_*R.fits
</pre>
</li>
<li>Stars detection and photometry
<pre>
$ munipack find -th 10 -f 6 m67_*.fits
$ munipack aphot m67_*.fits
</pre>
Warnings like:
<pre>
Object at coordinates: 739.055908 94.7188416
Are you sure your bad pixel thresholds are all right?
If so, then you need a larger outer sky radius.
8 20 1762 84700.0000 3.39999995E+38
</pre>
are reported for stars near of border (when aperture lie outsdie
of image) and can be safety ignored.
</li>
<li>Search an astrometric catalogue (required for astrometric calibration)
<pre>
$ munipack cone -r 0.2 132.8 11.8
</pre>
</li>
<li>Astrometry calibration of all images
<pre>
$ munipack astrometry -c cone.fits m67_*.fits
</pre>
</li>
<li>
Sum of all images
<pre>
$ munipack kombine --rcen 132.8304 --dcen 11.7771 -o m67_B.fits m67_*B.fits
$ munipack kombine --rcen 132.8304 --dcen 11.7771 -o m67_V.fits m67_*V.fits
$ munipack kombine --rcen 132.8304 --dcen 11.7771 -o m67_R.fits m67_*R.fits
</pre>
</li>
<li>Aperture photometry of final frames
<pre>
$ munipack find -th 10 -f 6 m67_?.fits
$ munipack aphot m67_?.fits
</pre>
</li>
<li>
<p class="li">
As the calibration stars, we had selected data
for <a href="http://binaries.boulder.swri.edu/binaries/fields/m67.html">M67 Standards Field</a> measured by Arne Henden (other calibration
sequences can be found at
<a href="http://binaries.boulder.swri.edu/fields/">fields</a>).
Unfortunately, the tables are in plain text format. Munipack needs
a structured table (FITS table or VOTable) as the reference catalogue.
The script <a href="henden_m67.sh">henden_m67.sh</a> has been prepared
for convert the catalogue to more reliable format (and as an example how
that catalogues can be created from own data).
</p>
<pre>
$ wget http://binaries.boulder.swri.edu/binaries/fields/m67ids.txt
$ bash henden_m67.sh
</pre>
The file <samp>m67ids.fits</samp> is created.
</li>
<li>
<p class="li">
The colour transformation is determined by <samp>phfotran</samp> action.
There is many parameters which can not be omitted. The identification
of instrumental and standard system (for documentation purposes and
for filter properties), the telescope area and the toleration for
star's cross-matching will usually required.
</p>
<p class="li">
The crucial is selection of magnitude columns from catalogue
<samp>--col-mag B,V,R</samp> for frames in appropriate filters.
The relation is determined on base of descending order
(B for m67_B.fits, etc).
</p>
<pre>
$ munipack phfotran \
--photsys-instr MonteBoo --photsys-ref Johnson
-c m67ids.fits \
--col-ra RAJ2000 --col-dec DEJ2000 \
--col-mag B,V,R \
--tol 0.0005 \
--area 0.283 \
m67_B.fits m67_V.fits m67_R.fits
</pre>
<p class="li">
The action creates the file <samp>phfotran.fits</samp> which contains
a table like this:
</p>
<table>
<tr><th></th><th>B</th><th>V</th><th>R</th></tr>
<tr><td>b</td><td>18.05</td><td>-0.87</td><td>0</td></tr>
<tr><td>v</td><td>-0.47</td><td>7.48</td><td>0.27</td></tr>
<tr><td>r</td><td>0</td><td>-0.72</td><td>7.78</td></tr>
</table>
<p class="li">
As we can see, the instrumental filters on MonteBoo
Observatory are nearly to Johnson filters (at least filters
used on calibration field). The off-diagonal elements are
negligible to diagonal ones. Also efficiency in <i>V,R</i> filters
is twice more than in <i>B</i> filter (due to quantum sensitivity of
used CCD camera).
</p>
<p class="li">
The result table can be used on precise of <a href="man_phcal.html">photometric calibration</a>.
</p>
</li>
</ol>
<h2>Colour Look</h2>
<p>
Just for a nice picture, the colour frame can be easy prepared:
</p>
<pre>
munipack coloring -o m67.fits -c 'Johnson BVR' m67_B.fits,B m67_V.fits,V m67_R.fits,R
</pre>
<figure>
<img src="m67.png" alt="m67.png" title="Color Image of M67">
<figcaption>
M67 in Colours
</figcaption>
</figure>
<h2>Notes</h2>
<p>
This example is illustrative only! The instrumental
magnitudes are also affected by the atmospheric extinction
and to get correct values, we need to determine extra-atmospheric magnitudes
by observing of the field in different air masses and an extrapolation
on null air mass.
</p>
<h2>See Also</h2>
<p>
<a href="man_phcal.html">Photometry calibration</a>,
<a href="man_phfotran.html">Photometric System Transformation</a>,
<a href="dataform_photometry.html">Photometry Format</a>.
</p>
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