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<h1>Color Calibration of an Instrumental Photometric System</h1>
<p>
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 which covers wide range of color indexes.
</p>
<p>
As the calibration stars, we are choose data
which has been carefully measured by Arne Henden
(<a href="http://binaries.boulder.swri.edu/binaries/fields/m67.html">M67 Standards Field</a>).
</p>
<h2>Sample Data</h2>
<p>
A sample data are available as
<a href="https://integral.physics.muni.cz/ftp/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>
<h2>Photometry Calibration</h2>
<p>
The main goal of photometry calibration is
to determine relations between instrumental fluxes
(magnitudes) and fluxes (magnitudes) defined
by a photometric system (with conventionally defined
conditions, especially by 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
v-filter by a standard V-filter:
</p>
<p>
v - V = a + b*(V-R)
</p>
<p>
The goal is to determine coefficients <i>a,b</i> by a fit
of a linear function. The precision depends on coverage of
color index V-R 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>.</li>
<li>Stars detection and photometry
<pre>
$ munipack aphot M67_Green_*.fits
$ munipack aphot M67_Blue_*.fits
</pre>
</li>
<li>Search an astrometric catalogue (required for astrometric calibration)
<pre>
$ munipack cone -o m67cat.fits -r 0.1 132.75 11.8
</pre>
</li>
<li>Astrometry calibration of all images
<pre>
$ munipack astrometry -c m67cat.fits M67_*.fits
</pre>
</li>
<li>
Sum of all images
<pre>
$ munipack kombine -o M67_Blue.fits M67_Blue_*.fits
$ munipack kombine -o M67_Green.fits M67_Green_*.fits
</pre>
</li>
<li>Aperture photometry of final frames
<pre>
$ munipack aphot -f 6 M67_Blue.fits M67_Green.fits
</pre>
</li>
<li>
Preparation of results in tables
<pre>
$ munipack phframe --table -q IMAG --naperture 7 M67_Green.fits,M67_Green_res.fits
$ munipack phframe --table -q IMAG --naperture 7 M67_Blue.fits,M67_Blue_res.fits
</pre>
<p>
The file M67_Green_res.fits contains the table:
</p>
<div class="table">
<table>
<tr><th>α [J2000]</th><th>δ [J2000]</th><th>instrumental magnitude</th><th>std. deviation</th></tr>
<tr><td>132.8228301</td><td>11.7562805</td><td>7.62841</td><td>.00036</td></tr>
<tr><td>…</td><td>…</td><td>…</td><td></td></tr>
</table>
</div>
<p>
The output table can be matched against to a standard field stars in
equatorial coordinates. The calibration coefficients can be easy
determined by the way.
</p>
<p>
To match and visualize data, <a href="http://www.star.bris.ac.uk/~mbt/topcat/">topcat</a>
(part of Virtual Observatory software) can be recommended.
</p>
</li>
</ol>
<figure>
<img src="M67_Green-graph.png" alt="M67_Green-graph.png" title="M 67">
<figcaption>M 67 calibration</figcaption>
</figure>
<figure>
<img src="M67_Blue-graph.png" alt="M67_Blue-graph.png" title="M 67">
<figcaption>M 67 calibration</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>
<p>
Please also don't be confused from filters designation and
graphs. The used filters are RGB photographic filters for a color
imaging. That's why the linear dependence doesn't exactly fit the data.
</p>
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© 1997 – 2025
<a href="https://integral.physics.muni.cz/" title="author's homepage"
class="foot">Filip Hroch</a>
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