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<title>Munipack ‒ Aperture Photometry</title>
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<section>
<h1>Aperture Photometry</h1>
<p class="abstract">
Aperture photometry determines sum of counts from a star in a set of
predefined apertures.
</p>
<h2>Synopsis</h2>
<code>
munipack aphot [.. parameters ..] file(s)[,result(s)]
</code>
<p>Running of photometry adds a HDU extensions to the original frame
as a table described in <a href="dataform_proc.html">Processing Format</a>.
<h2>Algorithm</h2>
<p>Aperture photometry is performed by the way:</p>
<ul>
<li>Read parameters (command-line and gain and LOBAD,HIBAD) and
list of detected stars (in FIND extension).
</li>
<li>
For every detected star, the sum inside of the specified apertures
as well as in sky determining ring is computed.
</li>
<li>
The mean background in the ring is computed.
</li>
<li>
The counts for all apertures are computed by subtracting of mean background.
</li>
</ul>
<p>The pixels near the border are approximated by only a fraction covering
the pixel inside.
</p>
<p>
By defaults, twelve apertures is used. Aperture radii are computed
as points of logarithmic spiral <i>r = r<sub>0</sub></i>exp <i>a φ</i>
with the initial radius <i>r<sub>0</sub>=2</i> and pitch angle 8.9073°
(to be compatible with DAOPHOT II).
</p>
<p>
For a correct determination of photometry errors, the camera-specific
parameters must by provided.
</p>
<p>
Strictly speaking, for further processing just one aperture is required.
The prepare of several apertures has profit in fast switching to another
aperture without needs to do photometry again. More apertures can be also
used in simultaneous use of ones for PSF of grow-curve photometry.
</p>
<p>
The results of aperture photometry are stored in columns of a newly created
APERPHOT extension.
</p>
<p>
The photometry is performed for all detected stars (all stars in FIND extension)
in all specified apertures. Sometimes it is impossible compute the sum,
the case is indicated by a negative value (-1).
Common situation are when the sum of counts with subtracted background
is negative (sky is polluted by a bright source, background has a fast gradient)
or the star is too near of border and summing pixels are out of area)
or a star is saturated.
</p>
<p>
The results of aperture photometry are stored to next PHOTOMETRY extension.
In the extension, the results in a selected aperture (by <samp>-s</samp>)
are selected. Just stars with valid (non-negative) values are presented here.
</p>
<h2>Data assumption</h2>
<p>
Aphot does <b>assumtion</b>, that data represents actually detected
<b>counts</b>.
</p>
<p>
While common digital devices detects single photons, the cameras
does not report their true counts. Rather, they reports a digitised
value which is multiplied by some amplifier gain of the electronic device.
Moreover, the value has included bias to suppress a non-linearity of
the devices.
</p>
<p>
Therefore,
it is very <b>important</b> to pre-correct the data.
The relative precision of star determination is driven by
<a href="https://en.wikipedia.org/wiki/Poisson_distribution">Poisson
statistics</a>; if actually detected counts of photons is <i>N</i>,
the relative error will be <i>σ=√N/N</i>. However, data multiplied
by factor <i>g</i> gives <i>σ/√g</i> (for <i>N</i>=10000, <i>σ</i>=1/100,
while a choice <i>g</i>=4 leads to 1/50).
</p>
<p>
Aphot does not check the assumption.
Carefully handled parameters of <a href="man_phcorr.html">phcorr</a>
will prepare such correct data. The gain value can be checked
by <a href="man_flat.html">flat-field</a>.
</p>
<h2>Elliptic apertures</h2>
<p>
Munipack improvement over the original DAOPHOT aperture photometry
implementation is possibility to use of elliptic apertures
enclosing trailed stars more tightly.
While this idea looks extremely attractive, the application
on real data shows minimal, if any, progress.
This is perhaps a dead way.
</p>
<p>
The implementation is pure experimental.
<a href="man_find.html">FIND</a> estimates both
eccentricity and inclination; the values are
used by this routine, if it is invoked with
<samp>--enable-ellipticity</samp>.
Elliptic apertures are missing intentionally in GUI.
</p>
<h2>Input And Output</h2>
<p>
On input, list of frames containing the table with already detected stars is expected.
</p>
<p>
On output, tables with the aperture photometry and results from the selected column,
represented by FITS extension, is added to all input images.
</p>
<h2>Parameters</h2>
<dl>
<dt><samp>--apertures r1, r2, .. rmax</samp></dt>
<dd>define apertures radii (in pixels),
count and sizes are arbitrary,
must be specified in increasing
order and separated by commas
</dd>
<dt><samp>--ring ri,ro</samp></dt>
<dd> inner and outer sky ring radius in pixels,
the inner radius must be equal or bigger than the greater aperture
</dd>
<dt><samp>--enable-ellipticity</samp></dt><dd>
Apertures are ellipses; their actual
shape is determined by FITS parameter in FIND extension,
or specified by following command line options.
</dd>
<dt><samp>--eccentricity <i>e</i></samp></dt><dd>
Eccentricity of apertures by a contour
<a href="https://en.wikipedia.org/wiki/Ellipse">ellipse</a>:
<i>0 ≤ e < 1</i>. The default value is <i>e=0</i> meaning
circular aperture.
</dd>
<dt><samp>--inclination <i>i</i></samp></dt><dd>
Inclination of major semi-axis of the
<a href="https://en.wikipedia.org/wiki/Ellipse">ellipse</a>
in degrees. Positive values of the angle are in mathematics sense
(counter-clockwise).
</dd>
<dt><samp>--coo "x1,y1 x2,y2..."</samp></dt>
<dd>
List of pixel rectangular coordinates: they are centroids of stars
to get photometry for. Their photometry processing, including accuracy
and robustness, is exactly the same as the canonical way.
FIND extension can not be presented in the FITS file.
</dd>
</dl>
<p>See <a href="man_com.html">Common options</a> for input/output filenames.</p>
<h2>History</h2>
<p>
The routine is on base of original code of DAOPHOT II by P.B.Stetson
(has been forked from Midas's implementation at 1996). Some additional
enhancements has been done:
</p>
<ul>
<li>Robust estimators replaces the original estimators of averadge.</li>
<li>All processing is done in memory (no disc buffering is used).</li>
<!--<li>Real numbers in double precision are implemented</li>-->
<li>The magnitude output has been abandoned.</li>
<li>Elliptic apertures can be choosed.</li>
<li>FITS files for both input and output are used</li>
<li>Log format is changed.</li>
<li>Code is updated for Fortran 90 and 95 (and perhaps above).</li>
</ul>
<h2>Examples</h2>
<p>
Run aperture photometry:
</p>
<code>
$ munipack find pleiades.fits
$ munipack aphot pleiades.fits
</code>
<p>
Select apertures and sky estimation by hand (as powers of 2):
</p>
<code>
$ munipack aphot --apertures 1,2,4,8,16,32 --ring 16,32 pleiades.fits
</code>
<p>
List of total counts (aperture photometry) in default apertures
for star at <i>x = 666, y = 666</i>:
</p>
<code>
$ munipack aphot --coo "666,666" pleiades.fits
</code>
<h2>See Also</h2>
<p>
<a href="grow.html">Growth Curve Overview</a>,
<a href="man_find.html">Find Stars</a>,
<a href="man_com.html">Common options</a>,
<a href="dataform_photometry.html">Photometry Format</a>.
</p>
</section>
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