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<!DOCTYPE HTML>
<html lang="en">
<head>
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="description" content="A general astronomical image processing software">
<meta name="author" content="Filip Hroch">
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<title>Munipack ‒ Astrometry Overview</title>
</head>
<body>
<header>
<a href="munipack.html"><img src="title_logo.png" alt="Munipack's logo" class="head"></a>
<div class="headhead">
<div class="headtitle">
<a class="headtitle" href="munipack.html">Munipack</a>
<a class="headsubtitle" href="munipack.html">A general astronomical image processing software</a>
</div>
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  <li class="menu">◈ <a href="docs.html" class="menu">Documents</a></li>
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<h1>Astrometry Overview</h1>

<p class="abstract">
  Astrometry calibration establishes mutual mapping between
  sky's coordinates and coordinates on frames.
  Astrometry is essential for any additional processing like photometry
  or frame composition.
</p>

<p>
  Usage of a command line astrometry tool
  can be found in <a href="man_astrometry.html">Astrometry</a> manual page.
</p>


<h2>Introduction</h2>

<p>
  Astronomical instruments works as devices which projects
  spherical coordinates (Right Ascension α or Declination δ)
  onto rectangular coordinates of imaging devices. The projection
  establishes an unique mapping for all objects (pixels).
  The mapping is usually complicated (nonlinear) because
  projected images of sky may be deformed. The calibration can
  be considered as the two step procedure:
</p>
<ul>
<li>
  spherical coordinates are projected
  (by <a href="https://en.wikipedia.org/wiki/Gnomonic_projection">gnomonic</a>
  or another projection) on to auxiliary rectangular coordinates,
</li>
<li>
  and
  <a href="https://en.wikipedia.org/wiki/Affine_transformation">affine mapping</a>
  (including rotation, shift, scaling and reflection) is applied to get
  the mutual transformation between the auxiliary projected and
  current on-chip coordinates.
</li>
</ul>

<p>
The calibration can be stored in FITS frame header as
<a href="http://fits.gsfc.nasa.gov/fits_wcs.html">WCS
  (world-coordinate system) calibration</a> which is
described at reference <a href="dataform_astrometry.html">Astrometry</a> header
page.
</p>

<div class="screenshots">
<figure>
<img class="figure" src="astrocoo.png" alt="screenshot">
<figcaption>Panel with the coordinate indicator</figcaption>
</figure>
</div>



<h2>How To Describe Of Astrometry Mapping</h2>

<p>
To describe of the astrometry calibration, Munipack uses
carefully selected set of parameters. Parameters
are easy for use (change in a single parameter doesn't affects others)
and supports robust fitting.
</p>

<dl>
<dt>Projection</dt>
  <dd>The type of projection of spherical coordinates onto rectangular. Currently only
      gnomonic projection is implemented.</dd>
<dt>Reference point on images <i>x</i><sub>c</sub>, <i>y</i><sub>c</sub></dt>
<dd>The reference point of rectangular coordinates,
  the image is rotated around the point, normally, centre of the image. </dd>
<dt>Centre of spherical projection <i>α</i><sub>c</sub>, <i>δ</i><sub>c</sub></dt>
  <dd>It's a centre of projection of spherical coordinates.
      One simply gives coordinates of the centre of captured field.
</dd>
<dt>Scale <i>c</i></dt>
  <dd>Scale of image in degrees per pixels.</dd>
<dt>Angle of rotation <i>φ</i></dt>
  <dd>It's an angle of the image rotation around the reference point
      <i>x</i><sub>c</sub>, <i>y</i><sub>c</sub>.
      The value increases in counterclockwise direction (according to
      mathematical sense) and with its origin on <i>x</i>-axis (on 3-th hour direction).
</dd>
<dt>Reflection</dt>
  <dd>Mutual reflection</dd>
</dl>

<p>
<b>All angles are in degrees.</b>
Also don't try use fractions like arcsecs or don't interchange degrees and radians.
</p>


<h2>Modes Of Astrometry Calibration</h2>

<p>
Munipack provides following modes of the calibration of FITS frames:
</p>
<h3>Match</h3>
<p>Stars, detected on frames, are identified in an astrometric catalogue
  by matching. The parameters are estimated by fitting of the transformation.
  Matching is intended for general use.
</p>

<h3>Sequence</h3>
<p>
User provides a sequence of identified stars and the transformation
is derived from coordinates of the stars by fitting. It can be useful
when matching has failed.
</p>


<h3>Manual</h3>
<p>
  Manual mode just save a calibration in WCS conventions using of parameters
  <i>α</i><sub>c</sub>, <i>δ</i><sub>c</sub>, <i>c</i>, <i>φ</i> and
  possible reflection
  provided by user. Any other information (detection of objects, catalogues)
  are not required. It can be useful when astrometry is already known.
</p>



<h2>Sources Of Reference Stars</h2>

<p>
These sources can be used as a references of the coordinates.
</p>
<dl>
<dt>Catalogue</dt><dd>Stars selected from an astrometric catalogue are
used as the reference.</dd>
<dt>Reference frame</dt><dd>Stars detected on already calibrated frame are
used as the reference.</dd>
<dt>Relative frame</dt><dd>Stars detected on a reference frame are
used as reference. A projection is not applied. There is only relative
calibration. Useful when a right projection is not available or possible.</dd>
</dl>

<p>
Note that the types of calibrations using catalogues and frames
requires detected objects (see <a href="man_aphot.html">aperture photometry</a>).
</p>

<h2>Projection</h2>

<p>
Projection maps spherical coordinates and rectangular coordinates.
Just only Gnomonic is implemented yet.
</p>

<p>
No projection is useful for relative matching of frames.
</p>


<h2>Matching</h2>

<p>
Matching between objects on reference (catalogue) and calibrated frames
is developed on base of a kind
of <a href="http://en.wikipedia.org/wiki/Backtracking">backtracking</a>
algorithm. All possible combinations of triplets are generated from
data and grouped to sequences. Sequences of catalogue and observed
data is searched for minimal distance in the triangle space
(an application of triangle similarity, one from basic triangle rules,
known from first school years).
</p>

<p>
The backtracking is affected by parameters: --minmatch
(minimal lenght of match sequence, --maxmatch (maximum length of match sequence),
--sig sets a typical deviation of coordinates
and --fsig is the dispersion in fluxes.
Ones are important for fitting (and successful calibration).
</p>

<p>
An another method for matching can be also used by setting --match NEARLY.
In this case, the correspondence between object's list is established
by looking for nearest stars. An initial transformation
needs to be known. The parameter --sig sets coordinate uncertainty.
</p>


<h2>Fitting</h2>

<p>
The matched stars are used for fitting of a transformation
(fit of scale, rotation) and projection (fit of centre of projection).
The standard least-squares and robust methods can be used (--fit).
</p>


<h2>Reference Catalogue</h2>

<p>
The catalogue is a FITS table with coordinates of objects.
The table is usually a list of selected stars from a catalogue
provided by a Virtual Observatory server.
</p>

<p>
The coordinates are arranged to a columns (defaulted to
RA, DEC). Catalogue columns with coordinates can be selected
with --col-ra, --col-dec parameters.
</p>



<h2>See Also</h2>


<p>
Manuals:
<a href="man_astrometry.html">Astrometry</a>,
Data Formats:
<a href="dataform_astrometry.html">Astrometry Header</a>.
</p>

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