# Astrometry Overview

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.

Usage of a command line astrometry tool can be found in Astrometry manual page.

## Introduction

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:

- spherical coordinates are projected (by gnomonic or another projection) on to auxiliary rectangular coordinates,
- and affine mapping (including rotation, shift, scaling and reflection) is applied to get the mutual transformation between the auxiliary projected and current on-chip coordinates.

The calibration can be stored in FITS frame header as WCS (world-coordinate system) calibration which is described at reference Astrometry header page.

Panel with the coordinate indicator

## How To Describe Of Astrometry Mapping

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.

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

All angles are in degrees. Also don't try use fractions like arcsecs or don't interchange degrees and radians.

## Modes Of Astrometry Calibration

Munipack provides following modes of the calibration of FITS frames:

### Match

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.

### Sequence

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.

### Manual

Manual mode just save a calibration in WCS conventions using of parameters αc, δc, c, φ 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.

## Sources Of Reference Stars

These sources can be used as a references of the coordinates.

Catalogue
  Stars selected from an astrometric catalogue are used as the reference.
Reference frame
  Stars detected on already calibrated frame are used as the reference.
Relative frame
  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.

Note that the types of calibrations using catalogues and frames requires detected objects (see aperture photometry).

## Projection

Projection maps spherical coordinates and rectangular coordinates. Just only Gnomonic is implemented yet.

No projection is useful for relative matching of frames.

## Matching

Matching between objects on reference (catalogue) and calibrated frames is developed on base of a kind of backtracking 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).

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).

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.

## Fitting

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).

## Reference Catalogue

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.

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

## See Also

Manuals: Astrometry, Data Formats: Astrometry Header.