An astrometry calibration of FITS frames.
munipack astrometry [.. parameters ..] file(s)[,result(s)]
Astrometry action derives astrometry calibration of FITS frames (Overview).
Astrometry is naturally separated on two parts:
The matching process is searching for a mutual correspondece in two list of coordinates. The mathcing is generaly slow and complex process. To increase of its reliability and speed, is is important to compare (and prepare) the list by such way so that the coordinates as well as magnitues overlaps. The overlap in coodinates means to use of catalogues selection with very similar centre and radius as the frames. Also magnitude overlap must corresponds with non-saturated (and non-faint) stars on images. (If both the conditions will not meet, the matching will probbaly also sucessufll.)
There two ways how to realise. The coordinate correspondece can be make with known object position and field of view (FOV) of telescope (it means angular diameter of the cone on sky) in degress. If the telescope has FOV 0.5 deg and the observed objects is Crab nebulae than the optimal selection from UCAC4 cataloguje is:
munipack cone -r 0.2 -- 83.63 22.01
The magnitude selection is simliar. It depends on all telescope, exposure time and filter. The mathcing (as well as photometry) will sucesfull only with non-saturated bright stars. If we have an experinece that the stars are saturated at 12, than the catalogue selection can be improved (syntax is column_name=[some constrain]):
munipack cone -r 0.2 --par 'f.mag=>12' -- 83.63 22.01
Alternatively, the filtration capabailities of FITSIO can be used
munipack astrometry -c 'cone.fits[1][$f.mag$>12]' crab.fits
We are selecting only non-saturated stars fainter than magnitude 12 in column f.mag. The usual linear range of 16-bit CCD cameras is about 3-5 magnitudes.
Parameter --maxmatch slices the catalogue on parts with similar magnitudes (magnitudes in certain range). This is due to sorting of both catalpogue and frame by magnitudes.
Parameter --minmatch sets minimal length of match sequence which is supposet to by complete (sucesfull match). For sparse fileds, the defaults are usually satisfactyory, but very dense fields like SMC, LMC needs increase this parameters. Munipack sets the default of 5. If the mean surface density exceeds the limit (?), the parameter is increased. The small values on crowded fiedls can produce false match (because probability of miss-match is getting appreciable).
| Case | Solution |
|---|---|
| sparse field, < 1 m telescope | defaults |
| crowded field, < 1 m telescope | --minmatch=7, --maxmatch=44 |
| sparse field, > 1 m telescope | -c 'cone.fits[1][$f.mag$>14]' |
| crowded field, > 1 m telescope | --minmatch=7, --maxmatch=44, -c 'cone.fits[1][$f.mag$>14 .and. $f.mag$<20]' |
Lets we denote the reference star coordinates as the catalogue and coordinates of detected stars as the frame.
The following algorithm is used for matching:
Function Sequence for next star
For all unused stars in catalogue:
Compute u1,v1
For all unused stars on image:
Compute u2,v1
Is Acceptable and distance({u1,u2} and {v1,v2}) < limit?
Has the sequence required length?
Got Solution!
Call Sequence for next+1 star
Did fail the Sequence?
Skip the star
End function Sequence
Variables u1,v1 and u2,v2 are coordinates of in a triangle space
of a triplet of stars. The distance is distance in triangle space.
An alternative sequence can be constructed from known transformation and the astrometry is just more precise.
The known sequence of stars can be used to determine astrometry transformation:
The matching needs at least of tree stars (to construct of a triangle. The astrometry algorithm needs at least 5 stars (for 4 parameters) but has lower-count alternative with minimum of two stars. Generally, the astrometry has recommended minimum of 7 stars, but ideal is over 20. Any modern (like Munipack default UCAC5) catalogue has more reference objects on medium crowded fields.
The calibration needs both detected stars and instrumental photometry.
On input, list of frames containing the table with already detected stars and photometry is expected.
On output, the WCS calibration in the header of primary FITS is created (or updated) for all input images.
See Common options for input/output filenames.
| Mode | Options |
|---|---|
| match | -c, -r, -R, Parameters for Matching |
| sequence | --seq1, --seq2, -c, -r, -R |
| manual | --projection, --xcen, --ycen, --rcen, --dcen, --scale, --angle, --reflex |
For manual calibration, use --projection, --xcen, --ycen, --rcen, --dcen, --scale, --angle and don't use -c, -r, -R. The parameters are just interpreted in WCS framework and stored to FITS header.
If an astrometry calibration is already presented in processed header, one is updated.
Any distortions, including atmospheric refraction, are not implemented yet. Gnomonic projection is available only.
Virtual Observatory (VO) is intended as the main source of catalogues. The following example uses cone search capability of VO to list part of UCAC5 catalogue
munipack cone -c UCAC5 -o 0716cat.fits -r 0.1 -- 110.25 71.34
UCAC5 is the recommended astrometric catalogue (default). We must provide coordinates of centre of frame (use coordinates of assumed object) and the cone radius (else a catalogue default will be used). Note parameter -s (sort by a column). The sorting requires knowledge of catalogue structure but strongly affects speed and success rate of matching.
Manual calibration is designed with its properties:
To save a calibration to FITS header, find the parameters by hand and adjust the example
$ munipack astrometry -m manual -p GNOMONIC --rcen=110.471 --dcen=71.351
--scale=5.64e-04 --angle=0.0 0716_1R.fits
This is an example for blazar 0716+71 which observation is in FITS file 0716_1R.fits included to munipack-blazar.tar.gz.
The calibration parameters are left untouched. There are are no limits and no any checks.
| Parameter | Description | Units |
|---|---|---|
| -p | Type of spherical projection | |
| --rcen | Right Ascension of centre of the projection αc (CRVAL1)[b] | degrees |
| --dcen | Declination of centre of the projection δc (CRVAL2)[b] | degrees |
| --xcen | Reference point on a chip xc (CRPIX1)[b] | pixels |
| --ycen | Reference point on a chip yc (CRPIX2)[b] | pixels |
| --scale | Scale of projection c | degrees/pixel |
| --angle | Angle of rotation around centre φ | degrees |
| --reflex | Reflected frame | degrees |
| file | a file to calibrate[c] |
[a] The manual calibration is invoked when -m manual is presented.
[b] Twines of parameters --xcen, --ycen and --rcen, --dcen must be specified together.
[c] This manual calibration works only on a single file. Others types of calibrations on a list of files.
Astrometric calibration is designed with its properties:
Astrometry calibration requires detected stars (see find), aperture photometry (see aphot) and an astrometry catalogue (cone search).
At the start, astrometry calibration itself can be done, a star table (list) of objects on an image must be prepared.
The object detection (as a side effect is the aperture photometry) is relative straightforward (detected objects are stored to another HDU with label FIND):
$ munipack find -f 2 -t 5 0716_1R.fits $ munipack aphot 0716_1R.fits
A catalogue with reference stars can be got with help of Virtual Observatory:
$ munipack -o 0716_cat.fits -r 0.2 cone -- 110.25 71.34
Selected astrometric stars in radius 0.2° around centre α = 110.25° and δ = 71.34° are saved to the FITS table 0716_cat.fits.
Note selection of catalogue UCAC5. The objects stored to the output file are sorted by magnitude designed as 'f.mag'. You must known catalogue structure before use of -s (simply get catalogue without -s option, look for structure and than use -s with right parameter). Sorting importantly increase probability of successful matching.
In case of matching, when your are a lucky user, following command would give you the excellent job:
$ munipack astrometry -c 0716_cat.fits 0716_1R.fits
$ munipack astrometry -m SEQUENCE \
--seq1 5,6,9,16,17,18,19,21,23,22,24,26,27,29,28,30,32 \
--seq2 1,2,3,5,4,8,11,13,7,10,6,12,9,18,14,19,17 \
-c 0716_cat.fits 0716_1R.fits
| Parameter | Description |
|---|---|
| -p | Spherical projection |
| -c | Reference astrometry catalogue[‡] |
| -r | Reference already calibrated frame[‡] |
| -R | Reference frame for relative astrometry (no projection)[‡] |
| --col-ra | Label of Right Ascension column |
| --col-dec | Label of Declination column |
| --col-pm-ra | Label of proper motion of Right Ascension column |
| --col-pm-dec | Label of proper motion of Declination column |
| --minmatch | match sequence minimal length[†] |
| --maxmatch | match sequence length[†] |
| file | a file to calibrate |
[‡] Parameters -c, -r and -R are exclusive mutual.
[†] Parameters --minmatch and --maxmatch affects both speed (greater is slower) and chance of matching (lower is worse). The recommended values for --minmatch are 5 - 10 (default is 5) and --maxmatch 20 - 200 (default 33).
Matching needs at least --minmatch common stars on frame and catalogue as selected --maxmatch. When matching is failed, check all centre, radius and proper reference catalogue.
As the best diagnostics tool is the astrometry in xmunipack (Tools->Astrometry).
The matching of the reference catalogue with detected stars is extremely complicated procedure. Therefore, there are tun-able parameters for both matching and fitting algorithms. In doubts, check ones:
$ munipack astrometry --verbose 0716_006V.fits
Debug: Launching `astrometry' ...
Debug: VERBOSE = T
Debug: COL_RA = 'RAJ2000'
Debug: COL_DEC = 'DEJ2000'
Debug: COL_PMRA = 'pmRA'
Debug: COL_PMDEC = 'pmDE'
Debug: COL_MAG = 'f.mag'
Debug: CAT = 'cone.fits'
Debug: FILE = '0716_006V.fits' '0716_006V.fits~' ''
Selecting catalogue stars in rank: 1 33
Matching... #: {seq1} -> {seq2} | scale,r: sq.(angle, scale, flux) < Xi2(0.95)
Astrometry calibration of `0716_006V.fits'.
17: 5 6 9 16 17 18 19 21 23 22 24 26 27 29 28 30 32 -> 1 2 3 5 6 4 13 10 7 11 12 9 8 18 14 21 16 | 1767.5 4.53: 1.36 .669E-001 15.7 < 26.0
17: 28 29 5 6 9 16 17 18 19 21 23 22 24 26 27 30 32 -> 14 18 1 2 3 5 6 4 13 10 7 11 12 9 8 21 16 | 1767.5 4.53: .553 .710E-001 15.7 < 26.0
=== Parameters estimation ===
# estim init scale [pix/deg]: 1767.6 0.1
# estim init reflexion: 1.
# estim init angle [deg]: 0.549 0.011
# estim init offset [deg]: 0.01313 0.10040 0.00001 0.00001
=== Absolute deviations fitting ===
# ifault mad acen dcen offset[pix] s[pix/deg] rot[deg]
Debug: MuniProcess elapsed time: 00h 00m 08.945s
Debug: MuniProcess::OnFinish: 24466 0.
1 2 3.16E-05 110.50989 71.29578 24. 92. 1767.4 0.6
2 2 3.17E-05 110.46739 71.34808 0.61E-03 -0.11E-03 1767.4 0.5
3 0 3.13E-05 110.46739 71.34808 -0.90E-02 -0.11E-02 1767.6 0.5
4 0 3.13E-05 110.46740 71.34807 -0.18E-05 -0.83E-05 1767.6 0.5
5 0 3.13E-05 110.46740 71.34807 0.0 0.0 1767.6 0.5
# absfit sign test (total, positive ra,dec): 17 9 8
# absfit final: 31.32E-06 1.768E+03 0.5 110.46740 71.34807 1.0
# astrofit mad=.313E-004 deg .113 arcsec
# astrofit stars to fit: 43
=== Robust fitting ===
Likelihood solution: status=0 (evaluations=2383), log L = -819.
# info s acen dcen offset[pix] [pix/deg] rot[deg]
0 0 3.98E-05 110.46740 71.34807 0.267E-01 0.927E-02 1767.4 0.5
1 2 3.98E-05 110.46740 71.34807 0.253E-01 0.704E-02 1767.4 0.5
2 2 3.97E-05 110.46736 71.34808 -0.355E-05 -0.311E-05 1767.4 0.5
3 2 3.97E-05 110.46736 71.34808 0.00 0.00 1767.4 0.5
# Hessian at minimum:
# 36.000 0.0000 -311.66 -0.35596
# 0.0000 31.000 572.02 0.43994
# -311.66 572.02 0.10717E+07 90.344
# -0.35596 0.43994 90.344 0.29904
# Covariance matrix (no regularisation):
# 0.28150E-01 -0.56872E-03 0.57410E-05 0.32610E-01
# -0.56872E-03 0.33159E-01 -0.14053E-04 -0.45214E-01
# 0.57410E-05 -0.14053E-04 0.96456E-06 -0.26390E-03
# 0.32610E-01 -0.45214E-01 -0.26390E-03 3.5291
# Correlation matrix:
# 1.000 -0.019 0.035 0.103
# -0.019 1.000 -0.079 -0.132
# 0.035 -0.079 1.000 -0.143
# 0.103 -0.132 -0.143 1.000
# solution: 0.000E+00 0.000E+00 5.658E-04 8.862E-03 3.975E-05
# deviations: 5.65E-06 6.13E-06 3.31E-08 6.33E-05 -1.00E+00
# s0,rms: 4.42E-08 3.41E-05 [deg] .123 [arcsec]
# s: 3.97E-05 [deg] .143 [arcsec]
# sign test (total, RA+, Dec+): 43/21.5 17+-2.1 21+-2.3
....