Astrometrical calibration of FITS images.
Optical devices maps spherical coordinates like Right Ascension or Declination to pixels. The astrometrical calibration is an inverse operation deriving the coordinates from a captured picture of a star field. The calibration can be mathematically described as two-step procedure. Firstly, the spherical coordinates are mapped (by gnomonical or another projection) on to rectangular coordinates and than the affine transformation (rotation, shift, scaling) is applied.
A known calibration can be stored in FITS image header. When an image is correctly calibrated, the direct transformation between pixels and spherical coordinates can be established.
The set of parameters used for interaction with user is different to set of parameters used in FITS header table, where the parameters are stored. The main reason for that is use of orthogonal parameters and robust fitting. In case of direct manipulation with parameters, use FITS utilities.
The meaning of parameters:
Munipack provides calibration via astrometry module. The module offers these types of calibration:
To write a calibration to FITS header, find the parameters by hand and type
$ munipack astrometry --disable-fit --disable-match -W --proj=GNOMONIC \
--xcen=255 --ycen=170 --acen=110.471 --dcen=71.351 \
--scale=5.64e-04 --angle=0.0 -o 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.
Before fitting can be started, we need provide a catalogue with stars and detects objects on the image.
The object detection is relative easy (detected objects are saved as the last HDU):
$ munipack -f 2 -t 5 photometry 0716_1R.fits
A catalogue with reference stars can be easy with help of Virtual Observatory:
$ munipack -t fits -o 0716_cat.fits --cat=UCAC3 -s "f.mag" \
-r 0.2 cone 110.25,71.34
Note selection of catalogue UCAC3. The objects stored to the output file are sorted by magnitude designed as "f.mag". You must known catalogue structure before use (simply get catalogue without -s option, look for structure and than use -s with right parameter). Sorting importantly increase probability of successful matching.
The fitting procedure is started as
$ cp 0716_1R.fits 0716_cal.fits
$ munipack astrometry --disable-match -W --key-alpha="RAJ2000" \
--key-delta="DEJ2000" --proj=GNOMONIC --xcen=255 --ycen=170 \
--acen=110.4743 --dcen=71.3508 --scale=5.6616e-4 --angle=0 \
-c 0716_cat.fits -o 0716_cal.fits 0716_1R.fits
Note initial file copy. We are working on copy of that original to prevent data loss in case of any fail.
In case of matching, when your are a lucky user, following command would give you excellent job:
$ cp 0716_1R.fits 0716_cal.fits
$ munipack -W --proj=GNOMONIC --key-alpha="RAJ2000" --key-delta="DEJ2000" \
-c 0716_cat.fits -o 0716_cal.fits 0716_1R.fits astrometry
The reference catalog matching with a detected stars is extremely difficult problem. Some parameters can help tune matching and fitting algorithms.
In doubts, check ones:
The transformation is stored in a selected FITS keywords. The original data are not affected by the astrometry calibration.
The affine transformation (translation, rotation, scale, mirroring, etc.) uses keywords described in table.
| Key | Description |
|---|---|
| CRTYPE1 | projection type along horizontal axis |
| CRTYPE2 | projection type along vertical axis |
| CRPIX1 | horizontal coordinate (in pixels) of center of rotation |
| CRPIX2 | vertical coordinate (in pixels) of center of rotation |
| CRVAL1 | longitudinal-like world coordinate (in degrees) of CRPIX1 |
| CRVAL2 | latitudinal-like world coordinate (in degrees) of CRPIX2 |
| CD1_1 | -cos φ ⋅ c |
| CD1_2 | -sin φ ⋅ c |
| CD2_1 | -sin φ ⋅ c |
| CD2_2 | cos φ ⋅ c |
The φ is the angle of rotation about center (position angle). The c is the scale in pixels per degrees.
The possible mappings uses keywords described in table.
| Value | Projection |
|---|---|
| RA--TAN, DEC--TAN | Gnomonic |
(Yes, Just only Gnomonic is implemented).
The detailed description of FITS world coordinates is in Greisen and Calabretta: A & A, 395, 1061-1075 (2002). See also links in FITS Support Office.
Usage: munipack [-c <str>] [-t <str>] [-o <str>] [-W] [--proj <str>] [--xcen <str>] [--ycen <str>] [--acen <str>] [--dcen <str>] [--scale <str>] [--angle <str>] [--disable-fit] [--tol <str>] [--disable-match] [--nmatch <str>] [--maxmatch <str>] [--uradius <str>] [--validity <str>] [--key-alpha <str>] [--key-delta <str>] [-h] [--verbose] astrometry [file(s)...] -c:<str> reference catalog -t:<str> reference table (image) -o:<str> output FITS -W, --wcs-write write WCS to header --proj=<str> projection: identity, gnomonic(default) --xcen=<str> center pixel for rotation (half of width of image) --ycen=<str> center pixel for rotation (half of height of image) --acen=<str> center projection in Right Ascension [deg] --dcen=<str> center projection in Declination [deg] --scale=<str> scale [deg/pix] --angle=<str> position angle [deg] --disable-fit disable fitting --tol=<str> uncertainty of centroids of objects [pix] --disable-match disable inital matching --nmatch=<str> no. stars in match sequence --maxmatch=<str> no. stars for matching --uradius=<str> tol. radius in triangle space --validity=<str> acceptable validity level --key-alpha=<str> name of Right Ascension column in catalog --key-delta=<str> name of Declination column in catalog
An example of calibration included in FITS header follows (irrelevant lines are hidden).
NAXIS = 2 / number of data axes NAXIS1 = 765 / length of data axis 1 NAXIS2 = 510 / length of data axis 2 CTYPE1 = 'RA---TAN' / the coordinate type for the first axis CTYPE2 = 'DEC--TAN' / the coordinate type for the second axis CRVAL1 = 2.6944069055870182E+02 / [deg] first axis value at reference pixel CRVAL2 = 4.6930039119824798E+00 / [deg] second axis value at reference pixel CRPIX1 = 3.8250000000000000E+02 / x-coordinate of reference pixel CRPIX2 = 2.5500000000000000E+02 / y-coordinate of reference pixel CD1_1 = -3.7717763701937851E-04 / partial of first axis coordinate w.r.t. x CD1_2 = 1.4673394322043144E-05 / partial of first axis coordinate w.r.t. y CD2_1 = 1.4673394322043144E-05 / partial of second axis coordinate w.r.t. x CD2_2 = 3.7717763701937851E-04 / partial of second axis coordinate w.r.t. y COMMENT Astrometric solution: COMMENT No. of objects used = 8 COMMENT Residual sum = 0.8325448827 ["] COMMENT RMS = 0.4080551146 ["] COMMENT Scale = 1.358866619 +- 2.12E-04 ["/pix] COMMENT cos(pa) = 0.9992441307 +- 1.17E-07 COMMENT sin(pa) = 0.0388737341 +- 3.00E-06 COMMENT Position angle (pa) = 2.2278622479 +- 1.72E-04 [deg] COMMENT RA center projection (CRVAL1) = 269.4406905587 +- 8.28E-07 [deg] COMMENT Dec center projection (CRVAL2) = 4.6930039120 +- 8.59E-07 [deg] COMMENT RA,Dec [deg] centroids [pix] residuals["] COMMENT 269.46645390 4.70561220 315.840 290.982 -21.2E-03 -54.7E-03 COMMENT 269.46575330 4.60649810 307.327 28.288 162.6E-03 -390.4E-03 COMMENT 269.53804220 4.65767420 122.113 171.831 -138.4E-03 478.1E-03 COMMENT 269.47676000 4.68059670 286.103 225.963 -58.9E-03 143.2E-03 COMMENT 269.37093860 4.68203110 565.604 218.981 -259.8E-03 254.0E-03 COMMENT 269.51065610 4.69915030 198.361 278.256 231.7E-03 -288.0E-03 COMMENT 269.42034500 4.73162720 440.132 354.947 18.5E-03 -287.9E-03 COMMENT 269.36353280 4.66275830 582.924 167.138 64.4E-03 154.2E-03
The calibration can be easy understand:
Copyright © 1997-2011, F. Hroch (✉, Blog⤴), DTFA, Masaryk University.