A detailed description of a form used by Munipack to store astrometry calibration in FITS header.
All parameters describing the precious astrometry calibration are presented in a table that follows. For parameters description, see Astrometry Overview.
The background description of representation of spherical coordinates in FITS is defined in the article Greisen and Calabretta: A & A, 395, 1061-1075 (2002). See also links in FITS Support Office.
Note, that the set of parameters used by Munipack is different to set of ones in standard FITS header. For direct manipulation with standard WCS keywords, FITS utilities can be used.
|CTYPE1||projection type along horizontal axis[a]|
|CTYPE2||projection type along vertical axis[a]|
|CRPIX1||xc||horizontal coordinate of reference pixel[b]||pix|
|CRPIX2||yc||vertical coordinate of reference pixel[b]||pix|
|CRVAL1||αc||longitude-like spherical coordinate related to CRPIX1||deg|
|CRVAL2||δc||latitude-like spherical coordinate related to CRPIX2||deg|
|CD1_1||- c ⋅ cos φ||element of matrix of rotation[c]||deg/pix|
|CD1_2||- c ⋅ sin φ||element of matrix of rotation[c]||deg/pix|
|CD2_1||- c ⋅ sin φ||element of matrix of rotation[c]||deg/pix|
|CD2_2||c ⋅ cos φ||element of matrix of rotation[c]||deg/pix|
|CRDER1||typical uncertainty in horizontal direction[d]||deg|
|CRDER2||typical uncertainty in vertical direction[d]||deg|
|CRUNIT1||units of spherical coordinates[e]|
|CRUNIT2||units of spherical coordinates[e]|
[a] The projection type is the same for both axis. Currently only Gnomonic projection (coded as RA---TAN, DEC--TAN) is implemented.
[b] Reference pixel is located at centre of an image (the origin around which the image is rotated). The centre is by default determined from image sizes: CRPIX1 = NAXIS1 / 2 (widht / 2), CRPIX2 = NAXIS2 /2 (height / 2).
[c] φ is an angle of rotation about the reference point (centre). One is an analogy to the position angle (PA), but the PA has origin on twelve and also the opposite direction. c is the image scale in degrees per pixel.
[d] RMS (root mean square) is used for both directions.
[e] Degrees are always used.
Munipack adds related comments to the header which includes some additional information describing astrometry calibration in detail.
Astrometry comments are included within the "bracket" lines:
=== Astrometry Solution by Munipack === .. .. === End of Astrometry Solution by Munipack ===
The form is designed for simple machine recognition and removing.
The items are parts of the comments:
An example of calibration included in FITS header follows (with removed irrelevant lines).
NAXIS = 2 / number of axes NAXIS1 = 768 / length of data axis NAXIS2 = 512 / length of data axis CTYPE1 = 'RA---TAN' / the coordinate type for the first axis CTYPE2 = 'DEC--TAN' / the coordinate type for the second axis CRVAL1 = 3.3069918316990805E+02 / [deg] first axis value at reference pixel CRVAL2 = 4.2273184170171220E+01 / [deg] second axis value at reference pixel CRDER1 = 3.96E-05 / [deg] random error in first axis CRDER2 = 3.97E-05 / [deg] random error in second axis CUNIT1 = 'deg ' / units of first axis CUNIT2 = 'deg ' / units of second axis CRPIX1 = 3.8400000000000000E+02 / x-coordinate of reference pixel CRPIX2 = 2.5600000000000000E+02 / y-coordinate of reference pixel CD1_1 = -1.8251021731683297E-04 / partial of first axis coordinate w.r.t. x CD1_2 = 2.1990049474366615E-06 / partial of first axis coordinate w.r.t. y CD2_1 = 2.1990049474366615E-06 / partial of second axis coordinate w.r.t. x CD2_2 = 1.8251021731683297E-04 / partial of second axis coordinate w.r.t. y COMMENT === Astrometry Solution by Munipack === COMMENT Type: absolute COMMENT Reference catalogue: UCAC5 Catalogue (Zacharias+, 2017) COMMENT Projection: GNOMONIC COMMENT Objects used = 44 COMMENT RMS = 142.3699873 [mas] COMMENT Scale = 657.0844718 +- 2.0E-02 [mas/pix] COMMENT cos(pa) = 0.9999274227 +- 2.1E-06 COMMENT sin(pa) = 0.0120477932 +- 1.7E-04 COMMENT Position Angle (pa) = 0.6903044013 +- 9.9E-03 [deg] COMMENT Reflexion = F COMMENT Alpha center projection (CRVAL1) = 330.6991831699 +- 2.5E-06 [deg] COMMENT Delta center projection (CRVAL2) = 42.2731841702 +- 3.9E-06 [deg] COMMENT Horizontal center (CRPIX1) = 384.000 [pix] COMMENT Vertical center (CRPIX2) = 256.000 [pix] COMMENT Catalogue RA,DEC [deg] Data X,Y [pix] Residuals [mas] COMMENT 330.68963830 42.26674250 422.700 220.245 -282.0E+00 878.9E-03 COMMENT 330.68923240 42.27652500 424.821 273.784 -174.0E+00 22.5E+00 COMMENT 330.67244740 42.31684500 494.557 493.933 412.9E+00 -20.5E+00 ... COMMENT 330.61571920 42.30084060 724.180 403.675 -108.1E+00 -47.7E+00 COMMENT 330.61550500 42.24693730 721.816 108.630 -131.7E+00 -224.3E+00 COMMENT 330.78309090 42.26153810 42.777 196.604 169.4E+00 -91.0E+00 COMMENT 330.68781030 42.24563480 428.254 104.291 32.5E+00 151.8E+00 COMMENT 330.78027980 42.29270640 56.484 366.877 110.6E+00 124.0E+00 COMMENT 330.63015890 42.26125810 663.472 187.155 -264.1E+00 165.2E+00 COMMENT 330.68914300 42.23852450 422.511 65.362 -50.4E+00 178.9E+00 COMMENT Munipack 0.5.4, (C) 1997-2013 F.Hroch (email@example.com), COMMENT http://munipack.physics.muni.cz, Masaryk University, Brno, CZ. COMMENT === End of Astrometry Solution by Munipack ===
In this example, the calibration can be easy interpreted as:
Astrometry Manual, Astrometry Overview