[AstroPy] Distortion coefficients - FITS Header of an image

Thu Sep 1 05:20:37 EDT 2016

Hello,

With a telescope, I took sky images in tracking ON. These images were saved in FITS format.
With MaximDL and PinPoint Atsrometry softwares, we can get the FITS Header of each image, i.e. image data (for instance Observation site, CCD camera, focal length, pixels, right ascension of the image center, declination of the image center, etc). I put an example for you (see below at the end of the message).

What I would like to find is a way to take into account distortion coefficients of an image (we can find them in the FITS Header of the image, see below), in order to convert any pixels of the image into world coordinates, and vice versa.
I am working with Python.

I have found with Astropy some useful functions, like w.wcs_world2pix to convert world coordinates into pixel coordinates. But would you know which distortion coefficients are taken into account in such a function ? The TRi_j distortion coefficients are they taken into account ? Because I could not find any information on them. I have found only papers like the following ones which are on A, B, AP, AB coefficients but not on TR coefficients :

http://docs.astropy.org/en/stable/api/astropy.wcs.Sip.html#astropy.wcs.Sip
http://irsa.ipac.caltech.edu/data/SPITZER/docs/files/spitzer/shupeADASS.pdf

Thank you in advance for your help.

Best regards

Alice

Example of the FITS Header of an image :

SIMPLE = T 
BITPIX = 16 /8 unsigned int, 16 & 32 int, -32 & -64 real 
NAXIS = 2 /number of axes 
NAXIS1 = 2184 /fastest changing axis 
NAXIS2 = 1472 /next to fastest changing axis 
BSCALE = 1.0000000000000000 /physical = BZERO + BSCALE*array_value 
BZERO = 0.00000000000000000 /physical = BZERO + BSCALE*array_value 
DATE-OBS = '2016-08-03T21:53:34' / [ISO 8601] UTC date/time of exposure start 

EXPTIME = 4.00000000000E+000 / [sec] Duration of exposure 
EXPOSURE = 4.00000000000E+000 / [sec] Duration of exposure 
SET-TEMP = -30.000000000000000 /CCD temperature setpoint in C 
CCD-TEMP = -29.968750000000000 /CCD temperature at start of exposure in C 
XPIXSZ = 6.7999999999999998 /Pixel Width in microns (after binning) 
YPIXSZ = 6.7999999999999998 /Pixel Height in microns (after binning) 

XBINNING = 1 / Binning level along the X-axis 
YBINNING = 1 / Binning level along the Y-axis 
XORGSUBF = 0 /Subframe X position in binned pixels 
YORGSUBF = 0 /Subframe Y position in binned pixels 
READOUTM = 'Raw ' / Readout mode of image 
IMAGETYP = 'Light Frame' / Type of image 
FOCALLEN = 1153.0000000000000 /Focal length of telescope in mm 
APTDIA = 254.00000000000000 /Aperture diameter of telescope in mm 
APTAREA = 50670.749319791794 /Aperture area of telescope in mm^2 
EGAIN = 0.80000001192092896 /Electronic gain in e-/ADU 
SBSTDVER = 'SBFITSEXT Version 1.0' /Version of SBFITSEXT standard in effect 
SWCREATE = 'MaxIm DL Version 6.08 160505 1A3Q6' /Name of software 
SWSERIAL = '1A3Q6-HWHSQ-A0990-J2QRF-SUTCT-QC' /Software serial number 

OBJCTRA = '21 28 50.00' / [hms J2000] Target right ascension 
OBJCTDEC = '-06 44 12.0' / [dms +N J2000] Target declination 
OBJCTALT = ' 30.8774' / Nominal altitude of center of image 
OBJCTAZ = '139.4337' / Nominal azimuth of center of image 
OBJCTHA = ' -2.2794' / Nominal hour angle of center of image 
SITELAT = '43 45 11' / Latitude of the imaging location 
SITELONG = '06 55 18' / Longitude of the imaging location 
JD = 2457604.4121990739 /Julian Date at start of exposure 
JD-HELIO = 2457604.4179293886 /Heliocentric Julian Date at exposure midpoint 

AIRMASS = 1.94149884803E+000 / Airmass (multiple of zenithal airmass) 
OBJECT = ' ' / Target object name 
TELESCOP = ' ' / Telescope name 
INSTRUME = 'SBIG STT-3200 3 CCD Camera' / Detector instrument name 

OBSERVER = ' ' / Observer name 
NOTES = ' ' 
FLIPSTAT = ' ' 
SWOWNER = 'THALES ALENIA SPACE FRANCE' /Licensed owner of software 
INPUTFMT = 'FITS ' / Format of file from which image was read 

HISTORY File was processed by PinPoint 6.0.6 at 2016-08-08T11:19:06 
DATE = '03/08/16' / [old format] UTC date of exposure start 
TIME-OBS = '21:53:34' / [old format] UTC time of exposure start 
UT = '21:53:34' / [old format] UTC time of exposure start 
TIMESYS = 'UTC ' / Default time system 
RADECSYS = 'FK5 ' / Equatorial coordinate system 
RA = '21 28 50.00' / [hms J2000] Target right ascension 
DEC = '-06 44 12.0' / [dms +N J2000] Target declination 
FWHM = 3.31912333965E+000 / [pixels] Mean Full-Width-Half-Max of image star
ZMAG = 2.22695229625E+001 / Mag zero point for 1 sec exposure 
EQUINOX = 2000.0 / Equatorial coordinates are J2000 
EPOCH = 2000.0 / (incorrect but needed by old programs) 
PA = 3.58967846401E+002 / [deg, 0-360 CCW] Position angle of plate 
CTYPE1 = 'RA---TAN' / X-axis coordinate type 
CRVAL1 = 3.22235640938E+002 / X-axis coordinate value 
CRPIX1 = 1.09200000000E+003 / X-axis reference pixel 
CDELT1 = -3.37671457816E-004 / [deg/pixel] X-axis plate scale 
CROTA1 = 1.03215359918E+000 / [deg] Roll angle wrt X-axis 
CTYPE2 = 'DEC--TAN' / Y-axis coordinate type 
CRVAL2 = -6.73039453583E+000 / Y-axis coordinate value 
CRPIX2 = 7.36000000000E+002 / Y-axis reference pixel 
CDELT2 = -3.38006539857E-004 / [deg/pixel] Y-Axis Plate scale 
CROTA2 = 1.03215359918E+000 / [deg] Roll angle wrt Y-axis 
CD1_1 = -3.37616668483E-004 / Change in RA---TAN along X-Axis 
CD1_2 = 6.08868227955E-006 / Change in RA---TAN along Y-Axis 
CD2_1 = -6.08264627773E-006 / Change in DEC--TAN along X-Axis 
CD2_2 = -3.37951696156E-004 / Change in DEC--TAN along Y-Axis 
TR1_0 = 1.09199958073E+003 / [private] X-axis distortion coefficients 
TR1_1 = 2.18399991151E+003 
TR1_2 = -6.18827693341E-001 
TR1_3 = -1.23992354888E+000 
TR1_4 = -1.21460280616E+000 
TR1_5 = -1.17006143126E+000 
TR1_6 = -2.36278669552E+001 
TR1_7 = 8.13968772630E-001 
TR1_8 = -1.05987616323E+001 
TR1_9 = -2.51664136543E+000 
TR1_10 = 7.75126811018E+000 
TR1_11 = 1.11725347231E+000 
TR1_12 = -1.15863502104E+000 
TR1_13 = 2.78034135924E+000 
TR1_14 = 5.04818239812E+000 
TR2_0 = 7.36000000896E+002 / [private] Y-axis distortion coefficients 
TR2_1 = -1.38948258924E-003 
TR2_2 = 1.47200000121E+003 
TR2_3 = -1.74854087048E+000 
TR2_4 = 3.06867323249E-001 
TR2_5 = -2.74476247742E+000 
TR2_6 = -2.95895994527E-001 
TR2_7 = -1.76582177998E+001 
TR2_8 = 2.41056596524E-001 
TR2_9 = -1.34421356097E+001 
TR2_10 = 6.81670566601E+000 
TR2_11 = -2.72087350085E+000 
TR2_12 = -2.86227884736E+000 
TR2_13 = 7.12777456134E+000 
TR2_14 = 1.02502948504E+001 
HISTORY WCS added by PinPoint 6.0.6 at 2016-08-08T11:19:06 
HISTORY Matched 142 stars from the Gray GSC-ACT Catalog 
HISTORY Average residual was 0.42 arc-seconds 
PLTSOLVD = T / Plate has been solved by PinPoint 
HISTORY Image data was modified, written back to file. 

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