Astrometry and Field Distorsion
!!!WARNING : The image quality of the large field mode had been modified at the end of august 2003. The optics had moved. So the estimations of the distortions that you can find here are not up to date. !!!!
SOFI has five imaging modes, mainly Large Field (LF), Small Field (SF), Large Field + Focal Elongator (FE), High Resolution (HR) and Spectroscopic Objective (SO). All modes have a very limited amount of distorsion over the entire field of view. In most cases a linear astrometric transformation will be able to provide a quite accurate astrometric calibration of the field. As an example for a linear transformation of the form:
xi = a + bx + cy ; eta = d + ex + dy
we obtained the coeficients and the rms of the fit in arcsecond given in the following table:
| b | c | e | f | rms (xi) | rms (eta) | |
|---|---|---|---|---|---|---|
| LF - J | 2.084e-4 | -0.2883 | -0.2882 | -6.946e-5 | 0.069 | 0.098 |
| LF - H | 2.314e-4 | -0.2883 | -0.2883 | -9.973e-5 | 0.069 | 0.096 |
| LF - Ks | 2.360e-4 | -0.2884 | -0.2883 | -9.788e-5 | 0.064 | 0.085 |
| SF - J | 9.288e-5 | -0.1435 | -0.1434 | 4.177e-5 | 0.092 | 0.103 |
| SF - H | 9.939e-5 | -0.1436 | -0.1436 | 5.141e-5 | 0.094 | 0.102 |
| SF - Ks | 1.396e-4 | -0.1437 | -0.1437 | 4.214e-5 | 0.095 | 0.105 |
| FE - J | 8.452e-5 | -0.1441 | -0.1442 | 5.897e-5 | 0.114 | 0.114 |
| FE - H | 1.462e-4 | -0.1442 | -0.1443 | 6.360e-5 | 0.107 | 0.109 |
| FE - Ks | 1.705e-4 | -0.1443 | -0.1443 | 8.313e-5 | 0.113 | 0.120 |
| HR -J | -8.259e-6 | -0.0720 | -0.0719 | 2.499e-4 | 0.109 | 0.092 |
| HR - H | 1.044e-4 | -0.0721 | -0.0719 | 2.602e-4 | 0.075 | 0.084 |
| HR - Ks | 1.018e-4 | -0.0722 | -0.0720 | 3.058e-4 | 0.092 | 0.076 |
| SO - J | 2.064e-4 | -0.2720 | -0.2718 | 1.233e-5 | 0.183 | 0.229 |
| SO - H | 2.281e-4 | -0.2731 | -0.2729 | -2.010e-6 | 0.169 | 0.179 |
| SO - Ks | 2.447e-4 | -0.2744 | -0.2743 | -5.642e-5 | 0.179 | 0.202 |
The coeficients a and d represent a linear shift that depends on the position and on the pointing model used. The coefficients c and e give the X and Y scale of the field. Of all the imaging modes available in SOFI the SO is the one more affected by distorsions, it is required a polynomial fit with order higher than 2 to bring the rms below 0.1 arcsec. This mode it is also affected by chromatism with a change in the scale of about 0.02 arcsec/pix from J to Ks.
To have an accurate astrometric calibration of a frame it is advisable to find the astrometric solution for that field or, if there are not enough stars, on a nearby field. We have found that the optical catalogs of stars, as for instance the USNO, are in general not good to calibrate near-infrared images. We have used succesfully the 2MASS Point Source Catalog that provides positions and near-infrared magnitudes for more than 155 milion stars over the entire sky. The typical accuracy provided by 2MASS is of the order of 0.10-0.15 arcsec that is suitable for most applications. The WCSTools sofware contains very usefull codes to handle the catalog of stars and the WCS keywords of the images, in particular the script imtmc allows quick selection of the stars in the field of an image from 2MASS Point Source Catalog. The WCS Keywords of SOFI are accurate enough to provide a good starting point.
Warning: the WCS Keyword CDELT1 and CDELT2 are set wrong in the case of the SO mode, they must be manually changed to 7.5e-5 and -7.5e-5 respectively. This will be fixed in the future.
Here you can find a second analysis of the distorsion on the large field, made by some visitor astronomers (postscript file).