NIRC Field Distortion

Any optical system has distortion. An evenly distributed grid of positions on the sky will not translate to an evenly spaced grid of positions on the detector. For many types of science the distortion will be small enough that it can be ignored. For other types of science it may be desirable to account for the distortion. With the latter in mind we have attempted to measure the distortion in normal NIRC images.

Technique

NIRC imaged the field of NGC 5634, a globular cluster which has been measured by George Gatewood of Allegheny Observatory, using the MAP astrometric instrument. Dr. Gatewood kindly provided R.A. and Dec. values for a number of stars. Many other stars were included in the fields imaged, and these provided further positions which can be used.

A field center within the cluster was chosen and imaged at the NIRC field center and near its four corners. (x,y) positions were measured in each frame. A least squares fitting routine was then used to fit a distortion map in the form of a second order, 2-D polynomial to the mapping of (RA, Dec) to (x,y) on the detector.

The fit was of the form:

X = x - 128, Y = y - 128

RA = c0 + c1 * X + c2 * Y + c3 * X^2 + c4 * Y^2 + c5 * XY
Dec = d0 + d1 * X +d2 * Y + d3 * X^2 + d4 * Y^2 + d5 * XY

In a distortion-free system oriented at angle theta, c3=c4=c5=d3=d4=d5=0, (c0,d0) would be the position of the field center, c1=d2=S*cos(theta), and c2=-d1=S*sin(theta), where S is the scale in arcsec/pixel. From observations of astrometric binaries the mean scale of NIRC is known to be 0.150 arcsec/pixel, and this serves as a comparison point.

The actual fitting required (RA,Dec) values of the stars without previously known astrometric positions to be fit with their (RA,Dec) positions as free parameters. Because each star was observed in at least two or more positions within the field, this still allows these stars to contribute to the determination of the distortion map.

Once the coefficients were determined from the fit, they were rotated to remove the uninteresting sky p.a. at which they were observed, in order to give a true picture of the optical distortion.

Results

The distortion map is shown below as a difference between the measured transformation and a linear transformation that assumes a constant 0.150 arcsec/pixel everywhere.

The longest vectors in the plot (near the corners of the frame) are 0.12 arcsec, or 0.8 pixels in length.

The coefficients (except for c0 and d0, which simply represent the field centers) measured in the 2-D polynomial fit were:

c1 0.1500 d1 0
c2 0 d2 0.1500
c3 -3.36e-6 d3 -3.95e-6
c4 4.04e-6 d4 3.41e-6
c5 4.72e-6 d5 -4.76e-6

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