PT Distortion Analysis
Robert Barkhouser
September 1, 1999

Zemax was used to determine the location of the chief ray at the CCD over a range of input angles from zero to half a degree (on the sky). A 3rd-order polynomial fit to the data provides a good approximation of angle on the sky vs. position on the CCD (radially from the center):

where

q
 is the angle on the sky, in arcsec
r
 is the distance from the center of the CCD, in mm
ai
 are the polynomial coefficients, given below
Wavelength (Å)
a0
a1
a2
a3
3521
9.3932·10-6
4.7721·10-2
4.0002·10-9
-6.9673·10-13
4791
9.4013·10-6
4.7737·10-2
4.0224·10-9
-6.9215·10-13
6313
9.4052·10-6
4.7746·10-2
4.0324·10-9
-6.8975·10-13
7733
9.4072·10-6
4.7750·10-2
4.0366·10-9
-6.8848·10-13
9312
9.4092·10-6
4.7754·10-2
4.0410·10-9
-6.8756·10-13

 

The "area" of a CCD pixel on the sky can then be calculated:

where

A
 is the angular "area" of a CCD pixel, in arcsec2
bi
 are the polynomial coefficients, given below
Wavelength (Å)
b0
b1
b2
3521
1.1453
1.9201·10-7
-5.0165·10-11
4791
1.1457
1.9308·10-7
-4.9835·10-11
6313
1.1459
1.9356·10-7
-4.9662·10-11
7733
1.1460
1.9376·10-7
-4.9571·10-11
9312
1.1461
1.9397·10-7
-4.9504·10-11

 

The following plots show the residual error in the polynomial fit to the Zemax data, as well as the area of a CCD pixel vs. radial distance from the center of the CCD. These plots are at 3521 Å and, for level of detail shown, are representative of all the wavelengths analyzed.



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September 11, 1999