WFPC2 Instrument Handbook for Cycle 11

Model PSFs

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Considerable effort has gone into the modeling of the HST point spread function (PSF), both in order to measure the optical aberrations in support of the WFPC2, COSTAR, and advanced scientific instruments, and to provide PSFs for image deconvolution in the aberrated telescope. Such PSFs are noise free and do not require valuable HST observing time. Software to generate model PSFs for any filter and at any location within the field-of-view is available from the STScI (TIM package, Hasan and Burrows 1993; TinyTIM package, Krist 1995). The results are illustrated in Table 5.3 and Table 5.4 for the PC1 and WF2 cameras, respectively. A representative PSF is on the left in each panel. It meets the wavefront error budget, with the measured mix of focus, coma, astigmatism, and spherical aberration. It has been degraded by the pixel response function as discussed in Section CCD Pixel Response Function. On the right is the diffraction limited case for comparison. In each case the percentage of the total flux in a central 5x5 pixel region of a point source is displayed. The peak of the star image can be at an arbitrary point relative to the boundaries of the CCD pixels. Two cases are shown: one where the star is approximately centered on a pixel, and one where it is approximately centered at a pixel corner. As a consequence of the under-sampling in the WFPC2, the limiting magnitude attainable in the background limit varies by about 0.5 magnitude, depending on the position of the source within the CCD pixel. This point is discussed in more detail in Chapter 6.

Neither observed nor modeled PSFs will provide a perfect match to the PSF in actual science observations, due to modeling uncertainties, the "jitter" in the HST pointing, and orbit to orbit variations in telescope focus ("breathing"-which seems to be generally limited to about 1/20 wave peak-to-peak). Jitter is not predictable but can be recovered to a reasonable extent for observations obtained in Fine Lock. In long exposures, up to about 10 mas of apparent pointing drift may occur as a result of the breathing effects in the FGS, although smaller variations of ~3 mas are typical.

Table 5.3: PC Point Spread Functions. Shown as percentages (out of 100 percent) of the total flux in a 5 by 5 pixel region. On the left in each case is a model PSF with the observed wavefront errors and pixel response function. On the right is the diffraction limited case for comparison.

WFPC2 Model PSF						Diffraction Limited PSF
2000 å: Peak near corner of PC pixel
0.9	2.3	2.3	0.9	0.3		0.2	0.6	0.5	0.3	0.1
2.5	10.3	12.7	2.5	0.5		0.6	17.6	20.9	0.5	0.1
1.9	11.2	13.3	2.6	0.5		0.5	20.9	26.0	0.6	0.2
0.9	2.1	2.7	1.4	0.3		0.3	0.5	0.6	0.3	0.1
0.3	0.5	0.5	0.4	0.2		0.1	0.1	0.2	0.1	0.2
Peak near center of pixel
0.3	0.7	1.3	0.8	0.5		0.1	0.3	0.4	0.2	0.2
0.7	2.6	6.4	3.2	0.8		0.3	0.6	4.9	0.6	0.3
1.2	6.3	25.0	6.9	1.4		0.4	4.9	62.9	6.3	0.4
0.6	2.2	5.9	3.6	0.9		0.3	0.5	6.3	0.7	0.4
0.4	0.8	1.4	1.1	0.4		0.2	0.3	0.4	0.4	0.2
4000 å: Peak near corner of PC pixel
0.9	2.5	3.5	1.2	0.2		0.3	2.5	2.5	0.3	0.1
3.6	10.8	12.0	3.1	0.4		2.5	14.3	15.8	2.7	0.2
2.7	11.5	12.9	3.5	0.4		2.5	15.8	17.6	3.0	0.2
0.8	3.0	3.4	1.3	0.3		0.3	2.7	3.0	0.4	0.1
0.2	0.4	0.4	0.3	0.2		0.1	0.2	0.2	0.1	0.1
Peak near center of pixel
0.3	0.6	0.8	0.9	0.3		0.1	0.2	0.3	0.2	0.1
0.9	4.0	6.6	4.9	0.8		0.2	3.8	4.4	3.8	0.2
0.9	6.9	26.1	7.0	0.8		0.3	4.5	49.4	5.1	0.4
0.5	3.4	6.8	4.9	0.9		0.2	3.8	5.0	4.3	0.2
0.2	0.6	0.8	0.9	0.4		0.1	0.2	0.4	0.2	0.1
6000 å: Peak near corner of PC pixel
2.0	2.6	3.4	2.4	0.5		2.1	2.3	2.0	2.1	0.2
3.4	9.8	10.4	2.9	0.6		2.2	11.4	12.8	2.1	0.6
2.8	10.6	11.2	3.2	0.6		2.0	12.9	14.1	2.1	0.6
1.6	2.8	3.1	2.4	0.5		2.0	2.0	2.1	2.3	0.2
0.4	0.6	0.7	0.5	0.2		0.2	0.5	0.6	0.2	0.1
Peak near center of pixel
0.5	1.2	1.7	1.7	0.6		0.2	1.5	1.8	1.4	0.3
1.7	3.1	5.9	3.6	1.6		1.5	2.4	4.3	2.2	1.6
2.0	6.0	20.7	6.6	1.8		1.8	4.4	31.6	5.3	2.0
1.2	2.9	6.2	3.7	1.7		1.4	2.1	5.4	2.3	1.7
0.4	1.3	2.0	1.7	0.6		0.2	1.5	1.9	1.7	0.3
8000 å: Peak near corner of PC pixel
1.6	1.9	2.2	1.9	1.1		1.8	0.9	0.9	1.5	1.1
2.1	9.3	9.7	2.1	1.1		0.9	11.7	12.6	1.0	1.4
2.0	9.8	10.1	2.4	1.1		0.9	12.6	13.3	1.0	1.5
1.4	2.1	2.1	1.8	1.1		1.5	1.0	1.0	1.6	1.2
0.8	1.2	1.3	1.1	0.4		1.1	1.4	1.5	1.2	0.2
Peak near center of pixel
1.2	1.4	1.5	1.8	1.4		1.3	1.8	1.1	1.6	1.4
1.8	2.5	6.0	2.8	1.6		1.8	1.5	6.2	1.7	1.6
1.6	6.0	15.4	6.6	1.5		1.1	6.2	22.5	7.1	1.0
1.3	2.7	6.3	3.0	1.7		1.6	1.7	7.1	1.9	1.7
1.0	1.4	1.5	1.7	1.4		1.4	1.6	1.0	1.7	1.5

 
 

Table 5.4: WFC Point Spread Functions. Shown as percentages (out of 100 percent) of the total flux in a 5 by 5 pixel region. On the left in each case is a model PSF with the observed wavefront errors and pixel response function. On the right is the diffraction limited case for comparison.

WFPC2 Model PSF						Diffraction Limited PSF
2000 å: Peak near corner of WF pixel
0.5	1.8	2.1	0.8	0.3		0.4	0.4	0.4	0.3	0.1
1.5	9.9	13.6	3.1	0.5		0.4	15.4	21.5	0.4	0.1
1.5	9.8	24.0	4.7	0.5		0.4	21.5	33.4	0.4	0.1
0.5	2.1	3.6	1.3	0.3		0.3	0.4	0.4	0.4	0.1
0.2	0.4	0.4	0.2	0.2		0.1	0.1	0.1	0.1	0.1
Peak near center of pixel
0.2	0.4	0.5	0.5	0.3		0.2	0.2	0.2	0.1	0.2
0.3	1.7	5.3	3.0	0.8		0.1	0.8	1.3	0.6	0.1
0.5	5.4	28.5	14.0	2.2		0.2	1.3	86.2	1.4	0.2
0.3	2.2	9.1	4.5	1.0		0.1	0.6	1.4	0.9	0.2
0.3	0.6	1.2	0.8	0.3		0.2	0.1	0.2	0.2	0.2
4000 å: Peak near corner of WF pixel
0.8	2.6	2.5	0.8	0.2		0.4	0.5	0.5	0.2	0.1
2.6	16.1	16.4	3.0	0.4		0.5	17.7	21.2	0.6	0.1
2.0	12.9	17.3	3.0	0.4		0.5	21.2	26.7	0.6	0.1
0.6	2.0	2.6	0.9	0.2		0.2	0.6	0.6	0.4	0.2
0.2	0.4	0.3	0.2	0.1		0.1	0.1	0.1	0.2	0.2
Peak near center of pixel
0.3	0.6	0.7	0.5	0.3		0.3	0.2	0.3	0.2	0.2
0.6	3.1	7.2	3.4	0.7		0.2	0.7	3.7	0.7	0.2
0.9	8.5	33.3	10.2	1.2		0.3	3.7	68.8	5.3	0.4
0.4	2.5	8.8	3.0	0.6		0.2	0.7	5.3	0.8	0.2
0.2	0.5	0.9	0.5	0.3		0.2	0.2	0.4	0.2	0.3
6000 å: Peak near corner of WF pixel
0.7	2.6	2.6	0.9	0.3		0.2	0.5	0.4	0.2	0.2
3.0	14.9	15.6	3.3	0.5		0.5	18.3	20.7	0.5	0.3
2.2	13.7	16.3	3.2	0.4		0.4	20.7	24.2	0.6	0.2
0.6	2.3	2.9	0.7	0.2		0.2	0.5	0.6	0.2	0.2
0.2	0.3	0.3	0.2	0.2		0.2	0.3	0.2	0.2	0.2
Peak near center of pixel
0.3	0.7	0.9	0.6	0.2		0.2	0.3	0.2	0.3	0.2
0.7	4.1	7.8	4.1	0.8		0.3	1.8	6.1	1.9	0.3
1.0	8.6	30.4	9.4	1.3		0.2	6.1	54.9	6.2	0.3
0.5	2.8	8.2	3.5	0.6		0.3	1.9	6.2	2.5	0.3
0.2	0.5	1.0	0.6	0.3		0.2	0.3	0.3	0.3	0.2
8000 å: Peak near corner of WF pixel
1.0	3.0	2.9	1.1	0.3		0.1	2.0	2.0	0.2	0.2
3.6	13.1	13.6	4.0	0.5		2.0	15.8	17.3	2.2	0.1
2.6	12.6	14.2	3.5	0.5		2.0	17.3	19.3	2.5	0.1
0.8	3.2	3.6	1.0	0.3		0.2	2.2	2.5	0.2	0.2
0.2	0.4	0.5	0.2	0.1		0.2	0.1	0.1	0.2	0.1
Peak near center of pixel
0.2	0.8	0.8	0.7	0.3		0.1	0.2	0.3	0.2	0.1
0.9	4.6	6.9	4.4	1.0		0.2	3.5	4.6	3.4	0.2
0.9	7.5	30.8	8.1	1.2		0.3	4.6	52.0	5.0	0.3
0.5	3.1	7.3	3.7	0.7		0.1	3.4	5.1	3.9	0.2
0.2	0.5	1.0	0.7	0.2		0.1	0.2	0.3	0.2	0.1