WFPC2 Instrument Handbook for Cycle 10

PSF Variations with Field Position

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The WFPC2 PSFs vary with field position due to field-dependent aberrations, obscuration shifting, and scattering. This will complicate photometry, PSF subtraction, and deconvolution (Krist, 1995).

The coma and astigmatism aberrations vary significantly within a camera across the field-of-view. These variations are simply part of the optical design. At the extreme corners of the WFC CCDs, away from the OTA axis, there is about 1/5 wave of astigmatism (referenced at 633 nm), which decreases to nearly zero at the CCD centers. Astigmatism at this level causes the PSF core to become elliptical and slightly less sharp; note flattening of PSF at pixels positions (54,777) and (605,148) in Figure 5.5. Coma also varies, but to a much lesser extent. Coma and astigmatism variations are considerably smaller in PC1 (though we note the astigmatism at the center of PC1 is fairly significant - see Table 5.2).

Figure 5.5: PSF Variations with Field Position - Aberrations. Nine observed PSFs (filter F814W) are shown from a widely spaced grid on WF3. CCD pixel position are labeled. Note flattening of PSF in the (54,777) and (605,148) positions.
 

The obscuration patterns due to the camera optics (relay secondary mirror and spiders) appear to shift with respect to the OTA obscurations, depending on field position. The interacting diffraction patterns of the WFPC2 and OTA spiders cause ripples in the spider diffraction spikes, which vary with field position as the two spiders shift relative to each other. In Figure 5.6 the OTA spider is hidden behind the WFPC2 spider at the field center and hence the diffraction spikes there have a simple, smooth appearance (c.f. position 446,425). At the CCD corners, however, one or more vanes of the OTA spider moves out from behind the WFPC2 spider, and the double set of obscurations causes a "beating" pattern in the diffraction spikes.

The spiders also interact with light diffracted from zonal errors in the OTA mirrors, causing streaks in the scattering halo which vary in position and intensity.

Figure 5.6: PSF Variations with Field Position - Obscuration Shifts. Five saturated PSFs observed in F814W are shown from a widely spaced grid on WF4. Note changes in spider diffraction spikes. CCD pixel positions are labeled.
 

Aperture Corrections vs. Field Position

The amount of energy encircled by an aperture used for stellar photometry will depend on both the aperture size, and also on any variations in the PSF with field position, time, etc. In general, larger apertures will provide more stable results in the presence of PSF variations. However, large apertures will also exacerbate many problems: contamination from residual cosmic rays, scattered light from nearby stars, and the lower signal-to-noise (S/N) that typically results.

Gonzaga et al. (1999) have measured aperture corrections and characterized their change as a function of field position and filter. The differences in photometric magnitude between apertures with various radii (i.e. aperture corrections), and their mean and standard deviations for the F555W filter, are presented in Table 5.5. For example, the first row of the table indicates that stars measured with a 1 pixel radius aperture will be about 0.887 magnitude fainter than if a 5 pixel radius aperture were used (averaged over entire PC CCD), and this difference will vary by about 0.054 magnitudes RMS across the CCD.

Variations in the PSF with field position will, of course, cause a position dependence in the aperture corrections. Figure 5.7 illustrates how the aperture correction varies with distance from the CCD center, R, for different pairs of aperture sizes. The scatter in the plots is due to contamination from residual cosmic rays and nearby faint stars within the larger aperture. While the data are somewhat incomplete, a clear trend is present: the aperture correction generally increases linearly as a function of distance from the CCD center. For example, the aperture correction between 1 to 5 pixel radius is about 0.82 magnitudes at the PC center, and increases to about 0.94 magnitude at the far corners of the CCD. (The average correction is about 0.89 magnitude, as given in the first line of Table 5.5.) The other WFPC2 CCD chips show results similar to the PC chip.

Table 5.5: Magnitude differences produced by different aperture sizes. Results given for PC, WF2, WF3, and WF4 in F555W.

Chip	Filter	Aperture Radii (pixels)	Number of Stars	Mean Magnitude Difference1	RMS of Magnitude Difference2
PC	F555W	1 vs. 5	116	0.887	0.054
PC	F555W	2 vs. 5	115	0.275	0.028
PC	F555W	2 vs. 10	115	0.401	0.075
PC	F555W	5 vs. 10	115	0.106	0.055
WF2	F555W	1 vs. 5	558	0.608	0.130
WF2	F555W	2 vs. 5	558	0.160	0.085
WF2	F555W	2 vs. 10	544	0.310	0.257
WF2	F555W	5 vs. 10	548	0.133	0.204
WF3	F555W	1 vs. 5	660	0.680	0.133
WF3	F555W	2 vs. 5	656	0.188	0.076
WF3	F555W	2 vs. 10	649	0.376	0.308
WF3	F555W	5 vs. 10	647	0.154	0.233
WF4	F555W	1 vs. 5	828	0.672	0.129
WF4	F555W	2 vs. 5	831	0.198	0.115
WF4	F555W	2 vs. 10	815	0.386	0.350
WF4	F555W	5 vs. 10	814	0.160	0.252

1 Magnitude difference averaged around CCD. 2 RMS magnitude difference around CCD.

In practice, the aperture correction also depends on defocus. The interplay between aperture correction and defocus may be complex, since the optimal focus changes with field position. A full correction has not been established, but the TinyTim PSF model (see next Section) can be used to estimate the extent of the variation in aperture correction. In general, we recommend that a minimum aperture radius of 2 pixels be used whenever possible, in order to reduce the impact of variations of the aperture correction with focus and field position. If the field is too crowded and a smaller aperture is needed, we recommend that users verify the validity of the corrections on a few well-exposed stars.

The following section includes a discussion of aperture corrections as a function of OTA focus.

Figure 5.7: Aperture correction (delta) between two given apertures within the PC chip versus radial distance of the target from the center of the chip. Open symbols indicate spurious data.