Cosmic Origins Spectrograph Instrument Handbook for Cycle 17

13.4 Modeling of the HST PSF at the COS Aperture

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13.4.1 Optical Modeling Procedure

The HST Point Spread Function (PSF) has been modeled at the nominal position of the COS PSA. These calculated PSFs are based on the known aberrations present in the HST optical design and the surface errors present on the HST primary and secondary mirrors. The method used involved three steps:

• First, the commercial optical design program Zemax was employed to calculate the low-order optical aberrations present in the HST PSF at the PSA location, due only to the HST optical design itself.
• Next, the amount of defocus, astigmatism, coma, and spherical aberration present in the PSF were calculated for the PSA location. This was done with value for the HST primary mirror conic constant determined by Krist and Burrows (1995).
• The HST PSF modeling program Tiny Tim was used to simulate the extent of the HST PSF at the COS aperture location. Tiny Tim incorporates actual surface maps based on measurements for the HST primary and secondary mirrors and the corresponding path differences (Krist & Burrows 1995). While the HST primary and secondary mirrors are among the most precise optics ever produced, they still exhibit a number of zonal surface errors that limit the quality of the PSF, especially at ultraviolet wavelengths.
• The Tiny Tim model was adjusted to account for the position of the COS aperture relative to the nominal HST focal plane, taking into account the defocus, astigmatism, coma, and spherical aberration determined from the Zemax model. Figure 13.5 and Figure 13.6 show the Tiny Tim models of HST (PSF) at the nominal position of the COS aperture for 1450 and 2550 Å.

Summary

At least 95% of the energy in the HST PSF is contained within the 2.5 arcsec-diameter COS PSA at both 1450 and 2550 Å. Those portions of the PSF that fall outside the PSA are primarily due to the surface errors in the HST optics themselves, not to the low-order aberrations present in the HST optical design.

13.4.2 PSF Model Results

Figure 13.5 and Figure 13.6 show the aberrated HST PSF at the nominal position of the COS aperture. The COS PSA is 2.5 arcsec in diameter and these models indicate that the PSA will pass at least 95% of the total flux from a perfectly-centered point source. The surface brightness of that portion of the PSF that is outside the PSA is extremely low. Note that most of the energy in the PSF is contained within a radius of 0.5 arcsec and that essentially all of that 95% is within about 0.7 arcsec radius.

Figure 13.7 shows a one-dimensional profile of the PSF for 2550 Å, scaled to unity at aperture center.

Figure 13.5: The HST Point Spread Function at the COS PSA for 1450 Å.


 
Note that the COS apertures lie near, but not in the HST focal plane, and their location was chosen to maximize throughput. This image was calculated with Tiny Tim. The top portion is displayed with a square root scale. The energy contained within the 2.5 arcsec PSA (red circle) is at least 95% of the energy in the total HST PSF. The bottom panel shows the PSF that falls within the PSA in a two-dimensional plot on a linear scale.
 
Figure 13.6: The HST Point Spread Function at the COS PSA for 2550 Å.


 
The top panel is displayed with a square root scale, and the red circle represents the PSA diameter of 2.5 arcsec. The bottom two-dimensional plot is on a linear scale and shows the portion of the PSF that falls within the PSA. As for 1450 Å, the energy contained within the 2.5 arcsec PSA (red circle) is at least 95% of that in the total PSF.
 
Figure 13.7: Profile of the aberrated HST PSF at the COS entrance aperture for 2550 Å.