The point spread function (PSF) has been determined using the Telecope and
Image Modelling (TIM) software (Hasan and Burrows 1994) with mirror wavefront
errors (excluding spherical aberration) as measured pre-launch and a wavefront error at 632.8 nm for the rest of the optics (secondary mirror
residual misalignment, COSTAR and FOC/FOS/HRS or WFPC II internal wavefront
errors). For the FOS an astigmatism term has been included to account for the
off-axis position of the instrument. The PSF has been finely sampled on 5
milliarcseconds pixels. Although the simulations have been performed for
WFPC II and FOS, the results are expected to apply to the FOC and GHRS,
respectively.
The results are shown in Figs. 1 to 7. The variation of Strehl ratio with
focus for eight wavelengths varying from 125 nm to 700 nm for the cameras is
plotted in Fig. 1. For the same wavelength set, variation with focus of
ensquared energies within 0.250.25 arcsec and 1
1 arcsec
apertures is plotted in Figs. 2 and 3, respectively.
Fig. 4 gives the tolerable focus error for the cameras as a function of wavelength (using the 20%Strehl ratio degradation criterion), and Fig. 5 the tolerable focus error for the spectrographs. In the case of the spectrographs, the small aperture criterion is the only driver, the 1%degradation for the large aperture always being met even for very large focus errors.
For the cameras we have also studied the effect of focus change on the
radius containing 80%of the energy as well as on the sharpness
criterion defined as
where is the intensity at pixel
. These are plotted in
Figs. 6 and 7, respectively. Note that in Fig. 6 the best focus shifts
for the 300 nm and 400 nm wavelengths. This is the result of mirror
figure errors and the additional
(at 632 nm) aberration
added to the system.
As expected, the most stringent focus requirement is set by the cameras. For
them, the focus should not change by more than 2 microns when working in
the far UV, and by not more than
5 microns in the blue. In terms of the
radius encircling
of the energy, these tolerances roughly correspond to
a radius increase of about 10%, while the sharpness criterion indicates an
increase in exposure time from
4%in the red to
35%in the UV.
The effect of focus changes on throughput in the large aperture in the
spectrographs is barely noticeable, while the small apertures will tolerate a
focus variation of about
microns without showing a degradation of
throughput
%.
It should be emphasized that these tolerances apply only to the variation of focus as seen by the instrument, and not to the pointing errors resulting from Fine Guidance Sensor (FGS) sensitivity to focus changes. The pointing error appears to be of order 20 mas, and may be more detrimental to science than the focus change itself, if left uncorrected. This pushes for establishing a deterministic model of the FGS pointing error in order to correct it via the Pointing Control System (PCS) (similar to the way corrections are done for velocity aberration or for moving targets).