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: http://www.stsci.edu/stsci/meetings/irw/proceedings/reddingd.dir/section3_2.html
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Ideal image formation can be modeled as the convolution of the true brightness distribution of the object with the telescope point spread function. The PSF is the spatial frequency impulse response of the telescope, which is to say, the image of an ideal point source such as a star. An approximate model of the PSF can be computed as the Fourier transform of the field in the exit pupil of the telescope. For unaberrated, unobscured telescopes, this pupil function consists of a spherical wavefront centered on the detector, with uniform intensity within the geometrically-defined circular aperture. The resulting PSF has the well-known form of the Airy pattern.
Real telescopes have PSFs that differ from the Airy pattern ideal. Optical aberrations due to misalignments, thermal gradients, outgassing, manufacturing errors and other effects change the configuration of the optics, causing the phase of the wavefront propagated through the telescope to deviate from a perfect sphere. This results in decreased amplitude and increased width of the PSF, causing blurring of the image and decreasing the sensitivity of the instrument. Vignetting or shadowing incurred at stops, spatial filters, and obscurations such as mirror support pads, spiders and secondary mirrors, further decreases the PSF amplitude and can alter the halo of the PSF, adding diffraction rings and tendrils. These effects are very apparent in images taken with the first set of HST instruments. They are also present, albeit at much lower levels, in images taken with the refurbished HST cameras.
For most telescopes, wavefront phase and vignetting effects vary as a function of field angle (or focus setting). These induced aberrations cause the PSF to vary both in structure and amplitude from point to point over the detector. Again, HST images show the effects of strong spatial variance of the PSF. Detector characteristics are also significant. These include pixel size as well as non-ideal behaviors such as spatially-variable quantum efficiency or pixel cross-talk. Other effects, such as high-frequency telescope jitter or atmospheric turbulence, can cause smearing of the PSF.
Image restoration can compensate for telescope aberrations, induced aberrations and detector effects by deconvolving a ``known'' PSF from the image data. Known jitter and turbulence effects can be compensated similarly. The variation of the PSF over the field can be handled by using multiple PSFs, each valid within a sub-region of the detector. The result of restoration using accurate PSFs is a recovered image whose accuracy is limited only by the noise content of the original image. These noise effects can be reduced by taking several images of the same source and averaging.
The success of image restoration depends critically on the accuracy of the known PSF. Our objective is to provide good predicted PSFs for restoration of HST images. To do this the PSF generation code should account for the effects of: