A set of observed noisy Hubble Space Telescope Faint Object Camera poi
nt-spread functions is used to recover the combined Hubble and Faint O
bject Camera wave-front error. The low-spatial-frequency wave-front er
ror is parameterized in terms of a set of 32 annular Zernike polynomia
ls. The midlevel and higher spatial frequencies are parameterized in t
erms of set of 891 polar-Fourier polynomials. The parameterized wave-f
ront error is used to generate accurate calculated point-spread functi
ons, both pre- and post-COSTAR (corrective optics space telescope axia
l replacement), suitable for image restoration at arbitrary wavelength
s. We describe the phase-retrieval-based recovery process and the phas
e parameterization. Resultant calculated precorrection and postcorrect
ion point-spread functions are shown along with an estimate of both pr
e- and post-COSTAR spherical aberration. (C) 1997 Optical Society of A
merica.