Sparse matrix approximation method for an active optical control system.

We develop a sparse matrix approximation method to decompose a wave front into a basis set of actuator influence functions for an active optical system consisting of a deformable mirror and a segmented primary mirror. The wave front used is constructed by Zernike polynomials to simulate the output of a phase-retrieval algorithm. Results of a Monte Carlo simulation of the optical control loop are compared with the standard, nonsparse approach in terms of accuracy and precision, as well as computational speed and memory. The sparse matrix approximation method can yield more than a 50-fold increase in the speed and a 20-fold reduction in matrix size and a commensurate decrease in required memory, with less than 10% degradation in solution accuracy. Our method is also shown to be better than when elements are selected for the sparse matrix on a magnitude basis alone. We show that the method developed is a viable alternative to use of the full control matrix in a phase-retrieval-based active optical control system.

Hubble Space Telescope Faint Object Camera calculated point-spread functions.

A set of observed noisy Hubble Space Telescope Faint Object Camera point-spread functions is used to recover the combined Hubble and Faint Object Camera wave-front error. The low-spatial-frequency wave-front error is parameterized in terms of a set of 32 annular Zernike polynomials. The midlevel and higher spatial frequencies are parameterized in terms of set of 891 polar-Fourier polynomials. The parameterized wave-front error is used to generate accurate calculated point-spread functions, both pre- and post-COSTAR (corrective optics space telescope axial replacement), suitable for image restoration at arbitrary wavelengths. We describe the phase-retrieval-based recovery process and the phase parameterization. Resultant calculated precorrection and postcorrection point-spread functions are shown along with an estimate of both pre- and post-COSTAR spherical aberration.

Maximum entropy restoration of blurred and oversaturated Hubble Space Telescope imagery.

A brief introduction to image reconstruction is made and the basic concepts of the maximum entropy method are outlined. A statistical inference algorithm based on this method is presented. The algorithm is tested on simulated data and applied to real data. The latter is from a 1024 × 1024 Hubble Space Telescope image of the binary stellar system R Aquarii, which suffers from both spherical aberration and detector saturation. Under these constraints the maximum entropy method produces an image that agrees closely with observed results. The calculations were performed on the MasPar MP-1 single-instruction/multiple-data computer.