Statistics – Computation
Scientific paper
Aug 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phdt.........7l&link_type=abstract
Thesis (PHD). AIR FORCE INSTITUTE OF TECHNOLOGY , Source DAI-B 58/02, p. 781, Aug 1997, 152 pages.
Statistics
Computation
Scientific paper
Due to mechanical aspects of fabrication, launch, and operational environment, space telescope optics can suffer from unforeseen aberrations, detracting from their intended diffraction-limited performance goals. This dissertation gives the results of simulation and theoretical studies designed to explore how wavefront aberration information for such 'nearly diffraction-limited' telescopes can be estimated via the Gonsalves (least-squares) phase diversity technique. Simulation studies utilized numerically simulated imaging models of both monolithic and segmented space telescope mirrors. The segmented case is a simplified model of the proposed Next Generation Space Telescope (NGST). The Monte-Carlo simulation results quantify the accuracy of phase diversity as a wavefront sensing (WFS) technique in estimating the pupil phase map. Simulation results give an indication of the minimum light level required for reliable estimation of a large number of aberration parameters under the least-squares paradigm. For weak aberrations averaging 0.10λ RMS, the average WFS estimation errors obtained here range from a worst case 0.057λ RMS to a best case of only 0.002λ RMS, depending upon the light level as well as the types and degrees-of-freedom of the aberration present. These studies are unique in their incorporation of photon statistical considerations. Theoretical investigation of space telescope phase diversity imaging consisted of Cramer-Rao lower bound analysis. The CRLB expressions given here provide a novel computational tool for assessing the merits of particular phase diversity imaging configurations. One key result of such an analysis is the proposal that phase diversity WFS estimation might, under certain conditions, be carried out using symmetrically defocused images, as in the curvature sensing technique. In the test cases demonstrated here, such a symmetrically defocused configuration resulted in smaller minimum mean-squared estimation errors. Phase diversity was also applied to the estimation of fixed optical aberrations in an operational adaptive optics system. Nineteen Zernike modes of an aberration that was present in the image path of an operational adaptive optics system were successfully estimated.
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