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13 November 2014 Cramer-Rao analysis of three-channel phase diverse wave-front sensing for Golay3 aperture
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The phase diversity wavefront sensing (PDWFS) technique is an a posteriori image-based wavefront sensing technique which has been successfully implemented to the Hubble Space Telescope. The analytical form for the phase diversity Cramér-Rao lower bound(CRLB) of Golay3 aperture is firstly derived. Monte Carlo analysis of the PDWFS CRLB is used due to the dependence of CRLB on the true values of aberration parameters being estimated. Then the ensemble average of mean-squared errors(MSE) quantities of CRLB is used to evaluate the performance of imaging schemes with different photon distributions and different amounts of defocus. The numerical simulation shows that for a point source target, if a third image implies the inclusion of extra photons, the MSE would be reduced to a degree in accordance with the amount of the extra photons, the MSE remains nearly unchanged if the totoal photons is finite, no matter for a two-channel or a three-channel system. We also find that varying the defocus of one image becomes meaningless if the defocus of the other image is at a high level.
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Junliu Fan, Quanying Wu, Jun Wang, and Xunwu Li "Cramer-Rao analysis of three-channel phase diverse wave-front sensing for Golay3 aperture", Proc. SPIE 9276, Optical Metrology and Inspection for Industrial Applications III, 92761S (13 November 2014);

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