22 October 2004 Use of adaptive optics to implement nonquadratic phase diversity imaging
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Phase diversity imaging is an established technique for deriving optical phase information from measurements of intensity. Knowledge of the optical phase can then be used to provide real time feedback control to adaptive optics or to perform post-detection image restoration. The work presented in this paper concerns the use of phase diversity to improve image restoration for aberrated optical systems. All previous implementations of phase diversity imaging of which the author is aware use defocus to introduce phase diversity. Defocus is rotationally symmetric with respect to the optical axis (no q dependence) and has an approximately quadratic dependence (ρ^2) on the radial coordinate in the exit pupil plane. Because of this rotational symmetry, defocus diversity is effective in improving the quality of image restorations only for even-order aberrations such as spherical (ρ4) and astigmatism (ρ2•cos2θ). However, simple defocus diversity fails to improve the quality of image restorations for odd-order aberrations such as coma (ρ3•cosθ). This paper explores the use of non-quadratic and rotationally non-symmetric phase diversity versus standard defocus diversity. Simulated image restorations are presented for a hypothetical system that would use an adaptive optic to introduce generalized phase diversity to remediate the impact of residual aberrations.
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Mark W. Smith, Mark W. Smith, } "Use of adaptive optics to implement nonquadratic phase diversity imaging", Proc. SPIE 5524, Novel Optical Systems Design and Optimization VII, (22 October 2004); doi: 10.1117/12.556355; https://doi.org/10.1117/12.556355

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