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T. D. Raymond, S. Farrer, P. Pulaski, D. R. Neal; Gerchberg-Saxton Phase Retrieval in Phase Diversity Wavefront Sensing. Invest. Ophthalmol. Vis. Sci. 2008;49(13):979.
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Phase diversity wavefront sensors (PDWS) offer promise in ophthalmic applications because of their ability to measure speckled and discontinuous wavefronts. We numerically investigate the efficacy of the iterative Gerchberg-Saxton (GS) phase retrieval method to ophthalmic instruments where large dynamic range in defocus and the presence of speckle make phase retrieval with standard methods based on the intensity transport equation difficult.
Simulated PDWS data covering a typical range of typical ophthalmic defocus aberration with a standard PDWS configuration were generated using the Rayleigh-Sommerfled propagation integral equation. We processed these data using the well-known iterative GS method. The input pupil diameter, sample plane spacing, and irradiance characteristics were varied to study the robustness of the method and its rate of convergence.
We found the convergence rate and robustness of the GS method to be particularly sensitive to the Fresnel number of the PDWS. The number of iterations required to achieve a specified level of defocus accuracy increased approximately exponentially with input pupil diameter for fixed sample spacing and diminished as the reciprocal of the sample spacing. In contrast, we found a quadratic rather than exponential dependence on the pupil diameter when speckle was introduced into the irradiance pattern. This serendipitous effect significantly reduced the number of iterations required for beams containing large numbers of speckle cells, as is typical in ophthalmic aberrometers.
We found the GS method to be applicable to problems in ophthalmic wavefont sensing and to be particularly well-suited to measurements in the presence of speckle. The method worked best when sampled beams had significantly disparate irradiance distributions and/or small Fresnel numbers. This method therefore complements phase retrieval methods based on the intensity transport equation.Figure 1:The number of iterations required to achieve a level of defocus accuracy increased with aperture and diminished for beams with speckle.
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