The Iterative Transform Phase Diversity algorithm is designed to solve the problem of recovering the wavefront in the exit pupil of an optical system and the object being imaged. This algorithm builds upon the robust convergence capability of Variable Sampling Mapping (VSM), in combination with the known success of various deconvolution algorithms. VSM is an alternative method for enforcing the amplitude constraints of a Misell-Gerchberg-Saxton (MGS) algorithm. When provided the object and additional optical parameters, VSM can accurately recover the exit pupil wavefront. By combining VSM and deconvolution, one is able to simultaneously recover the wavefront and the object.

To recover the exit pupil wavefront, and the unknown object, first one must collect image plane data of the optical system under test. To increase convergence robustness, diversity images are collected. Next, a guess of the wavefront is made. This can be based on a prior estimate, or a simpler random solution of small values. This guess of the exit pupil and the image data will provide a starting point for VSM phase retrieval.

After several iterations of VSM phase retrieval, the algorithm will estimate the point spread function (PSF) based on the current estimate of the exit pupil wavefront. This estimated PSF is then deconvolved from the image data to provide an estimate of the object. At this point, one has an estimate of the object, and the estimated wavefront. The process is then repeated with the object included in the model in VSM. The entire process is repeated until a convergence criterion is met.

This work was done by Jeffrey Smith for Goddard Space Flight Center. GSC-15963-1

NASA Tech Briefs Magazine

This article first appeared in the August, 2012 issue of NASA Tech Briefs Magazine.

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