Comparison and unification of speckle-based phase retrieval and holography with applications in phasefront alignment and recognition
Comparisons between various wavefront reconstruction methods such as wavefront curvature sensing and phase diversity  have been reported in the literature. These comparative studies highlight the differences, similarities, relative advantages, operating regimes and main applications of the various reconstruction methods. For coherent light metrological applications, especially on rough objects, Digital Holography (DH) is considered one of the established interferometric methods because of its sub-wavelength accuracy. For investigations of smooth surfaces, Phase Retrieval (PR) or the non-interferometric approach offers a simple setup since no reference beam (RB) is required. In PR, recent trends favour the use of multiple intensity images, rather than a few images, due to its robustness against quantization error. Recently, a multiple speckle-pattern PR method was utilized in the interferometric analysis of object rotation and deformation  and in the numerical correction of aberrations , indicating a point of convergence between the two, traditionally parallel, reconstruction methods. To the best of our knowledge, no comparative study has been done between PR and DH. Recognition of test objects has been carried out by correlation with a reference object wavefront obtained through DH . Since no RB is used, PR may offer a more robust recognition method. The objectives of this study are: 1) compare off-axis DH and PR in terms of setup and reconstruction algorithm; 2) present a new model for the PR method interpreting it as a special case of holography called “phase-shifting broadband DH”; 3) describe a novel method for phasefront alignment of uncorrelated laser beams using PR; and, 4) describe a novel method for object recognition using PR.
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