Optical EngineeringAnalysis of in-line Fresnel holograms via chirp separation
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A two-step computational technique for object reconstruction from digitized in-line Fresnel holograms of particle fields is proposed that eliminates the preliminary stage of depth extraction, when the goal is recovery of only the object cross-sectional shape. The first step involves a space/spatial-frequency domain chirp separation algorithm based on a two-dimensional (2-D) separable space-varying filtering scheme to separate a hologram into its single-object components. As the second step, a recently proposed Fourier synthesis technique is applied to separated components to reveal the cross-sectional morphology of individual 2-D objects, if they are sufficiently small as compared to the hologram size. The proposed method and a modified version of it based on 1-D filtering for performance improvement are illustrated on synthesized holograms. These simulations indicate that closely spaced planar objects can be recovered without significant dispersion, and back-to-back objects can also be reconstructed with tolerable leakage if they are sufficiently apart.