Imaging performance of generalized holography

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Abstract
Generalized holography is understood as a heuristic solution of an inverse-scattering problem based on the time-harmonic formulation of Huygens’s principle. It is checked against a scalar two-dimensional numerical-scattering experiment: Simulated data for a cylindrical object with arbitrary elliptical cross section are inserted into the algorithm, and the results are critically discussed. We find that generalized holography yields only sparse improvement over conventional holography—the images obtained are only poor solutions to the inverse-scattering problem—but, on the other hand, its mathematical consequences, such as the Porter–Bojarski integral equation, may serve as an intuitive means to predict the performance of holographic schemes for certain specialized canonical inverse-scattering problems; once the limitations are known, considerable advantage can be drawn for practical applications, and improved extensions are readily proposed yielding very general diffraction tomography algorithms.

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