17 June 2009 Towards deconvolution in holography
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Abstract
In this paper we present a way to formulate the holographic reconstruction of a wavefield throughout a volume by means of a sequence of convolutions. The discussion is based on the assumption that the field is generated by a set of real valued scattering sources within the volume. In analogy to two dimensional imaging this enables the application of deconvolution techniques to the holographic scheme. We show, that the proposed formalism can theoretically be used to perform a three dimensional deconvolution of the reconstructed amplitude in order to recover object information, e.g. the position of scattering sources. In the ideal case of an infinite aperture of the hologram the deconvolution may be employed by a simple inverse filter. However, for the more realistic case of finite apertures an iterative technique called Out of Hologram Extrapolation (OHE) is introduced, which is based on the projected Landweber method. Finally, the novel method is applied to a synthetic example in order to recover the positions of a set of distributed point sources.
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Nan Wang, Claas Falldorf, and Christoph von Kopylow "Towards deconvolution in holography", Proc. SPIE 7390, Modeling Aspects in Optical Metrology II, 73900Y (17 June 2009); doi: 10.1117/12.827507; https://doi.org/10.1117/12.827507
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