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J Opt Soc Am A Opt Image Sci Vis. 2010 Jul 1;27(7):1630-7. doi: 10.1364/JOSAA.27.001630.

Edge-preserving sectional image reconstruction in optical scanning holography.

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  • 1Imaging Systems Laboratory, Department of Electrical and Electronic Engineering, University of Hong Kong,Pokfulam Road, Hong Kong, China.


Optical scanning holography (OSH) enables us to capture the three-dimensional information of an object, and a post-processing step known as sectional image reconstruction allows us to view its two-dimensional cross-section. Previous methods often produce reconstructed images that have blurry edges. In this paper, we argue that the hologram's two-dimensional Fourier transform maps into a semi-spherical surface in the three-dimensional frequency domain of the object, a relationship akin to the Fourier diffraction theorem used in diffraction tomography. Thus, the sectional image reconstruction task is an ill-posed inverse problem, and here we make use of the total variation regularization with a nonnegative constraint and solve it with a gradient projection algorithm. Both simulated and experimental holograms are used to verify that edge-preserving reconstruction is achieved, and the axial distance between sections is reduced compared with previous regularization methods.

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