Least-squares based inverse reconstruction of in-line digital holograms

We present a least-squares solution for the inverse problem in in-line digital holography which is based on a point source model. We demonstrate that by reformulating the reconstruction problem as an inverse problem and by integrating a contour gradient based auto-focus search algorithm into the rec...

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Bibliographic Details
Published inJournal of optics (2010) Vol. 15; no. 7; pp. 75716 - 1-10
Main Authors Kamau, Edwin N, Burns, Nicholas M, Falldorf, Claas, von Kopylow, Christoph, Watson, John, Bergmann, Ralf B
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.07.2013
Subjects
auto-focus schemes
diffraction
Digital
Holograms
Holography
interference
Inverse problems
Inversions
Least squares method
Mathematical models
Reconstruction
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Summary:We present a least-squares solution for the inverse problem in in-line digital holography which is based on a point source model. We demonstrate that by reformulating the reconstruction problem as an inverse problem and by integrating a contour gradient based auto-focus search algorithm into the reconstruction routine, a more fundamental solution for the inversion of a hologram can be attained. With this approach the inversion can be calculated without any prior knowledge of the object's shape/size and without imposing any constraints on the imaging system. In a proof-of-concept study we show that our method facilitates a more accurate reconstruction, as compared to conventional methods, and that it facilitates object localization with an accuracy on the order of the optical wavelength.
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ISSN:2040-8978
2040-8986
DOI:10.1088/2040-8978/15/7/075716