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Two plus two equals five: the cost of non-additive reconstruction algorithms in digital holography

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Abstract

The Fresnel transform and other linear canonical transforms are widely used to reconstruct digital holograms by numerical back-propagation. However, while the Fresnel transform exhibits index additivity, this useful feature is missing from many digital implementations of the Fresnel transform. In this paper, we discuss the interaction of algorithm and additivity, and show how the angular spectrum method is always unitary providing a unitary fast Fourier transform is used, but single-fft algorithms are not.

© 2017 Optical Society of America

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