General formulation of digital in-line holography from correlation with a chirplet function

S. Coëtmellec; N. Verrier; M. Brunel; D. Lebrun

doi:10.2971/jeos.2010.10027

Journal of the European Optical Society - Rapid publications, Vol 5 (2010)

General formulation of digital in-line holography from correlation with a chirplet function

S. Coëtmellec, N. Verrier, M. Brunel, D. Lebrun

Abstract

Digital in-line holography is revisited to propose a mathematical model that describes the recording-reconstruction process as a linear shift-invariant system with a pseudo-point spread function even when the images are out of the optimal plane in the sense of signal processing. A particular case is treated to show that the optimal plane is the best focus plane in the sense of optics. Next, an exact solution of the holographic reconstruction by correlation is given. By means of the previous results, we study the behavior of the result of the correlation function between the diffraction pattern function produced by an opaque disk and a chirplet function and between the diffraction pattern produced by a phase disk and the same chirplet function.

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