A new method of digital phase contrast based on fractional-order Fourier reconstruction is proposed. We show that the diffraction patterns produced by pure phase objects exhibit linear chirp functions that can be advantageously processed using the fractional Fourier transform. The optimal fractional orders lead to the longitudinal location of the phase object, while the analysis of the reconstructed pattern leads to its diameter and to the value of the phase shift. Simulations and experimental results are given. The configuration tested in this paper is a very general Gaussian illumination.
© 2009 Optical Society of America
Fourier Optics and Signal Processing
Original Manuscript: September 29, 2008
Manuscript Accepted: November 28, 2008
Published: January 16, 2009
Marc Brunel, Sebastien Coëtmellec, Denis Lebrun, and Kamel Aït Ameur, "Digital phase contrast with the fractional Fourier transform," Appl. Opt. 48, 579-583 (2009)