We show that the fractional Fourier transform is a suitable mechanism with which to analyze the diffraction patterns produced by a one-dimensional object because its intensity distribution is partially described by a linear chirp function. The three-dimensional location and the diameter of a fiber can be determined, provided that the optimal fractional order is selected. The effect of compaction of the intensity distribution in the fractional Fourier domain is discussed. A few experimental results are presented.
© 2002 Optical Society of America
Original Manuscript: April 13, 2001
Revised Manuscript: September 10, 2001
Published: January 10, 2002
Sébastien Coëtmellec, Denis Lebrun, and Cafer Özkul, "Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier transform," Appl. Opt. 41, 312-319 (2002)