Abstract

The Fresnel diffraction of periodic objects at rational fractions of the Talbot distance is described in terms of the Wigner distribution function (WDF). The analysis provides a heuristic model for understanding the formation of the diffraction patterns as well as for evaluating the complex amplitude at any fractional Talbot plane. Furthermore, certain symmetry properties of the Fresnel-diffracted wave field can be derived directly from the WDF. Additionally, a discussion is given on how periodic signals and information about the phase are encoded in the WDF.

© 1996 Optical Society of America

Designing Talbot array illuminators with phase-space optics

Markus Testorf
J. Opt. Soc. Am. A 23(1) 187-192 (2006)

Numerical optimization of phase-only elements based on the fractional Talbot effect

Markus Testorf, Victor Arrizón, and Jorge Ojeda-Castañeda
J. Opt. Soc. Am. A 16(1) 97-105 (1999)

Quantitative analysis of imperfect frequency multiplying in fractional Talbot planes and its effect on high-frequency-grating lithography

Daniel Thomae, Oliver Sandfuchs, and Robert Brunner
J. Opt. Soc. Am. A 31(7) 1436-1444 (2014)

Matrix formulation of the Fresnel transform of complex transmittance gratings

Victor Arrizón, Juan G. Ibarra, and J. Ojeda-Castañeda
J. Opt. Soc. Am. A 13(12) 2414-2422 (1996)

Fractional Talbot effect in phase space: A compact summation formula

Konrad Banaszek, Krzysztof Wódkiewicz, and Wolfgang P. Schleich
Opt. Express 2(5) 169-172 (1998)