title: Analytic phase-factor equations for Talbot array illuminations.
abstract: Under specific circumstances the fractional Talbot effect can be described by simplified equations. We have obtained simplified analytic phase-factor equations to describe the relation between the pure-phase factors and their fractional Talbot distances behind a binary amplitude grating with an opening ratio of (1/M). We explain how these simple equations are obtained from the regularly rearranged neighboring phase differences. We point out that any intensity distribution with an irreducible opening ratio (M(N)/M) (M(N) < M, where M(N) and M are positive integers) generated by such an amplitude grating can be described by similar phase-factor equations. It is interesting to note that an amplitude grating with additional arbitrary phase modulation can also generate pure-phase distributions at the fractional Talbot distance. We have applied these analytic phase-factor equations to neighboring (0, pi) phase-modulated amplitude gratings and have analytically derived a new set of simple phase-factor equations for Talbot array illumination in this case. Experimental verification of our theoretical results is given.
authors.affiliation: Institute of Applied Physics, Technical University of Darmstadt, Hochschulstrasse 6, D-64289 Darmstadt, Germany.
authors.forename: C
authors.initials: C
authors.lastname: Zhou
authors.forename: S
authors.initials: S
authors.lastname: Stankovic
authors.forename: T
authors.initials: T
authors.lastname: Tschudi