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Applied Optics

Applied Optics


  • Vol. 38, Iss. 2 — Jan. 10, 1999
  • pp: 284–290

Analytic phase-factor equations for Talbot array illuminations

Changhe Zhou, Svetomir Stankovic, and Theo Tschudi  »View Author Affiliations

Applied Optics, Vol. 38, Issue 2, pp. 284-290 (1999)

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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, π) 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.

© 1999 Optical Society of America

OCIS Codes
(050.1380) Diffraction and gratings : Binary optics
(050.1950) Diffraction and gratings : Diffraction gratings
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects

Original Manuscript: April 1, 1998
Revised Manuscript: August 20, 1998
Published: January 10, 1999

Changhe Zhou, Svetomir Stankovic, and Theo Tschudi, "Analytic phase-factor equations for Talbot array illuminations," Appl. Opt. 38, 284-290 (1999)

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