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/<i>M</i>). 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 (<i>M</i><sub><i>N</i></sub>/<i>M</i>) (<i>M</i><sub><i>N</i></sub> < <i>M</i>, where <i>M</i><sub><i>N</i></sub> and <i>M</i> 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
(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
Changhe Zhou, Svetomir Stankovic, and Theo Tschudi, "Analytic Phase-Factor Equations for Talbot Array Illuminations," Appl. Opt. 38, 284-290 (1999)