Abstract

We consider field distributions in fractional Talbot planes behind a periodic two-dimensional complex-amplitude transparency that is illuminated by a unit-amplitude plane wave. In the paraxial approximation the field in various fractional Talbot planes is expressed as a sum of contributions from a finite number of points in the plane of the transparency, yielding compact algebraic formulas for the diffracted field. Given the desired intensity distribution in the fractional Talbot plane, we synthesize the transmission function from nonlinear equations. An experimental illustration that uses a binary phase grating is given.

© 1994 Optical Society of America

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