Abstract

Self-imaging means image formation without the help of a lens or any other device between object and image. There are three versions of self-imaging: the classical Talbot effect (1836), the fractional Talbot effect, and the Montgomery effect (1967). Talbot required the object to be periodic; Montgomery realized that quasiperiodic suffices. Classical means that the distance from object to image is an integer multiple of the Talbot distance $z_T=2p^2∕\lambda$, where p is the grating period. Fractional implies a distance that is a simple fraction of $z_T$: say, $z_T∕2,z_T∕4,3z_T∕2\dots$ . We explore the most general case of the fractional Montgomery effect.

© 2005 Optical Society of America

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