Abstract

It has been discovered that a phase grating producing multiple spot patterns can also have the focusing property of a lens designed into it. Such gratings are nonperiodic. Consequently, the entire structure must be designed as a unit (except for possible reflection symmetry), as opposed to Dammann gratings wherein only the structure within each periodic unit needs to be designed as a unit. Non-periodic gratings are readily designed by flip-flop optimization of a single-quantity merit function. A suitable merit function specifies the position and relative intensity of each spot. The aperture plane is subdivided into a large number of incremental cells, each having either zero or radians phase shift. The merit function is evaluated from an initial random state. Each cell is then "flipped" to its opposite state and remains there if the merit function is improved. Unlike Dammann or other periodic gratings, these flip-flop designs can generally achieve spots of arbitrary intensity and position. Furthermore, the flip-flop approach can be used in conjunction with a lens to produce a uniform spot array (providing an alternative method for designing Dammann gratings) as well as spots with arbitrary intensities and almost arbitrary positions. The lens seems to force a reflection symmetry on the generated spot array.

© 1990 Optical Society of America