Symmetries that simplify design of spot-array phase gratings

Abstract

Dammann gratings1 are diffraction gratings that produce replicated images or arrays of spots from an incoming beam of monochromatic light. This property makes them useful for image duplication applications and spot array generation in optical computing. The process of designing an appropriate pattern typically involves an optimization procedure; therefore, the primary limitation in designing gratings that produce complex arrays is the computational resources required. Fortunately, symmetry properties can be incorporated into the grating design, significantly reducing the number of independent parameters required to describe a solution. First, we will extend the use of the translation symmetries that were introduced to produce an even-numbered spot array from binary phase gratings.2 Then we shall describe other symmetry properties that may be used to reduce the complexity of locating an optimal solution set. These symmetry properties will be generalized to cover binary phase gratings, discrete multilevel phase gratings, and continuous phase gratings.