Design of binary-phase and multiphase Fourier gratings for array generation

A review and comparison of design procedures for binary-phase and multiphase Fourier gratings used as array generators is presented. Grating structures include one- and two-dimensional binary-phase Dammann gratings, general binary-phase gratings, quarternary-phase Dammann gratings, and kinoforms for which coherent and incoherent designs are considered. One coherent method of design is that due to Dammann, which involves the solution of a set of N nonlinear equations in N unknowns. Although Dammann’s method generates little error, it does not permit the explicit maximization of diffraction efficiency. To increase diffraction efficiency, Dammann’s method is modified such that diffraction efficiency is a design parameter. To ensure the existence of a grating that has high diffraction and generates the desired source array, the number of grating parameters are increased, and an incoherent design is considered. Simulated annealing is applied to the solution of this problem. Examples of grating design using the different techniques are presented.