Abstract

We have developed an iterative algorithm for generating the transmittance function of binary onaxis holograms. The hologram is divided into rectangular cells so that each cell imparts a phase delay of 0 or ϕ rad on the incident wavefront. An iterative optimization routine based on simulated annealing is used to determine (1) the binary state of each cell and (2) the value of the phase difference ϕ between cells of different states. The algorithm is similar to the direct binary search encoding method.¹ In particular, this encoding method was applied to the design of multiple-beam holograms or holograms designed to reconstruct an M × N array of equally bright spots centered on the z axis. The encoding algorithm maximizes the diffraction efficiency for a specified allowed variance in intensity among the M × N signal spots. In addition the CGH transmittance pattern can be designed to compensate for phase mismatch problems (variations in the phase delay ϕ from the specified value due to fabrication process tolerances) at the expense of a reduction in diffraction efficiency and/or signal power errors. Theoretical results indicate that binary HOEs with diffraction efficiencies larger than 70% are possible. An experimentally fabricated hologram reconstructed a 3 × 3 array of spots with a diffraction efficiency of 59% and with less than a ±10% deviation in spot signal powers.

© 1988 Optical Society of America