Analytic approach for optimal quantization of diffractive optical elements

One of the most important factors that Limit the performance of diffractive optical elements (DOE's) is the depth accuracy of the relief structure. A common procedure for fabricating DOE's is the binary optics procedure, in w hich binary masks are used for the fabrication of a multilevel relief struc ture. Here an analytic procedure for calculating the optimal depth levels o f DOE's, the phase bias, and the decision levels is presented. This approac h is based on the minimization of the mean-squared error caused by the quan tization of the continuous profile. As a result of the minimization an opti mal value for the etching depth of each photolithographic mask is determine d. The obtained depth values are, in general, different from the depth valu es used by the conventional multilevel approach. Comprehensive mathematical analysis is given, followed by several computer simulations that demonstra te the advantages of the proposed procedure. (C) 1999 Optical Society of Am erica.