Optimal design of optical reference signals by use of a genetic algorithm

A new technique for the generation of optical reference signals with optimal properties is presented. In grating measurement systems a reference signal is needed to achieve an absolute measurement of the position. The optical signal is the autocorrelation of two codes with binary transmittance. For a long time, the design of this type of code has required great computational effort, which limits the size of the code to approximately 30 elements. Recently, the application of the dividing rectangles (DIRECT) algorithm has allowed the automatic design of codes up to 100 elements. Because of the binary nature of the problem and the parallel processing of the genetic algorithms, these algorithms are efficient tools for obtaining codes with particular autocorrelation properties. We design optimum zero reference codes with arbitrary length by means of a genetic algorithm enhanced with a restricted search operator.