Design of two-dimensional zero reference codes with cross-entropy method

We present a cross-entropy (CE)-based method for the design of optimum two-dimensional (2D) zero reference codes (ZRCs) in order to generate a zero reference signal for a grating measurement system and achieve absolute position, a coordinate origin, or a machine home position. In the absence of diffraction effects, the 2D ZRC design problem is known as the autocorrelation approximation. Based on the properties of the autocorrelation function, the design of the 2D ZRC is first formulated as a particular combination optimization problem. The CE method is then applied to search for an optimal 2D ZRC and thus obtain the desirable zero reference signal. Computer simulation results indicate that there are 15.38% and 14.29% reductions in the second maxima value for the 16 x 16 grating system with n(1) = 64 and the 100 x 100 grating system with n(1) = 300, respectively, where n(1) is the number of transparent pixels, compared with those of the conventional genetic algorithm. (C) 2010 Optical Society of America