title: Design of two-dimensional zero reference codes with cross-entropy method.
abstract: 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 16x16 grating system with n(1)=64 and the 100x100 grating system with n(1)=300, respectively, where n(1) is the number of transparent pixels, compared with those of the conventional genetic algorithm.
authors.affiliation: Department of Optoelectronics and Communication Engineering, National KaohsiungNormal University, Kaohsiung 802, Taiwan. jcchen@nknucc.nknu.edu.tw
authors.forename: Jung-Chieh
authors.initials: JC
authors.lastname: Chen
authors.forename: Chao-Kai
authors.initials: CK
authors.lastname: Wen