Design of bar code systems for accurate alignment: a new method

Design of zero reference codes using cross-entropy method

This paper considers the use of autocorrelation properties to design zero reference codes (ZRCs) for optical applications. Based on the properties of the autocorrelation function, the design of an optimum ZRC problem is transformed into a minimization problem with binary variables, and the objective is to minimize the second maximum of the autocorrelation signal sigma. However, the considerable computational complexity for an exhaustive search through all combinations of (nn (1)l) different code patterns is a potential problem especially for large codes, where n and n1 are the length of the ZRC and the number of transparent slits, respectively. To minimize sigma while reducing the computational complexity at the same time, we introduce the Cross-Entropy (CE) method, an effective algorithm that solves various combinatorial optimization problems to obtain a good code. The computer simulation results show that compared with the conventional genetic algorithm (GA), the proposed CE obtains the better sigma with low computational complexity.

Two-dimensional patterns for optical alignment

Two-dimensional patterns that have properties suited for optical alignment have been constructed from one-dimensional binary Barker codes. Applications include automated alignment of masks with patterns in photolithography.