Two dimensional binary pattern exhibiting zero correlation over a wide range of phase shift

Abstract

A two-dimensional binary pattern is used as a two-dimensional bar-code, a position detection pattern, a diffraction pattern for calibration of a laser beam, and so on. Most applications of two-dimensional binary data require a wide zone of zero-correlation. There exist reports on a one-dimensional binary sequence with wide range of zero-correlation. We extend one of the methods to synthesize one dimensional binary sequences with wide zero-correlation previously reported by our group to two-dimensional data. The size of the synthesized pattern is (2/sup u+2/m)/spl times/(2/sup v+2/n), where mn is equal to the rank of a Hadamard matrix (not restricted to be a Walsh-Hadamard matrix) and u /spl ges/ 0, and v /spl ges/ 0. The size of zero correlation zone is (2/sup u/)/spl times/(2/sup v/). The number of synthesized patterns is 4 mn. The flexibility of the number of patterns, the size of a pattern, and the size of zero correlation zone is very useful for the design of its applications. The applications of the synthesized pattern for measurement are also discussed.