Two-dimensional gold matrix method for encoding two-dimensional optical arbitrary positions

In this study, a novel two-dimensional spatial coding pattern called two-dimensional Gold matrix method is proposed for general two-dimensional positioning. Considering the difficulty in representing a two-dimensional position in a single binary matrix, constructing a matrix while each submatrix refers to its location is a challenging mathematical problem. The general two-dimensional signal can be labeled by the two-dimensional Gold matrix, which results from a preferred pair of two m-sequences. For a pseudorandom m-sequence, the span-n property of the two-dimensional Gold matrix states that every n×n submatrix is unique and the decoding is fast and convenient. Numerical simulation and a proof-of-principle experiment are performed, and experimental results verified that the two-dimensional Gold matrix method is effective for high resolution and large range two-dimensional measurements.