Open AccessTwo-dimensional gold matrix method for encoding two-dimensional optical arbitrary positions
Author(s) -
Li Hao,
Changhe Zhou,
Shaoqing Wang,
Yunqing Lu,
Xiansong Xiang
Publication year - 2018
Publication title -
optics express
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.26.012742
Subject(s) - matrix (chemical analysis) , binary number , algorithm , optics , sequence (biology) , coding (social sciences) , computer science , mathematics , physics , materials science , arithmetic , statistics , biology , composite material , genetics
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.