Replacing Two-Dimensional Binary Phase Matrix by a Pair of One-Dimensional Dynamic Phase Matrices for Laser Speckle Reduction

In this paper, a method is proposed to create a pair of one dimensional binary phase modulator matrices 1D-BPMs, which is mathematically equivalent to a single two-dimensional binary phase modulator matrix 2D-BPM based on Sylvester constructed Hadamard matrices. An advantage of 1D-BPM over 2D-BPM is that the number of drive electrodes can be reduced from N² to 2N for a N×N Hadamard phase matrix, thus simplifying the drive interconnects and drive electronics. 1D-BPM can be based on electro-optical material and hence can be driven electrically, which is an advantage over the 2D-BPM which is usually etched on a glass substrate and actuated mechanically to implement the speckle reduction in laser projectors. We have discussed the algorithm for constructing the pair of dynamic 1D-BPMs to replace the 2D-BPM. Preliminary experiments are performed to demonstrate the validity of our concept.