New matrix solution of the phase-correlation technique in a Brillouin dynamic grating sensor

Abstract

In the phase-correlation measurement technique of Brillouin dynamic grating sensors, two counterpropagating pump waves are modulated by a pseudo-random bit sequence (PRBS) that applies a random phase shift of either 0 or π with a specified period. In order to define the sensing length and spatial resolution, the shape of the correlation peak has to be found. So far, many methods have been used to demonstrate the phase correlation, but they often require several lengthy and sometimes complicated mathematical assumptions and equations. One of the techniques that has the best reported spatial resolution is called the time gated phase-correlation technique. We introduce a novel method based on a matrix solution to show the phase modulation in the phase-correlation technique. It is a straightforward and intuitive pattern to visualize the phase modulation of the pumps and to attain the shape of the phase-correlation peaks. Finally, the results of the matrix method are completely consistent with the previous results.