Spherical Gaussian beam model for prediction of three-dimensional fringe patterns in a laser Doppler anemometer measuring volume

Abstract

A general and rigorous spherical Gaussian beam model is introduced to predict the threedimensional fringe field based on the paraxial approximation for Gaussian beams. It has been proved that for any dual-beam LDA system with the knowledge of beam cross-angle, waist locations and sizes, the interfering surfaces and the fringe spacings can be obtained by directly solving the phase condition equation in which all the phase terms including the Guoy phase shift are taken into account. As examples, computations were carried out for typical configurations including those with initial phase difference, partial intersection and different waist sizes. The results which are presented in graphical form, for the first time, reveal the detailed three-dimensional fringe fields formed by the interference of two Gaussian beams.