Geometry of the fringe field formed in the intersection of two Gaussian beams

A general expression is obtained for the exact computation of the fringe field in the intersection volume of two paraxial Gaussian beams for arbitrary beam waist positions and sizes. The expression is then simplified to allow easy fringe field computation while retaining good accuracy. By relating the simplified expression to the system parameters relevant to dual-beam laser Doppler velocimeters, simple design equations are obtained. These equations permit rapid evaluation of the fringe field variation along the major and minor axes of the intersection volume and clearly identify the system parameters controlling this variation.