Experimental Investigations and Modeling of Interference Fringe Geometry in Line-Shaped Gaussian Beam Intersections for Laser Doppler Sensors

Line-shaped beam-based Doppler distance sensors enable 3D shape measurements of rotating objects, for instance for working lathe monitoring with a simultaneous, multipoint velocity, and distance measurement. The velocity and distance estimations are fundamentally referred to the interference fringe spacing of the sensors. In this case, the fringe spacing variation-caused measurement error is significant; however, a complete, accurate model of the fringe geometry distribution for the line-shaped fringe volume is still missing and required to identify and minimize the error. Therefore, this work presents a high-accuracy 3D model for the fringe spacing evaluation of the sensors with experimental investigations. The model is derived from the phase expression of Gaussian beams introducing extension ratio, and can be universally applied to describe fringe geometry distribution throughout the intersection volume of spherical and line-shaped beams. With an experimental setup of a laser Doppler sensor, a full-field fringe spacing estimation using a high-resolution matrix camera is performed with dual-wavelength beams. The numerical modeling and experimental results show an average relative difference below 0.6%.