Theoretical analysis of rotational Doppler effect when vortex beam is misaligned with rotational axis

The rotational Doppler effect provides a non-contact way to detect the angular velocity of a rotating rough surface. Previous research focus on the condition that the axis of structured beam is aligned with rotational axis. However, it is hard to align the axis of beam and rotational axis especially in remotely detection and behavior of rotational Doppler shift in misaligned arrangement is still unclear. Here, we investigate rotational Doppler effect in misaligned arrangement from the view of Doppler shift distribution. Based on the Monte Carlo method, the influence of scatterer which is a random rough surface is considered in the analysis of misaligned RDE. The variation of spectrum of fundamental scatter mode in misaligned illumination is revealed, which may provide theoretical reference for the measurement of angular velocity based on RDE.