Influence of the acousto-optic effect on laser Doppler anemometry signals

Abstract

When laser Doppler anemometry (LDA) is used to measure sound fields in water it is important to take into account the refractive index variations in the water due to the sound wave. These have the effect of creating a phase difference between the two laser beams in the LDA setup so that when they intersect they create moving fringes. In some situations this acousto-optic effect can dominate over the movement of the particles due to the sound wave, thereby influencing the Doppler signal. This article determines in which situations the acousto-optic effect can be ignored and in which situations it has a dominant effect. Theoretical expressions are derived for the magnitude of the acousto-optic effect on the LDA signal in terms of the distance of the laser beam propagation and acoustic wave number. The results show that varying the value of the wave number, the distance the laser beams have traveled in the direction perpendicular to the optical axis, or the angle of the sound wave, has an effect on the amplitude, yamp, of the fringe movement. For low wave number values, an angle of 0, ±π from the optic axis (y direction) corresponds to the situation in which the laser beams have been affected to the same degree by refractive index changes in the water and thus the path difference is zero and the value of yamp is a minimum. A maximum value of yamp is obtained for an angle of ±π/2 from the y direction for low wave number values. It is shown that the ratio of the acousto-optic effect to the amplitude of the particle movement due to the sound wave varies as the square of both the acoustic wave number and the distance of the laser beam propagation for low wave number values. An equation for the apparent motion of the particles in the fringes is determined and is used to show that the acousto-optic effect dominates as the value of the wave number and the distance of propagation of the beams increases. Also, for very low wave numbers and short distances, the acousto-optic effect is negligible. This is because at low wave numbers, corresponding to low sound frequencies, the refractive index gradients, and hence the phase changes along the lengths of the laser beams, are small.