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

When laser Doppler anemometry (LDA) is used to measure sound fields in wate r it is important to take into account the refractive index variations in t he water due to the sound wave. These have the effect of creating a phase d ifference between the two laser beams in the LDA setup so that when they in tersect they create moving fringes. In some situations this acousto-optic e ffect 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 magni tude 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 t hat 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, gamma(amp), of the fring e movement. For low wave number values, an angle of 0, +/- pi from the opti c axis (gamma direction) corresponds to the situation in which the laser be ams have been affected to the same degree by refractive index changes in th e water and thus the path difference is zero and the value of gamma(amp) is a minimum. A maximum value of gamma(amp) is obtained for an angle of +/- p i/2 from the gamma direction for low wave number values. It is shown that t he ratio of the acousto-optic effect to the amplitude of the particle movem ent due to the sound wave varies as the square of both the acoustic wave nu mber and the distance of the laser beam propagation for low wave number val ues. 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 i ncreases. Also, for very low wave numbers and short distances, the acousto- optic effect is negligible. This is because at low wave numbers, correspond ing to low sound frequencies, the refractive index gradients, and hence the phase changes along the lengths of the laser beams, are small. (C) 1998 Am erican Institute of Physics. [S0034-6748(98)03112-8].