A fourier optical model for the laser Doppler velocimeter

Abstract

The treatment is based on a fourier optical model. It is shown how the various configurations (i.e. “differential mode” and reference beam mode with both one and two incident beams) are incorporated in the model, and how it can be extended to three dimensions.

The particles are represented by a sum of weighted delta functions of random position with respect to their influence on the scalar field.

The influence of the receiver configuration is investigated: it is shown that the aperture size is roughly inversely proportional to the effective area in the measuring plane from which beams are heterodyned on the detector.

The purpose of the pinhole, namely to filter the measuring volume out from the rest of space, is shown to depend on the aperture size. The diameter of the pinhole should never be smaller than the real image- found by geometrical optics- of the measuring volume (naturally), but its filtering ability vanishes as the aperture size converges towards zero.

The results based on fourier optics are compared with the rough estimates obtainable by using the “antenna formula” for heterodyning (A_rΩ_r≈λ ²).