Typical laser Doppler anemometers use two equal-intensity laser beams (split from a single beam) that intersect across the target area at a known angle q, as shown in the schematic below.
Given that the laser light has a wavelength l, we would like to find the spacing d of the interference fringes where the combined laser light intensity is zero.
Consider an isosceles triangle bounded by a fringe and two wave fronts, as illustrated by the blue triangle in the schematic above. Recalling basic geometric properties of triangles, we find that the following three triangles (and subtriangles) are geometrically similar,
Furthermore, letting the angle , we have the following relationships amongst three of the triangle's angles,
Simplifying the above equations gives,
which yields the solution for a,
In order to link d to l and q, the base of the triangle ABC is used in the following equations,
The fringe spacing d can now be expressed in terms of the laser properties,