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Interference of Two Plane Waves

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,

Laser Doppler Anemometer

A typical laser Doppler anemometer issues two split laser beams to form a fringe pattern across the targeted area, as described above. When the targeted area is within a flowfield, as shown in the schematic below, entrained particles passing through the fringes produce a burst of reflected light whose flicker frequency depends on the fringe spacing and the particle velocity normal to the fringes.

Laser Doppler Optical System

The frequency of the Doppler burst fD is the velocity of the particle normal to the fringes vn divided by the fringe spacing d,

fD = vn / d

Since the fringe spacing s is a function of the laser wavelength l and crossing angle q, the Doppler frequency becomes,

The normal velocity of the particle is found to be,

Note that there are no negative terms in the above formula. In other words, the direction of the particle motion can not be determined by this formula. Furthermore, the measured velocity of the particle is the velocity component normal to the fringe pattern, not the actual velocity.