Consider a monochromatic light source, such as a laser, that has frequency f and wavelength l, that sends a light beam to illuminate a moving target. Further assume that the target moves toward the observer at the velocity v. According to the Doppler effect, the wavelength of the reflected light is compressed to lr and the frequency increases to fr.
A light detector can collect both incident and reflected light. Mathematically, the sum of these two light beams is,
where A is the amplitude of the incident light and Ar is the amplitude of the reflected light.
The irradiance is found to be,
Simplifying the third term in the last equation above (via a trigonometric product rule), we have,
Suppose the relative velocity v is much less than the speed of light (v « c). The observed frequency fr does not change very much from the original frequency f. As a result, the final term in the equation above is the only low frequency component. All of the other terms in the equation are at a frequency of f, fr, or higher.
By adding a low pass filter to the measurement, the frequency difference between the incident and reflected light beams can be obtained, allowing one to find the velocity of the target based on the Doppler effect. Such a low-pass filter is usually employed by Ultrasonic Doppler velocimeters.
In Laser Doppler anemometry, optical methods such as the interference of two laser beams are more preferable.