## What is doppler effect?

Wind Lidars are based on the theory of Doppler effect. The following is an overview of LiDAR Solutions and what describes what is Doppler effect.

In 1842, Doppler, an Austrian mathematician and physicist, passed by the railway and a train passed him. He found that when the train came from a distance, the sound of the whistle became louder and the pitch increased, and when the train was leaving, the sound becomes weaker and the pitch lowers.

Learn more from the video below – **Brass band on train demonstrates Doppler effect**

This physical phenomenon has aroused great interest in Doppler, and the following conclusions have been drawn after research.

When the sound source moves toward the observer, the wavelength of the sound wave decreases (the frequency increases), so the pitch increases; when the sound source moves away from the observer, the wavelength of the sound wave increases (the frequency decreases), so the pitch decreases as demostration below:

The change in pitch is related to the ratio of the relative velocity to the sound velocity between the source and the observer. The larger the ratio, the more significant the change, which is the “Doppler effect”, and the resulting frequency change is called the Doppler shift.

The mathematical expression of the Doppler effect:

The frequency relationship between the observer and the source is

**F1** is the observed frequency;**F** is the original emission frequency at which the emission originates from the medium;**V** is the traveling speed of the wave in the medium;**V0** is the movement speed of the observer. If it is close to the emission source, the front operation symbol is +, otherwise, it is -, and the observer is stationary, it is 0;**Vs** is the moving speed of the emission source. If it is close to the observer, the front operation symbol is – sign, otherwise, it is + sign.

**The Doppler effect applies not only to sound waves, but also to radio waves and light waves.**

## Working Principle of Doppler Wind LiDAR

Wind LiDAR has many complexities. There are many aerosol particles in the air, which refer to solid particles and liquid particles uniformly dispersed in the atmosphere, such as fog, smoke, haze, fine dust and smog. The wind-measuring lidar emits a laser beam into the air, and when the laser irradiates these aerosol particles, it will reflect, and the reflected wave of the moving particles will have a Doppler frequency shift. The frequency shift is the difference between the frequencies of the transmitted wave and the reflected wave.

In the figure below, the angle between the laser wave emitted by the lidar and the vertical line on the ground is φ. The laser will be reflected when it encounters aerosol particles, and the lidar will process the reflected wave after receiving it. The distance L between the aerosol particle and the radar is obtained by the time difference between the aerosol particle of the transmitted wave and the received wave

The height of the aerosol particle h=L·cosφ

The velocity Vs of the aerosol particles relative to the radar is calculated by the frequency shift Δf of the transmitted wave and the received wave,

The horizontal moving speed of aerosol particles V=Vs sinφ

The internal structure of the doppler Wind monitoring LiDARs: