Figure 1 illustrates the basic principal of the Doppler shift. When radiation hits a scattering centre, such as a particle in a flow, the radiation is re-radiated at a different wavenumber. If K_i is the incident wavenumber and K_s is the wavenumber of the scattered light, then the wavenumber of the difference is given by the following expression:

Provided that K and u are in fact collinear (as is the case in the diagram), the Doppler frequency difference may be expressed as follows:

…where λ_i is the wavelength of the incident radiation. From the above treatment it is possible to conclude that only the component of velocity that is parallel to K influences the Doppler frequency. Further, any component of velocity can be measured by properly orientating the wavenumber difference vector K by altering the geometry of the incident and scattered light. This is an important feature of Laser Doppler Anemometer, allowing the measurement of up to three velocity components.