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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 Ki is the incident wavenumber and Ks is the wavenumber of the scattered light, then the wavenumber of the difference is given by the following expression:

The symbol u is utilised in order to denote the velocity vector of the scattering centre. The frequency shift (expressed as wD in terms of fD) between the incident and scattered light is therefore given by the following expression:

Figure 1

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 λi 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.