# Imaging Flow Velocimetry with Laser Mie Scattering
## 2 Measurement Approaches
### Scattered Light Evaluation  
The velocity measurement approaches differ in the type of evaluation of the detected scattered light. One approach is to make use of the optical Doppler effect and to evaluate the momentum of the scattered light photons. Note that the photon momentum is Planck's constant divided by the wavelength, so that the photon momentum also represents the wavelength property or the energy of a photon. The second approach follows from the kinematic definition of the velocity and the evaluation of the position property of the scattered light photons. Hence, the developed measurement principles can be categorized into two groups [28]:  
* Doppler principles,
* Time-of-flight principles. The **Doppler principles** are based on the optical Doppler effect that occurs for light scattering at a moving object. In this fashion, the frequency shift (Doppler frequency) of the light scattered on a single particle (or multiple particles) is measured, and the Doppler frequency depends on the particle velocity. The relation between the particle velocity \(\vec{v}_{\mathrm{p}}\) and the Doppler frequency \(f_{\mathrm{D}}\) reads: [29; 30]  
\[v_{\mathrm{oi}}=\frac{\vec{o}-\vec{i}}{|\vec{o}-\vec{i}|}\cdot\vec{v}_{ \mathrm{p}}=\frac{\lambda}{|\vec{o}-\vec{i}|}f_{\mathrm{D}}, \tag{1}\]  
where \(\lambda\) denotes the wavelength of the incident light and \(v_{\mathrm{oi}}\) is the measured velocity component along the bisecting line of the angle between the light incidence direction \(\vec{i}\) from the illumination source and the observation direction \(\vec{o}\) of the scattered light, cf. Figure 2. Note that the relation is an approximate solution for particle velocities significantly smaller than the light velocity, which applies for the flows considered here. As a result, a single velocity component is obtained with the given measurement configuration, and the vector \((\vec{o}-\vec{i})\) is the sensitivity vector. The measurement of all three velocity components requires three measurements with different incidence or different observation directions, so that the three sensitivity vectors span a three-dimensional space. Note further that Equation (1) is an approximate solution for velocities significantly smaller than the light velocity, which is applicable for the considered flows here. The remaining task is to determine the Doppler frequency of the scattered light signal, where the different measurement principles can be subdivided into Doppler principles with amplitude-based and frequency-based signal evaluation procedures. The Doppler principles with an amplitude-based signal evaluation make use of the spectral transmission behavior of an optical filter. The optical filter converts the frequency information of the scattered light into an intensity information, which is finally measurable with a photodetector or camera. As the optical filter, an atomic or molecular filter or an interferometric filter is used. The interferometer can be a two-ray or a multiple ray interferometer. Note that the use of a filter requires laser light illumination with a significantly smaller linewidth than the linewidth of the filter transmission curve. Otherwise, the transmission curve of the filter is not resolved. The Doppler principles with frequency-based signal evaluation also use interferometry. However, the scattered light is not superposed with itself, but with light with a different frequency. If the superposed light has no velocity-dependent shift in frequency, the measurement method is called a reference method. The superposed light is, e.g., from the illumination light source or a frequency comb. If the superposed light is also scattered light, but with a different Doppler frequency shift due to a different light incidence or observation direction, the difference of both Doppler frequencies is evaluated, and then, the measurement method is called the difference method.