# Imaging Flow Velocimetry with Laser Mie Scattering
## 2 Measurement Approaches
### Scattered Light Evaluation
The **time-of-flight principles** are based on the kinematic velocity definition, which reads for one velocity component:  
\[v_{\mathrm{p,}x}=\dot{x}\approx\frac{\Delta x}{\Delta t}, \tag{2}\]  
with \(\Delta x\) as the change in space during the time period \(\Delta t\). The approximation in Equation (2) is valid when the particle acceleration during the measurement is negligible. This is a common assumption, which reduces the required number of pairs of position and time to two, cf. Figure 3. Either the change of the particle position for a given time period or the time period for a given spatial distance is then measured. Accordingly, the time-of-flight principles can be subdivided into two categories using time measurements or space measurements. Instead of two pairs of position and time, also a higher number of pairs can be acquired to take the acceleration into account where necessary [31; 32; 33]. Furthermore, the time-of-flight principles are also capable of performing three component measurements, e.g., with planar illumination, planar detection and at least two observation directions for triangulation. An overview of the proposed categorization of the different measurement approaches is shown in Figure 4. Referring to the \"16 th International Symposium on Applications of Laser Techniques to Fluid Mechanics\" in the year 2012, 79% of the 220 contributions contain or concern flow velocity measurements. An amount of 90% of these contributions is related to time-of-flight principles, while 10% is related to Doppler principles. For the articles concerning time-of-flight measurement principles, a majority of 99% considers or applies space measurement methods. This strong focus on space measuring time-of-flight principles is due to the commercial availability of respective measurement systems that are capable of simultaneously acquiring up to three components of three-dimensional velocity fields. As a result, these systems are widely applied, and the related research work is reported. Figure 3: Measurement arrangement of time-of-flight principles illustrated for the position measurement of a scattering particle (measurement of one velocity component, acceleration neglected). Figure 2: Measurement arrangement of Doppler principles illustrated for the light scattering on a single particle (measurement of one velocity component, acceleration neglected). In contrast to this, measurement systems based on other principles currently seem to have a lag in development. However, in particular, Doppler principles are widely used as well and are advantageous for certain applications, which are illustrated for two examples. With a perpendicular arrangement of the illumination and observation direction, Doppler and time-of-flight principles allow one to measure different velocity components. For narrow optical accesses, which means low numerical apertures, the measurement of all three velocity components with a single principle is only achievable with additional observation or light incidence directions. If the additional optical access is not available or undesired, then the combination of both principles allows one to obtain measurements of all three velocity components with only one light incidence direction and one observation direction [34; 35; 36]. A further example of a beneficial combination of Doppler and time-of-flight principles is reported in [37], where a time-of-flight principle is used to resolve the velocity field image, but with a lower spatial and temporal resolution than the simultaneous single point Doppler measurement. As a result, turbulence investigations in an unsteady swirl flow could be performed together with an analysis of the global flow structures. The two examples show that hybrid approaches of combining Doppler and time-of-flight principles are possible and can offer advantages. The examples further demonstrate that each of the two fundamental measurement approaches has its own characteristics and benefits and that both approaches complement each other.