# Imaging Flow Velocimetry with Laser Mie Scattering
## 2 Measurement Approaches  
### Application of Mie Scattering  
In order to obtain Mie scattering, the measurement approaches require scattering particles in the flow to be measured. If no natural scattering particles exist, artificial particles are added to the flow, which is known as seeding. The generation, the characterization and the application of different seeding particles is described in [26]. As an example, a typical liquid seeding material for flows with ambient temperature is diethylhexyl sebacate (DEHS), and a typical solid seeding material for flame flows is titanium dioxide (TiO\({}_{2}\)). Due to the typically necessary seeding, the flow measurement approaches based on Mie scattering are intrusive techniques.  
Since the light that is scattered on the particles is detected and evaluated, the velocity of the particle motion is measured. Note that it is a common case that the desired quantity is not the particle velocity. However, the particle velocity equals the flow velocity, if the particles follow the flow with no slip, if the particles have no self-motion and if the inserted particles do not change the flow behavior. For the derivation of the different measurement approaches, these ideal conditions are assumed to be fulfilled. The otherwise resulting limits of measurability are treated in Section 4.  
The drawbacks of using seeding particles to achieve Mie scattering are accepted due to the advantage of a significantly increased scattered light intensity in comparison with flow velocity measurements based on Rayleigh scattering with no seeding particles. In order to quantify the improvement of the scattered light intensity, the calculated scattering cross-section is shown in Figure 1 as a function of the radius of a scattering particle that is assumed to be spherical and made of DEHS. The calculation is conducted according to [25] for a refractive index of 1.45, which is valid for DEHS at a light wavelength of 650 nm. In the Rayleigh scattering regime, the scattering cross-section increases proportional to the sixth power of the particle radius. For an increased scattering particle size from 0.1 nm (order of magnitude of a molecule, Rayleigh scattering) to 1 \(\upmu\)m (typical order of magnitude of a seeding particle, Mie scattering), the scattering cross-section is increased by more than 16 orders of magnitude. Considering a spatial resolution of 100 \(\upmu\)m\({}^{3}\) with air at normal pressure and room temperature as fluid, about \(2\times 10^{13}\) fluid molecules are present according to the ideal gas law. Hence, the advantage of the higher scattering cross-section of seeding particles is partially equalized by the low number of scatterers. As a result, an increase of the scattering power of 1000 remains for the considered example. Another beneficial aspect of using seeding particles is the reduced light extinction, because the seeding is usually applied locally. Furthermore, the angular-dependent scattering and polarization effects have to be taken into account. For instance, Mie scattering has in general a stronger forward scattering than sidewards and backward scattering, which means a reduced light extinction in comparison to Rayleigh scattering. As a result, the potential of Mie scattering approaches for imaging flow measurements with acceptable uncertainty also at high measurement rates is illustrated, in particular with respect to the necessary distribution of the available light energy over space and time.  
Figure 1: Calculated scattering cross-section over the particle radius normalized by the wavelength for a spherical particle made of diethylhexyl sebacate (DEHS) with a refractive index of 1.45 at 650 nm.