# A Review of Experimental Techniques for Measuring Micro- to Nano-Particle-Laden Gas Flows
## 3 Specific Measurement Methods
### Optical Particle Characterization
#### 3.1.2 Laser Doppler Anemometry and the Phase Doppler Analyzer  
As with PIV, LDA is a non-intrusive online measurement technique, with pointwise detection based on light interference. In LDA measurements, two laser beams having similar wavelengths are  
Figure 5: Development of particle image velocimetry over the last two decades. induced to a focus, forming a small measurement volume. A slight frequency shift generated using a Bragg cell results in interference fringes near this focus. The interference of the two laser beams leads to alternate bright-dark fringes, reflecting the intensity modulation. These fringes are parallel to the angular bisector of the incident laser beams. According to the plane wave theory, the width of these interference fringes is given by:  
\[d=\frac{\lambda}{2\sin\frac{\theta}{2}} \tag{3}\]  
where \(d\) is the interference fringe width, \(\lambda\) is the wavelength of the incident laser beams and \(\theta\) is the angle between the two incident beams. As a tracer particle crosses these fringes, the scattered light intensity is strongest in the bright fringes and weakest in the dark fringes. This light scattering is measured, producing a modulation signal with a Doppler shift, which is directly proportional to the particle velocity component perpendicular to the angular bisector of the incident beams, as described in Equations (4) and (5). \[f_{D}=\frac{1}{t}=\frac{U_{p}}{d} \tag{4}\]  
\[f_{D}=\frac{2\sin(\
icefrac{{\theta}}{{2}})U_{p}}{\lambda}\Leftrightarrow U _{p}=\frac{1}{2}\frac{f_{D}\lambda}{\sin(\
icefrac{{\theta}}{{2}})} \tag{5}\]  
where \(f_{D}\) is the Doppler shift, \(t\) is the transition time to cross a fringe and \(U_{p}\) is the particle velocity component perpendicular to the angular bisector of the incident beams. Photomultipliers transform the fluctuations in the scattering intensity into an electrical signal of Doppler pulses. This signal is filtered and amplified using a signal processor, and the Doppler shift is obtained from spectral analysis of the processed digital signal using FFT, as shown in Figure 6. Therefore, the particle velocity component can be calculated using Equation (5). Similarly, two other velocity components can be measured using supplementary laser beam pairs of different wavelength. The scattering intensity distribution for a spherical particle predicts that the photodetector would receive the most powerful scattering signal when placed in front of the incident beams, with a 0\({}^{\circ}\) scattering angle. An LDA system with this configuration is called a forward LDA, whereas a backward LDA has the incident laser and photodetector on the side having the weakest signal. The principle of the LDA may be described in the other way using the Doppler effect, which indicates the change in frequency or wavelength of sound or light for an observer moving relative to its emitter. In LDA, a moving particle receives the plane light waves, which are emitted from laser  
Figure 6: Schematic showing laser Doppler anemometry. beams, and transmits them to the stationary photodetectors simultaneously. This process leads to an additional Doppler shift when the scattered light is received from a stationary observer. Then, the frequency of light received at the photodetector can be given by:  
\[f_{r}=f_{e}\frac{1-\frac{\overrightarrow{v}\cdot\overrightarrow{l}}{c}}{1- \frac{\overrightarrow{v}\cdot\overrightarrow{k}}{c}} \tag{6}\]  
where \(f_{e}\) is the frequency of the laser source, \(\overrightarrow{v}\) is the velocity of the moving particle, \(c\) is the velocity of the light and \(\overrightarrow{k}\) and \(\overrightarrow{l}\) are unit vectors in the direction of the incident light and the direction of the light transmitted from the particle to the receiver.