# Impacts of Micro-Deviations of Aperture on the Characteristics of Collision Atomization Field
## 3 Principle and Methods
### The Extraction Method of Atomized Particle Information  
Droplet diameter is estimated by laser interferometric particle imaging technology [7; 32; 33; 34], which was initially proposed by [PERSON] nig et al. [32] in 1986 based on the scattered light distribution of particles. The relationship between light intensity distribution and particle diameter is accessed by Mie scattering theory. A focused laser beam is experimented to irradiate the particle field, and a one-dimensional light intensity detector is employed to receive the scattered light in the forward scattering region of the particle. Instantaneous particle size distribution is achieved, which convinces that this arrangement incarnates ultra-precision. IPI technology has become a hot topic in particle field measurement because of its non-contact and high-precision characteristics. It is also suitable for collision atomization particle field.  
Figure 4 is the IPI measurement optical path for colliding particle field. The specific measurement process is as follows: the laser emits a thin beam, which is expanded, filtered and collimated, compressed into a sheet by a cylindrical lens and irradiates the particle field to be measured. Scattered light imaging of the single droplet is shown in Figure 5. When the spherical particles are irradiated by laser beam, the focused images of reflected light and refracted light are generated on the focusing image plane of particles, and the interference fringe pattern is formed on the defocusing image plane of particles. The diameter information of particles can be obtained by analyzing two-point image or interference particle fringe pattern. Based on the phase difference method, the formula of droplet size is deduced as follows  
\[d_{p}=\frac{2\lambda}{n_{1}f}\left(\cos\frac{\theta}{2}+\frac{n\sin\frac{ \theta}{2}}{\sqrt{1+n^{2}-2n\cos\frac{\theta}{2}}}\right)^{-1} \tag{3}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Nozzle ID** & **Designed Value (mm)** & **Inlet \(D_{i}\) (mm)** & **Outlet \(D_{o}\) (mm)** & **Mean Error (\%)** \\ \hline \(N_{1}\) & 0.95 & 0.94736 & 0.95152 & \(-\)0.059 \\ \(N_{2}\) & 0.96 & 0.96273 & 0.96084 & 0.186 \\ \(N_{3}\) & 0.97 & 0.96933 & 0.97216 & 0.077 \\ \(N_{4}\) & 0.98 & 0.97879 & 0.97753 & \(-\)0.188 \\ \(N_{5}\) & 0.99 & 0.98785 & 0.99219 & 0.002 \\ \(N_{6}\) & 1.00 & 1.00085 & 1.00337 & 0.211 \\ \(N_{7}\) & 1.01 & 1.00978 & 1.01198 & 0.087 \\ \(N_{8}\) & 1.02 & 1.02327 & 1.02423 & 0.368 \\ \(N_{9}\) & 1.03 & 1.02892 & 1.02826 & \(-\)0.137 \\ \(N_{10}\) & 1.04 & 1.04204 & 1.03775 & \(-\)0.010 \\ \(N_{11}\) & 1.05 & 1.04502 & 1.05174 & \(-\)0.154 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Geometric dimension of nozzles measured by the optical fiber probe system.  
Figure 3: Experimental setup of the fiber probe.  
where \(f\) is the ratio of \(\alpha\) (the collection angle) to \(N\) (the number of interference fringes), which means the frequency of interference fringes, \(\lambda\) is the wavelength of the laser (nm), \(n\) is the relative refractive index, \(n_{1}\) is the air refractive index and \(\theta\) is the scattering angle (\({}^{\circ}\)).  
The measurement of the atomization cone angle is completed by image shooting and post-processing of atomization field. Through image processing and experimental shooting, the collision atomization image is obtained, and the specific software is used for programming to realize the filtering and denoising (mean filter), binarization and morphological edge extraction of the original image, so as to obtain the outer contour of the atomization field. The atomization cone angle can be obtained by importing the processing image into the IPF6.0 software and automatic recognition processing. Taking an atomization simulation result as an example, the original, process and result images of the atomization cone angle detection are shown in Figure 6a-c, respectively.  
Figure 4: Schematic diagram of the IPI measurement optical system for colliding particle field.  
Figure 5: Scattered light imaging of single droplet.