A New Method for Determining the Sampling Volume and the Number of Particles Within It for Particle Concentration Identification in Defocused Interferometric Particle Imaging

Interferometric particle imaging (IPI) is a robust technique for measuring particle size and velocity. In defocused IPI that is uniquely valuable to quality control of a spray field, a reliable method for identifying the particle concentration in the volume sampled by the sheet beam remains outstanding. This paper proposes a new approach to the determination of the sampling volume of defocused IPI and the number of particles within the sampling volume for informing the particle concentration. The methods for determining the sampling volume and the number of particles within the sampling volume are documented with a new set of formula derived using conventional ray-tracing and interferometry principles. For any defined measurement geometry, the sampling volume is quantitated when the lateral and elevational dimensions of the sheet beam and the defocusing distance are known. The number of particles in the sampling volume is counted by determining whether or not a particle is within the sampling volume, upon the analysis of the size range [Φ
_pix2
, Φ
_pix1
] of the interference circle. The method for identifying particle concentration in defocused IPI is tested on synthetic interferogram (1% noise) corresponding to first, particles of the same size of 45 μm at different concentrations ranging from 0.0040 to 0.239 mm-3 and, second, particles of 0.0119 and 0.119 mm-3 concentrations with the sizes ranging from 10 to 90 μm. This new method for quantitating particle concentration in defocused IPI is then examined against experimental concentrations of particles of 10, 21.3, and 45 μm in size, respectively. The largest experimental error for 45 μm particles with the concentration of 0.006 mm-3 is 10.4% and decreases with the increase of the particle concentration. This method for identifying particle concentration is expected to be applicable to various areas wherein particle analysis is to be rendered by defocused IPI.