Modeling and experiment on 3D position and size measurement of opaque droplet cloud with astigmatic dual-beam interferometric particle imaging (ADIPI)

Abstract This work investigates the astigmatic dual-beam interferometric particle imaging (ADIPI) to enable the measurement of the three-dimensional (3D) spatial position and particle size of spherical opaque particles. A general theoretical model based on the generalized Huygens-Fresnel integral and the ray transfer matrix model is established to characterize ADIPI signal, revealing the orientation and spacing of typical ADIPI fringes relating to the depth position and size. The model is applied to study the effects of several parameters, such as the focal length of cylindrical lens, the focal length of spherical lens and the distances between the elements in the optical system, on the relationship between the inclination angle of fringes and depth position by theoretical simulation. Experiments of ADIPI, incorporating dual-view digital inline holography (DIH), is performed to demonstrate the utility of ADIPI in the measurement of opaque spherical particles. Through the analysis of the general ADIPI signal based on two-dimensional Fourier transforms, 3D position and the particle size are obtained. The results of ADIPI, in both of the depth position and size measuring, exhibit a high degree of consistency with DIH's, given the average relative deviations of 5% in size measuring and 1% in depth position, respectively. As a new measurement approach, the ADIPI signal exists at arbitrary angle except the two laser beam axes, determining the flexibility of ADIPI configurations which facilitates its great prospect in opaque particles measurement, e.g., metal combustion, chip manufacturing, 3D metal printing.