Determination of the Size of Irregular Particles Using Interferometric Out-of-Focus Imaging

Abstract

We present a mathematical formalism to predict speckle-like interferometric out-of-focus patterns created by irregular scattering objects. We describe the objects by an ensemble of Dirac emitters. We show that it is not necessary to describe rigorously the scattering properties of an elliptical irregular object to predict some physical properties of the interferometric out-of-focus pattern. The fit of the central peak of the 2D autocorrelation of the pattern allows the prediction of the size of the scattering element. The method can be applied to particles in a size range from a tenth of micrometers to the millimeter.

Interferometric Ice Particle Imaging in a Wind Tunnel

“…where I is the intensity of the out-of-focus pattern of the particle, G0 is the electric field scattered by the illuminated particle, λ is the wavelength of the laser and λBtot is the scaling factor between both functions which is deduced from the set-up. Experimentally, this correspondence between the two-dimensional autocorrelation of in-focus images with the corresponding two-dimensional Fourier transform (2DFT) of the IPI images has been validated in size and shape in many cases [13][14][15][27][28][29]. In the present study, we will use this formalism to estimate the dimensions of particles from the 2D-FT of the speckle images.…”

“…The analysis of interferograms requires methods covering the case of interferograms of single particles to the more complex case of overlapping interferograms of closed particles. We see that the IPI technique can be used in an extreme environment where the wind speed can reach 70 m/s by following the same procedure as for IPI measurements in conventional environments [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Thus, the IPI technique seems usable for carrying out airborne measurements.…”

“…Set-ups have been optimized [4][5][6], and the technique has found many applications in different types of flows [7][8][9][10][11]. The technique has been extended to the analysis of irregular rough particles in a flow (such as sand, ice or coal particles and ashes) [12][13][14][15][16][17][18]. The technique is thus well adapted to the characterisation of triphasic flows such as the mixing of liquid water droplets and ice crystals in clouds .…”

3D-reconstructions for the estimation of ice particle’s volume using a two-views interferometric out-of-focus imaging set-up

“…Neglecting the role of the aperture of the imaging system (large aperture), the electric field G(x, y, z) can be calculated in the plane of the CCD sensor using a generalized Huygens-Fresnel integral. 20,21 It is given vs coefficients Atot, Btot, Ctot, and Dtot of the optical transfer matrix between the plane of the different emitters and the plane where the CCD sensor is located. The 2D Fourier transform of the intensity in the plane of the CCD sensor FT 2D [I](λBtotu, λBtotv) and the 2D autocorrelation of the initial repartition of the point emitters A 2D [G 0 ](dx, dy) are not rigorously equal.…”

“…4 Initially developed to analyze spherical droplets or bubbles, [5][6][7][8][9][10][11][12][13][14][15][16] it can be extended to rough particle sizing through the processing of speckle-like patterns. [17][18][19][20][21][22][23][24] The field of view can reach tens of cm 2 , the working distance can exceed 10 cm, and the technique is scalable in such a way that the size range can cover 2 decades: from tens of micrometers to a few millimeters. In recent years, configurations enabling a 3D location of particles with a sole CCD sensor, or multiviews acquisition systems that can perform a 3D shape recognition of particles have been demonstrated.…”