Interferometric out-of-focus imaging simulator for irregular rough particles

Abstract

We present the development of an original simulator to predict interferometric out-of-focus patterns created by irregular rough particles. Despite important simplifications of the scattering properties, this simulator allows to predict quantitative properties of the speckle-like patterns: i.e. the dimension of the central peak of the 2D-autocorrelation of the pattern. This parameter can then be linked to the size and the shape of the particle projected on the CCD sensor, in cases where there is no exact theoretical formulation to calculate the scattered intensity. An experimental demonstration is performed with irregular NaCl salt crystals.

On the morphology of irregular rough particles from the analysis of speckle-like interferometric out-of-focus images

“…Its coefficients depend on the coefficients of the optical transfer matrix describing the optical elements encountered between the particle and the sensor. The procedure has been detailed in references [12,17] in the case of droplets represented by a pair of Dirac emitters, and has been validated in all cases that could be tested experimentally [7,8,12,17]. We obtain the following expression of the electric field in the plane of the CCD sensor [12]:…”

“…It is then possible to evaluate the expression of the electric field in the plane of the CCD sensor. According to reference [12], and neglecting the role of the aperture of the imaging system (big aperture), the electric field can be evaluated in the plane of the CCD sensor from a generalized Huygens Fresnel integral [17]. Its coefficients depend on the coefficients of the optical transfer matrix describing the optical elements encountered between the particle and the sensor.…”

“…Recently, it was demonstrated that the analysis of irregular rough particles could be done with this technique [12]. In this case, the-out-of-focus images are speckle-like patterns.…”

“…The aim of this paper is to establish and verify such a relation with experimental data. As in reference [12], particles will be modeled as a collection of a large number of coherent point emitters (the so-called glare points in the case of droplets, which are then only two [14][15][16][17]). Under this assumption we will show theoretically that the 2-dimensional Fourier transform of the speckle-like out-of-focus pattern is directly linked to the 2-dimensional autocorrelation of the particle's shape.…”

Numerical Models for Exact Description of in-situ Digital In-Line Holography Experiments with Irregularly-Shaped Arbitrarily-Located Particles

“…In the case of irregular rough particles such as ice crystals, the out-of-focus image shows a speckle-like pattern. The size of the droplet is deduced from the frequency of the fringes, while size and ellipticity of irregular particles are deduced from size and ellipticity of the speck of light in the speckle pattern [40]. In this last case, it can be demonstrated that the 2-Dimensional Fourier transform of the speckle pattern gives the 2-Dimensional autocorrelation of the global shape of the object [41].…”