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Exp Fluids (2014) 55:1851

DOI 10.1007/s00348-014-1851-0

RESEARCH ARTICLE

Irregular particle sizing using speckle pattern for continuous wave laser applications

Pedro García Carrascal · Sara González Ruiz ·

Jeroen van Beeck

Received: 30 July 2014 / Revised: 25 October 2014 / Accepted: 27 October 2014 / Published online: 5 November 2014 © Springer-Verlag Berlin Heidelberg 2014 to access to both sides of a particle to perform measurements (Tropea 2011). In order to overcome this problem, new ways to measure and characterize irregular particles are required. A technique that requires the access to only one side of the particle allows its implementation in a compact measurement device. As a contribution to such goal, a technique to measure the size of irregular particles using the speckle pattern produced from the backscattering of laser light is proposed. This technique uses a continuous wave laser as a low-cost alternative to a pulsed laser. 2 Interferometric laser imaging for irregular particle sizing

The speckle pattern is an interference pattern that presents a granular intensity distribution (Fig. 1b). It is created in the out-of-focus plane by the light scattered by an irregular object when it is illuminated with coherent light, like the one coming from a laser source (Goodman 1975; Formin 1998).

The retrieval of irregular particles size from its speckle pattern has been studied in different ways by several authors as Ulanowski et al. (2012), Brunel et al. (2014) or González Ruiz et al. (2014). This paper continues with the work introduced by the latter, based on the frequency analysis of the speckle pattern. The relation between the frequency content of the speckle pattern and the particle size is briefly introduced in this section, but a more detailed mathematical background can be found in the reference of

González Ruiz et al. (2014).

When an irregular and rough particle is illuminated by parallel light, the surface of the particle appears totally covered by radiant points when observed in-focus (Fig. 1a).

Abstract A technique to retrieve the size of irregular particles using the speckle pattern produced from the scattering of laser light is presented. A sizing algorithm based on the maximum curvature peak detection of the Fourier transform of the speckle pattern is introduced, and its application to sand particles with and without motion is studied, using a continuous wave laser. The sizes obtained with this algorithm are in good agreement with the sizes resulting from shadowgraph measurements. It was also observed that the properties of the speckle pattern are independent on the scattering angle. When using a continuous wave laser, special attention is paid to the exposure time while recording the speckle pattern. This special care avoids the images to be blurred as a consequence of the speckle pattern displacement and reshaping due to particle rotation. Finally, further recommendations to define the setup parameters are given in order to apply the technique, focusing on a continuous wave application. 1 Introduction

The main current techniques to characterize irregular particles in the micrometer range, shadowgraphy and forward

Fraunhofer diffractometry (Onori and Barbosa 2013) need

Electronic supplementary material The online version of this article (doi:10.1007/s00348-014-1851-0) contains supplementary material, which is available to authorized users.

P. García Carrascal (*) · S. González Ruiz · J. van Beeck von Karman Institute for Fluid Dynamics, Chaussée de Waterloo 72, 1640 Rhode-St-Genèse, Belgium e-mail: pgarciacarrascal@gmail.com

S. González Ruiz e-mail: sara.gonzalez.ruiz@vki.ac.be

Exp Fluids (2014) 55:1851 1 3 1851 Page 2 of 10

These radiant points are called glare points, and their distribution along the particle surface is called glare point pattern (van de Hulst and Wang 1991). Therefore, the glare point pattern of an irregular particle represents the particle shape seen from a certain direction. The shape of a profile g(x) taken through a certain direction in the glare point pattern (with x meaning distance in the image) corresponds to a box whose base is equal to the size of the particle D in such direction (Fig. 2a).

Using Fourier optics, the glare point pattern can be defined as the Fourier transform (F ) of the far-field amplitude function S1(θ) over the angles covered by the lens, being θ the scattering angle (van de Hulst and Wang 1991; van Beeck and Riethmuller 1996):

The normalized light intensity in the far-field i1(θ) is defined as follows: (van de Hulst 1957):

By means of the Wiener–Khintchine theorem, the relation between speckle pattern and glare point pattern is expressed in Eq. 3: where g(x)⊙ g∗(x) is the autocorrelation of the function g(x). (1)g(x) = F{S1(θ)} (2)i1(θ) = |S1(θ)|2 (3)g(x)⊙ g∗(x) = F{i1(θ)} 3 Data inversion algorithm

Equation 3 shows the connection between angular frequencies in the speckle pattern and distances within the glare point pattern.

In the case of an irregular particle, g(x) corresponds to a box with the base equal to the particle size D. Its autocorrelation produces therefore a triangle of base equal to 2D (Fig. 2b).

According to this and using Eq. 3, the Fourier transform of an intensity profile i1(θ) of a speckle pattern produces a triangle with a base equal to a frequency FD that can be related to the particle size D through the incident light wavelength λ, in accordance to the expression shown in Eq. 4 (González Ruiz et al. 2014):

The latter assumes that the relation between speckle frequencies and distances in the particle is the one that results from the analogy with Young’s double slit experiment (Fig. 3). Using this, the irregular particle size D can be calculated from its speckle pattern.

Applying this relation, two different experimental studies were performed, analyzing particles with and without motion. In all cases, only one particle at a time was measured.

The proposed technique was applied to both situations following the next main steps (Fig. 4): 1. Speckle pattern recording and calibration. 2. Intensity profiles extraction from speckle pattern along a certain direction. 3. Fourier transformation of parallel intensity profiles and ensemble averaging of them. 4. Detection of FD appearing in the Fourier transformed profile. 5. Particle size calculation using Eq. 4.