3D boundary line measurement of irregular particle ...

Powder Technology 295 (2016) 96–103

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3D boundary line measurement of irregular particle with digital holography Yingchun Wu a,b, Xuecheng Wu a,⁎, Longchao Yao a, Marc Brunel b, Sébastien Coëtmellec b, Denis Lebrun b, Gérard Gréhan b, Kefa Cen a a b

State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China UMR 6614/CORIA, Normandie Université, CNRS, Université et INSA de Rouen, BP12 76801 Saint Etienne du Rouvray, France

a r t i c l e

i n f o

Article history: Received 25 June 2015 Received in revised form 5 October 2015 Accepted 28 November 2015 Available online 28 January 2016 Keywords: Digital holography Irregular particle 3D boundary line Particle morphology

a b s t r a c t The morphology of an irregular particle plays a key role in its interactions with the surroundings, and the 3D characterization of an irregular particle is of essential importance. Digital inline holography in Gabor configuration is applied to measure the 2D shadow texture and 3D position, as well as the 3D boundary line of irregular particles. The depth position of the 3D boundary line can be determined with a criterion of the local deviation of the directional gradient over a small tilted rectangle, which covers the interrogated boundary section. The method is firstly verified by rigorous simulated particle holograms and then by accurate experimental fiber hologram. The 3D boundary line of an irregular coal particle is also measured. Results show that the 3D boundary line of an irregular particle can be accurately retrieved from the reconstructed volumetric optical particle field. This capability of 3D boundary line measurement enables the application of digital inline holography to the 3D diagnostic of the morphology and dynamics of irregular objects, including 3D rotation. © 2016 Elsevier B.V. All rights reserved.

1. Introduction The particulate is a common existing form of both natural and artificial materials, and is widely encountered in both daily activities and scientific and industrial processes. A non-exhaustive list of examples includes food powders, soil and sand, drops and solid fuel particles [1]. Studies of particles and their interactions with the surroundings have attracted attention for millennia. Apart from regular particles, such as spheres, cubes and so on, which can be described by simple analytic parameters and are consequently widely used in numerical investigations of particle systems [2], irregular particles have a complicated 2D image texture or even a 3D surface, which can be mathematically expressed as a 2D Fourier series or a 3D spherical harmonic series respectively [3]. In order to characterize the geometrical properties of irregular particles, several descriptors have been proposed. Based on the dimensions of the associated variables and methods, those descriptors can be classified into 1D “form”, 2D “shape”, and 3D “surface” descriptors [4–8]. The term “form” is usually used for the 1D parameters, i.e. length, width and thickness [4,6], and the 2D “shape” usually refers to the characterization of the particle projection image, i.e. roundness and area, and consequently, “surface” is related to the real 3D geometrical properties which are beyond the descriptions offered by both 1D “form” and 2D “shape”, such as volume and sphericity. In recent decades, several optical techniques have been developed to measure those geometrical properties. ⁎ Corresponding author. E-mail address: [email protected] (X. Wu).

http://dx.doi.org/10.1016/j.powtec.2015.11.061 0032-5910/© 2016 Elsevier B.V. All rights reserved.

The laser diffraction based methods and devices have been widely used to measure the particle size distribution [9]. Phase Doppler anemometry (PDA) [10] can measure the size as well as the translational motion of transparent spheres inside a small control volume. Interferometric laser imaging for droplet sizing (ILIDS) has been extended to measure the size, as well as the 3D position, of transparent, spherical particles [11], and even to characterize the 2D dimensions of irregular particles [12]. Direct imaging with a lens or an objective is a common approach that has been extensively employed for the characterization of 2D morphology of irregular particles with image analysis [13]. To gain a deeper understanding of an irregular particle, it is of interest to measure the real 3D surface, and three dimensional laser scanner (LS) [14] and computed tomography (CT) have been introduced as experimental solutions to achieve this. The laser scanner (LS) technique scans the exterior surface of an object and then reconstructs the 3D external enveloping surface from the measured points [14]. The computed tomography (CT) method provides both external and internal 3D information of the scanned irregular particle, since the slices used for 3D reconstruction depend on the transmission which is related to both absorption and scattering process [15–17]. The laser scanning and computed tomography methods require sampled data from multiple viewpoints, and measurements are usually made in an off-line manner with the particle well positioned, which could be furthered to the in-situ measurements of moving irregular particles. Holography is a real 3D imaging technique. Digital holography has been demonstrated to be a promising tool for the 3D diagnostics of a particle field [19], because it can not only measure the shape, size and

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3D position of the particle from its reconstructed in-focus image [19,20], but is also capable of measuring the particle's 3D motion in the manner of particle tracking/image velocimetry (PTV/PIV) [19,21,22,29]. Moreover, digital holography for particle measurement has a relatively larger depth of field compared with direct imaging. Due to these attractive features, comprehensive investigations have been performed on the particle hologram reconstruction [24–26], particle detection [27], 3D locating [28] and even 3D velocity [29] and rotation evaluation for irregular particles [30–32]. Successful demonstrations of applying digital holography to measure a variety of particles, including irregular solid particles [21], overlapped droplets [27,33], microorganisms [19], etc. have been reported. The inline holography in Gabor configuration is widely employed because of its easy implementation and robust performance. However, digital inline holography has usually been used to reconstruct only the 2D shadow texture for the measured irregular particle in most past applications, even the 3D information of the irregular particle encoded in the reconstructed optical 3D particle field. As regards 3D morphology measurement, side or even backward reflected light is used as the object wave for the opaque object to reconstruct the 3D surface [37], and attention should be paid to the scattering properties of the object in this configurations, especially in the case of glory points. Another approach to surface contouring is phase-shifting digital holography, which determines the morphology from the difference of the reconstructed phases [38], and which needs to record a series of holograms. Besides the 2D shadow texture and 3D position, this work aims to retrieve the 3D boundary line of the shadow image of an irregular particle with digital inline holography in Gabor configuration. The methodology, including the wavelet reconstruction method and 3D position determination, as well as the algorithm which uses the local deviation of directional gradient, will first be introduced. Then rigorous simulated particle holograms and experimental tilt carbon fibers holograms are used to test the proposed method. Finally, the 3D boundary line of an irregular coal particle is measured.

extracted from the 3D optical particle field. Details of the algorithms, including reconstruction, are presented below. 2.1.1. Reconstruction The holograms are reconstructed using the wavelet reconstruction method [25], and a slice image in the reconstructed 3D optical particle field can be generated through a convolution of the particle hologram Iholo(x, y) and the wavelet function ψz(x, y): Iðx; y; zÞ ¼ 1−I holo ðx; yÞ⊗ψz ðx; yÞ: 2

We first briefly review particle measurement using digital holography. Digital holography involves two steps: digital recording and numerical reconstruction. In digital recording, the holographic interference fringes of the reference wave and the light scattered by the particles (object wave) is recorded by an array sensor (CCD) to produce a particle hologram, as shown in Fig. 1. Numerical reconstruction is used to reconstruct the 3D optical particle field slice by slice by illuminating the hologram with the reference wave, as illustrated in Fig. 1. Then the 3D information (size, 3D position and 3D boundary line) can be

2

2

2

σ tion. The term Mψ ¼ 1þσ 4 , is to ensure a zero mean value of ψz(x, y). 2

þy The windowing function expð−π xλzσ 2 Þ, with a width of σ, is used to meet the two conditions [25]: 1) the wavelet function is confined within CCD area; 2) the Shannon's sample condition should be satisfied in the wavelet function, in avoidance of the under-sampling effect of the CCD. 2

2

2.1.2. 3D position and shape The 3D position of the particle's centroid and the 2D morphology are determined from the reconstructed 3D optical particle field according to the algorithm in Ref. [28]. First, an image is synthesized from the reconstructed 3D optical particle field using a wavelet image fusion algorithm, called the extended focus image (EFI). The depth of field of EFI is extended to cover the whole particle field, and all of the reconstructed particles are focalized in the EFI [28]. Then the EFI is used to detect the particles through binarization using an adaptive threshold algorithm, and thus the particle morphology including transversal centroid and 2D outline can be obtained. The Tenengrad variance (TENV) [39] in a local window n × m over the centroid of each detected particle is computed as the focus metric: o2 XXn S obel½I ðn; m; zÞ−Sobel½Iðn; m; zÞ ; n

2.1. Reconstruction and 3D position

ð1Þ

þy þy π ½ sinðπ x λz Þ−Mψ  expð−π xλzσ The linear chirp function: ψz ðx; yÞ ¼ λz 2 Þ, is the mother wavelet function used for particle hologram reconstruc-

FcðzÞ ¼ TENV ¼

2. Methodology

97

ð2Þ

m

where the S obel denotes the Sobel operator, and □ is the average of □. The particle's optimal depth position is determined at the peak position of its focus metric curve, which corresponds to the features of the in-focus image: there is large gradient at the particle image boundary and uniform intensity extremum. Note the obtained particle depth position is an optimal and averaged one for its centroid. The transversal centroid (x, y) of the particle can be precisely calculated up to sub-pixel accuracy in the Gabor inline holography configuration under a plane wave illumination. Due to the twin image and finite aperture as well as the resolution of CCD, the particle depth position (zme) determined from the focus metric curve Fc(z), suffers from an

Fig. 1. Illustrations of particle holography including recording and reconstruction.

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inevitable uncertainty of (zerr = zme − zre), where the zme and zre are the measured and the actual recording depth position of the particle respectively. The absolute uncertainty zerr of the particle depth position is usually of order of the magnitude of the particle size using the local Tenengrad variance criterion in Eq. (2), with a range from dozens of even up to thousands of micrometers [22,23,28]. The relative uncertainty of the depth position zerr/zre could be as small as to 1% in the far field particle holography, and thus this uncertainty, and the obtained depth position, could be acceptable for 3D position determination. 2.2. 3D boundary measurement The synthesized EFI, or the reconstructed optimal in-focus image, depicts the 2D shape of the shadow projection of the irregular particle. In fact, the irregular particle could have a complex 3D surface, and its projections from different directions could be different and each projection partially reflects its 3D morphology, as shown in Fig. 2. Fig. 2 illustrates two key terms used in this paper: silhouette and 3D boundary line (or contour generator). The 2D outline of the particle's projection image (or EFI) is called the silhouette, which separates the particle from the background in the image plane. A collection of possibly discontinuous 3D space curves and points located on the surface of the irregular particle, and whose projection matches the silhouette, is called the 3D boundary line, (or contour generator [40] in the computer vision community), as shown in Fig. 2. If the particle surface is smooth, a point on the surface with its surface normal perpendicular to the sight line (plane wave in inline holography) could be the silhouette point. Points on the surface edge if the particle surface is non-smooth or even discontinuous, can also be silhouette points. These points strongly affect the diffraction properties of the irregular particle, and thus information of the 3D boundary line of the particle is encoded in the particle hologram through the objective wave, and decoded in the 3D optical particle field after reconstruction. The 3D boundary line associated with the silhouette could be discontinuous, and similar to a piecewise function with step changes. The scanning step between the slice images is usually less than the particle size in order to obtain high depth resolution. Consequently, part of the 3D boundary line located in a slice image is in-focus, while other parts outside of the slice image are out-of-focus. The reconstructed optical field of a ROI image over the in-focus particle outline, is dominated by the in-focus optical field of its associated local 3D boundary line, and the out-of-focus optical field of other parts is minor. Thus, the 3D boundary line can be retrieved from its local region, and is determined with a criteria for local deviation of the directional

Fig. 2. Illustration of the silhouette of the projection image and the corresponding 3D boundary line of an irregular particle.

intensity gradient. The procedure to compute the 3D boundary line is as follows: a) Compute the 2D silhouette of the irregular particle image from its EFI, and the normal unit vector n of the local outline, as illustrated in Fig. 2. b) For each small section of the silhouette, select a small tilted rectan^ gular window, whose orientation is parallel to the normal vector n the local silhouette, as shown in Fig. 2. Then calculate the intensity gradient G of each slice image, and its scalar projection Gn in the di^ through their inner product: rection of the local normal vector n

^: Gn ¼ G  n

ð3Þ

Here, the use of a tilted rectangle, rather than the axis-parallel rectangle whose sides are parallel to the axes of Cartesian coordinates, ensures that the rectangle is as narrow as possible, in order to avoid any disturbance by the 3D boundary line of its neighbor silhouette outside of the window. The directional gradient is employed to minimize the uncertainty caused by other boundary points inside the tilted window, ^ and depth position differ significantly whose local normal vector n from those of the interrogated boundary segment. This usually occurs at the corner of the irregular polygonal particle image, with concave and convex silhouettes. c). Compute the standard deviation of the directional gradient Gn inside the window, and the optimal in-focus position is reached at the maximum. This algorithm is performed for every section of the particle's silhouette to retrieve the 3D boundary line, as illustrated in Video 1. 3. Simulation validation This local deviation of directional gradient algorithm for a particle's 3D boundary measurement is first verified using simulated standard particle holograms. The holograms of homogeneous, spherical particles are simulated in the framework of generalized Lorenz–Mie theory [34], which can take the parameters of the particle (3D spherical surface, size and refractive index), CCD and laser beam into account. Holograms of a single particle located at different depth positions are processed to test the accuracy of the proposed method in the depth determination of boundary sections. The particles have a refractive index of (1.33− i0.5) and (1.33− i0.0) for opaque and transparent particles, respectively. The typical simulated hologram of a single spherical particle, whose centroid is located 20.0 mm from the CCD, is shown in Fig. 3(a), and it is characterized by concentric circular fringes. The reconstructed in-focus image of the spherical image is a circular disk, as shown in Fig. 3(b). The silhouette of the particle image is circular, which is the projection of the outer periphery of the particle. The measured 3D boundary line of the simulated spherical particle is a circular curve, as shown in Fig. 3(b). The depth positions of the boundary sections measured by the local deviation of the directional gradient method, as plotted in Fig. 3(b), range from 19.97 mm to 20.03 mm. The average boundary depth position is 20.01 mm, with a standard deviation of 0.02 mm. The light scattering by an irregular object with a complex 3D surface has not yet been analytically solved, and thus neither does the rigorous simulation of an irregular particle hologram by interfering the reference wave and object wave (scattering light). Here a cloud of spherical particles, whose surfaces do not intersect but whose projections overlap, are used to form an irregular projected image. Holograms of this particle cloud are used to verify the depth position determination method in the scenario of the silhouette projected from the 3D curves at multiple depth positions with a discontinuity. This is a situation that often occurs in real dense particle field in which the particles' projections overlap [27,33]. Assuming the effect of other particles on the light scattering of

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Fig. 3. 3D boundary measurement of simulated single particle hologram.

each particle is negligible, and omitting the multiple scattering between the particles, the light scattering of individual particle is computed, and then summed as the object wave which interferes with the reference wave to form the hologram. Details of the particle hologram simulation can be found in Ref. [34,35] for sprayed droplet field. A typical hologram of three overlapping particles is shown in Fig. 4(a), with complicated hologram fringes. The diameters of the three particles from left to right are 240 μm, 250 μm and 240 μm, respectively. The depth displacement between each of the two particles is 1000 μm. The extended focus image synthesized from the reconstructed 3D optical field, presents the irregular morphology with a complex silhouette through

overlapping in the transversal directions, as shown in Fig. 4(b). A local window covering the overlapped particle images is employed to determine the depth centroid in the classic approach. This approach actually obtains an averaged value, which could yield an unacceptable erroneous evaluation, and thus a special algorithm has been proposed to deal with this problem by separating the holographic pattern of an individual particle via iterative optimization [33]. The 3D boundary line of the irregular particle is shown in Fig. 4(c). The extracted 3D boundary line can be divided into three parts, with each part corresponding to one particle. The depth positions of the 3D boundary line of each particle are quite stable, and consequently two apparent jumps in the depth position

Fig. 4. 3D boundary line measurement of overlapping particle cloud.

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between each two overlapping particles can be observed, as shown in Fig. 4(c). The depth position jumps are 1020 μm and 990 μm for two consecutive overlapping particles from left to right, respectively, which agree well with the exact value. The 3D boundary line can be extended for particle cloud assessment. For example, in the spray field with the prior knowledge that the particles are spherical, we can judge that they are three dispersed particles rather than one irregular object, because the depth position jumps are about four times larger than the particle sizes. In the regions near to the intersections of the particle projections, the extracted depth position of the 3D boundary line might be located between two particles, and the fluctuation of the determined depth position of the 3D boundary line could increase. This is because the reconstructed optical field of this region is affected by the two overlapping particles, and the focus metric in the local directional window might give an average depth position. 4. Experimental results Calibrated experiments on tilted carbon fibers were performed to validate the proposed local deviation of directional gradient method for 3D boundary line determination, and then this method is applied to measure the 3D boundary line of an irregular particle from experimental holograms. 4.1. Micro-holography of tilted fibers In the digital holography experiment for the 3D boundary line measurement of a small irregular particle with the equivalent diameter ranging from dozens to hundreds of microns, it is very difficult to know the exact 3D morphology and the 3D boundary line of the dispersed particle, which could lead to the lack of a benchmark for validating the measurement accuracy of the proposed algorithm. An elaborately designed experiment using continuous carbon fibers measured by micro-holography, was used for accuracy validation. A typical microholography system was set up to capture the holograms of continuous carbon fibers, as shown in Fig. 5. In the micro-holography system, the magnification of the virtual recording plane [29,36], which is located at the imaging plane of the CCD through the objective, was 13.2. The equivalent pixel size of the recorded hologram is 0.56 μm. The tested irregular “particle” was two overlapping carbon fibers, as illustrated in Fig. 5, and each carbon fiber had a diameter of 7 μm. The two fibers crossed at one side with a very small angle, and were well separated at the other side, and thus in the center part, the two fibers overlapped, as shown in Fig. 5. The fibers were placed at a tilt angle of 70 degrees with respect to the collimated laser beam axis. In this configuration, each side of the image of the two overlapped fibers had a small stable

displacement in the depth position, and the depth positions of both sides change along the transverse directions, and a 3D morphology with a predictable boundary was generated with a combination of the two effects. A hologram of the overlapping carbon fiber is shown in Fig. 6(a). The holographic fringes are comprised of a series of oblique lines, whose frequency increases along the y direction from the top to the bottom, resulting from the decrease of the recording distance. The volumetric slice images were reconstructed by scanning from 150 μm to 450 μm, with a depth step of 1 μm. In each slice image, only a small part is infocus, while other parts are out-of-focus. The EFI of the reconstructed fibers is shown in Fig. 6(b), and the light intensity distribution crossing the in-focus part approaches an almost uniform extremum inside the fiber, with a sharp gradient at the fiber boundary, and appears almost the same as that of one fiber. A ROI of the projected image of the tilted fibers with a length of 400 μm, is investigated. The local deviation of the directional gradient method is applied to extract the 3D boundary line of the fiber image, and the measured 3D boundary line is shown in Fig. 6(c). The depth positions of the fiber boundaries at both sides are located between 220 μm and 380 μm, and linearly decrease in the y direction. The slopes of the two boundaries in the depth position are 0.383 and 0.385, corresponding to tilt angles of 69.1° and 69.0° with respect to the laser beam axis, respectively. Fig. 6(d) compares the depth positions of the 3D boundary lines at two sides, and it shows that there is an obvious and stable displacement between the two boundaries. The averaged displacement is 5.0 μm, which is approximately the fiber diameter. This depth displacement of the two boundaries coincides with the fact that it is an overlapping of the two fibers rather than one large fiber, even though the reconstructed image resembles that of one large fiber. Both the measured tilt angle and the boundary depth displacement of the two overlapping oblique fibers present good agreement with the experimental setup, demonstrating the proposed algorithm's capability of accurately measuring the 3D boundary line. 4.2. Irregular particle The 3D boundary of an irregular coal particle is measured by digital holography. A single axis acoustic levitator is used to manipulate the coal particle. The schematic of the experimental setup was the same as that shown in Fig. 5, but the objective was removed and consequently no magnification was introduced. Thus, the pixel size of the hologram was 7.4 μm. The acoustic levitator (SY-2000F, from Shanxi Boyou ultrasonic technology Co. LTD, China) consists of two parts: a transducer and a reflector. The piezoelectric transducer, which is driven by an electrical signal, produces ultrasonic waves. The reflector has a concave surface to enhance the reflected sound field. It was placed opposite to the transducer, and installed on a linear translation stage to adjust the distance

Fig. 5. Schematic of experimental setup for the 3D boundary measurement of tilted fibers and an irregular coal particle with digital holography.

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Fig. 6. Results of experimental calibration by two crossing carbon fibers with micro-holography.

between the transducer and the reflector. In this work, the frequency of the ultrasound was 20 kHz, with a wavelength of 17 mm in ambient air. The sound pressure was about 130 dB. The distance between the transducer and the reflector was 17 mm, producing a one-node acoustic standing wave. An irregular coal particle was placed into the standing ultrasonic wave field, and levitated at the position where the acoustic radiation force exerted on the coal particle balances its gravity. Because of the irregularity of the coal particle surface, the radiation force exerted on the suspended coal particle is not symmetrical, and thus yields a net torque. This torque drives the coal particle to rotate in the levitator. The levitated coal particle also oscillates around its equilibrium point. Fig. 7(a) shows the hologram of an irregular coal particle in the acoustic levitator. The overall projected image of the coal particle is presented in its extended focus image, as shown in Fig. 7(b). The EFI of the coal particle occupies 5048 pixels, with an equivalent diameter of 593 μm. The minimum-area bounding rectangle of the irregular coal particle (possibly rotated) was computed. The lengths of the long and short sides of the enclosing rectangle were 836 μm and 384 μm, respectively, and the aspect ratio was 2.17. The farthest distance between two points in the 3D boundary was 844 μm. The global depth position of the particle centroid measured by the criterion in Eq. (2) was 159.40 mm. The local deviation of the directional gradient method was iteratively applied to each silhouette section, as shown in Video 1, and the typical focus metric curves of two sections are shown in the subfigure of Fig. 7(b). The depth displacement between the maxima of the two

curves denotes the relative depth displacement of the two sections, indicating that the irregular coal particle was not a planar aperture but a 3D object. Fig. 8(a) shows the measured 3D boundary line of the irregular coal particle. The filled irregular region denotes the projected shadow image of the irregular coal particle, and the colored scatters indicate the 3D positions of the 3D boundary line, with the color proportional to the depth position. The depth positions of the 3D boundary line were distributed between 158.68 mm and 160.16 mm. The global depth position of the particle centroid is located within the range of the depth positions of the 3D boundary line, because it is evaluated from the local window covering the whole particle shadow image and therefore is an average depth position of the whole particle boundary and inner region. The probability distribution of the depth positions of the 3D boundary line is shown in the histogram in Fig. 8(b). The bar, which has the highest probability and dominates the distribution, corresponds to the global depth position of the particle centroid (z = 159.40 mm). The depth position distribution of the 3D boundary line presents a bimodal shape for the interrogated irregular coal particle, with the two peaks' positions corresponding to the nearest z part (z = 158.68 mm) and global center part (z = 159.40 mm), while the farthest z part (z = 160.16 mm) corresponds to a small section of the 3D boundary and thus is not pronounced in the distribution. In fact, the depth position histogram could be bimodal or even multimodal for an irregular particle with a complicated 3D boundary line, since the positions of the 3D boundary line are mixtures of different parts located at different

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Fig. 7. Hologram of an irregular coal particle and the corresponding reconstructed particle image.

depth positions. This agreement between the 3D boundary line positions and the global depth position of the particle centroid partially testifies to the validity of the measured 3D boundary line by the proposed criterion. The depth displacement between the nearest and farthest sections in the 3D boundary line is up to 1480 μm, which is much larger than the farthest transversal distance (844 μm) between two arbitrary points in the particle image boundary. Since each hologram can reconstruct a shadow image of the moving irregular coal particle from a certain projected view, over three hundred holograms have been recorded and processed, aiming to possibly obtain complete information of the irregular coal particle from those randomly projected shadow images. The farthest transversal distance of each reconstructed coal particle image is computed. The farthest distance of those shadow images is 1260 μm. Comparing the farthest distance of the coal particle's shadow image with the larger depth position displacement in the 3D boundary line, it is found that they agree well with each other in magnitude, which validates the measured 3D boundary line. It can also be found that the farthest distance of the coal particle's shadow image is

220 μm smaller than the larger depth position displacement in the 3D boundary line, and this discrepancy might be interpreted as due to the incompleteness of the shadow images as well as the intrinsic error in depth position determination [23,28]. The measurement results for the irregular coal particle demonstrate the 3D boundary line measurement of an irregular particle by the proposed local deviation of directional gradient method with acceptable accuracy. 5. Conclusions The measurement of the 3D boundary line of irregular particles with digital inline holography has been demonstrated in this work. The local deviation of the directional gradient over a small tilted rectangle which covers the interrogated silhouette section, is proposed as the criterion for measuring the depth position of the 3D boundary line. The method is first verified by rigorous simulated particle holograms and then by an accurate experimental fiber hologram, and subsequently is applied to measure the 3D boundary line of an irregular coal particle. Results

Fig. 8. 3D boundary measurement of an irregular coal particle by digital holography.

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show that the 3D boundary line of an irregular particle can be accurately retrieved from the reconstructed volumetric optical particle images. Thus, digital inline holography is capable of measuring the planar shadow shape, 3D particle centroid position as well as the 3D boundary line of the irregular particle simultaneously. This capability of digital inline holography enables its application to 3D diagnostics of the morphology and dynamics of irregular objects, including 3D rotation. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.powtec.2015.11.061. Acknowledgments The authors gratefully acknowledge the financial support from the National Nature Science Foundation of China (grant 51176162), the Major Program of the National Natural Science Foundation of China (grant 51390491), the Program of Introducing Talents of Discipline to University (B08026), and the LABEX EMC3-3D. References [1] Y. Zhang, W. Zhong, B. Jin, Experimental investigation on the translational and rotational motion of biomass particle in a spout-fluid bed, Int. J. Chem. React. Eng. 11 (2013) 453. [2] C.L. Pei, C.Y. Wu, D. England, S. Byard, H. Berchtold, M. Adams, Numerical analysis of contact electrification using DEM-CFD, Powder Technol. 248 (2013) 34–43. [3] E. Garboczi, J. Bullard, Contact function, uniform-thickness shell volume, and convexity measure for 3D star-shaped random particles, Powder Technol. 237 (2013) 191–201. [4] P. Barrett, The shape of rock particles, a critical review, Sedimentology 27 (1980) 291–303. [5] A.J. Hickey, N.M. Concessio, Descriptors of irregular particle morphology and powder properties, Adv. Drug Deliv. Rev. 26 (1997) 29–40. [6] S.J. Blott, K. Pye, Particle shape: a review and new methods of characterization and classification, Sedimentology 55 (2008) 31–63. [7] J.W. Bullard, E.J. Garboczi, Defining shape measures for 3D star-shaped particles: sphericity, roundness, and dimensions, Powder Technol. 249 (2013) 241–252. [8] G. Bagheri, C. Bonadonna, I. Manzella, P. Vonlanthen, On the characterization of size and shape of irregular particles, Powder Technol. 270 (2015) 141–153. [9] A. Califice, F. Michel, G. Dislaire, E. Pirard, Influence of particle shape on size distribution measurements by 3D and 2D image analyses and laser diffraction, Powder Technol. 237 (2013) 67–75. [10] H.-E. Albrecht, Laser Doppler and Phase Doppler Measurement Techniques, Springer Science & Business Media, 2003. [11] H. Shen, S. Coetmellec, M. Brunel, Cylindrical interferometric out-of-focus imaging for the analysis of droplets in a volume, Opt. Lett. 37 (2012) 3945–3947. [12] M. Brunel, S.G. Ruiz, J. Jacquot, J. van Beeck, On the morphology of irregular rough particles from the analysis of speckle-like interferometric out-of-focus images, Opt. Commun. 338 (2015) 193–198. [13] S. Tafesse, J. Fernlund, F. Bergholm, Digital sieving-matlab based 3-D image analysis, Eng. Geol. 137 (2012) 74–84. [14] D. Asahina, M. Taylor, Geometry of irregular particles: direct surface measurements by 3-D laser scanner, Powder Technol. 213 (2011) 70–78. [15] C. Lin, J. Miller, 3D characterization and analysis of particle shape using X-ray microtomography (XMT), Powder Technol. 154 (2005) 61–69. [16] D. Garcia, C. Lin, J. Miller, Quantitative analysis of grain boundary fracture in the breakage of single multiphase particles using X-ray microtomography procedures, Miner. Eng. 22 (2009) 236–243.

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