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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 5 — Mar. 11, 2013
  • pp: 6466–6479
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Separation of overlapped particles in digital holographic microscopy

Ahmed El Mallahi and Frank Dubois  »View Author Affiliations


Optics Express, Vol. 21, Issue 5, pp. 6466-6479 (2013)
http://dx.doi.org/10.1364/OE.21.006466


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Abstract

In this paper, we present a procedure to separate aggregates of overlapped particles in digital holograms, based on a focus plane analysis applied to each particle. The method can be applied either on phase or on amplitude objects, according that each object has a border in one focus plane. Numerical simulations are performed to quantify the robustness of the process by increasing the overlapping areas between the particles. The separation algorithm is successfully demonstrated experimentally on different types of aggregates.

© 2013 OSA

1. Introduction

Digital holography is a powerful technique enlarging considerably the depth of investigation of optical microscopy. In one single digital hologram, the different objects can be digitally refocused in the volume without any mechanical scanning as in conventional microscopy. Post-processing of digital holograms is an indispensable step for the analysis of the holographic information. They include among other the extraction of the complex amplitude and the numerical reconstruction [1

1. U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002). [CrossRef]

], processes to correct phase aberrations [2

2. P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. 42(11), 1938–1946 (2003). [CrossRef] [PubMed]

], analysis of living cells [3

3. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30(5), 468–470 (2005). [CrossRef] [PubMed]

-5

5. B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47(4), A52–A61 (2008). [CrossRef] [PubMed]

], 3D velocity measurements [6

6. D. Allano, M. Malek, F. Walle, F. Corbin, G. Godard, S. Coëtmellec, B. Lecordier, J.-M. Foucaut, and D. Lebrun, “Three-dimensional velocity near-wall measurements by digital in-line holography: calibration and results,” Appl. Opt. 52(1), A9–A17 (2013). [CrossRef] [PubMed]

] or furthermore automated 3D object detection and classification [7

7. A. El Mallahi, C. Minetti, and F. Dubois, “Automated three-dimensional detection and classification of living organisms using digital holographic microscopy with partial spatial coherent source: Application to the monitoring of drinking water resources,” Appl. Opt. 52(1), A68–A80 (2013). [CrossRef] [PubMed]

].

In any automatic object detection process, a major limitation is the number of objects simultaneously under observation. When working with high concentration, the probability that an object goes in front of another increases and it results overlapping of objects. During the recording, those overlapped objects are grabbed and look like an aggregate, considered by processing as one big object instead of the individual ones. An error in the detection/counting process is therefore resulting. In digital holographic microscopy, this problem is recurrent in practical situations when huge quantities of species have to be dynamically analyzed. It is of high importance to overcome this limitation of digital holographic microscopy (DHM) when working with biological samples (like red blood cells or alga cell) for which highly concentrated samples should be considered to get close to realistic situation.

There are two categories of aggregates: those ones constituted by particles in contact (touching particles) and those created by particles lying in different focus planes. In the case of particles in contact, where the constituting objects are approximately in the same focus plane, different separation techniques of images processing are available in the literature. These techniques can be partitioned into model-free and model-based methods.

A well-known model-free approach is the watershed transformation [8

8. S. Beucher, “The watershed transformation applied to image segmentation,” Scanning Microsc. Suppl. 6, 299–314 (1992).

], which is a segmentation technique able to detect the ridgelines in an image, by considering its gray-levels as a topographic surface. By combining the watershed segmentation with the distance transform or with the gradient magnitude, clustered nuclei of cells can be divided as demonstrated in several biological studies [9

9. N. Malpica, C. O. de Solórzano, J. J. Vaquero, A. Santos, I. Vallcorba, J. M. García-Sagredo, and F. del Pozo, “Applying watershed algorithms to the segmentation of clustered nuclei,” Cytometry 28(4), 289–297 (1997). [CrossRef] [PubMed]

-10

10. F. Long, H. Peng, and E. Myers, “Automatic segmentation of nuclei in 3D microscopy images of C. Elegans,” in Proceedings of IEEE Conference on Biomedical Imaging: From Nano to Macro (IEEE, 2007), pp 536–539. [CrossRef]

]. However, this technique suffers often from over-segmentation due to noise and local irregularities in the image gradient. To overcome this issue, the definition of markers prior to the segmentation is mandatory in many applications. Those markers can be extracted by filtering out all local extrema, irrelevant for the segmentation problem. In [11

11. A. Pinidiyaarachchi and C. Wählby, “Seeded watersheds for combined segmentation and tracking of cells,” in Proceedings of the 13th international conference on Image Analysis and Processing, (Springer Berlin, 2005), pp. 336–343. [CrossRef]

], the extended h-maxima transform [12

12. P. Soille, Morphological Image Analysis: Principle and Applications (Springer, 1999).

] permits to mark cells recorded in in-vitro cultures with inverted light microscopy. More recently, the marker extraction based on the h-minima transform [12

12. P. Soille, Morphological Image Analysis: Principle and Applications (Springer, 1999).

] allows segmenting clustered nuclei of cells in fluorescent microscopy images [13

13. J. Cheng and J. C. Rajapakse, “Segmentation of clustered nuclei with shape markers and marking function,” IEEE Trans. Biomed. Eng. 56(3), 741–748 (2009). [CrossRef] [PubMed]

] and cervical cells in light microscopy images [14

14. C. Jung and C. Kim, “Segmenting clustered nuclei using H-minima transform-based marker extraction and contour parameterization,” IEEE Trans. Biomed. Eng. 57(10), 2600–2604 (2010). [CrossRef] [PubMed]

].

Digital holography offers the possibility to handle aggregates with particles lying in different focus planes. In [20

20. S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express 15(4), 1505–1512 (2007). [CrossRef] [PubMed]

], preliminary results are shown to analyze occluded spherical objects along the optical axis using in-line digital holographic microscopy. By computing the square of the imaginary part of the complex amplitude as a function of the reconstructed distance, local maxima can be slightly highlighted along axial traces revealing the depth positions of the occluded objects. However, the method is only demonstrated for spherical particles of the same sizes, and a robustness estimation of the procedure is not given. Another approach to analyze overlapped objects by digital holography consists to deconvolve the volumetric reconstruction with an optimal kernel that permits to emphasize objects responsible of the scattered patterns [21

21. L. Dixon, F. C. Cheong, and D. G. Grier, “Holographic deconvolution microscopy for high-resolution particle tracking,” Opt. Express 19(17), 16410–16417 (2011). [CrossRef] [PubMed]

]. If the sizes of the objects are comparable to the wavelength of light, bright features in the deconvolution reconstruction should lie on the objects themselves. This approach can then only be applied to very small particles, around 1µm. On the other hand, by combining digital holography and Mie scattering theory, recorded holograms of clusters of colloidal spheres can be analyzed to extract their 3D positions. In [22

22. J. Fung, K. E. Martin, R. W. Perry, D. M. Kaz, R. McGorty, and V. N. Manoharan, “Measuring translational, rotational, and vibrational dynamics in colloids with digital holographic microscopy,” Opt. Express 19(9), 8051–8065 (2011). [CrossRef] [PubMed]

], different clusters of touching colloidal spheres have been fitted to measure translational, rotational and vibrational dynamics. In [23

23. J. Fung, R. W. Perry, T. G. Dimiduk, and V. N. Manoharan, “Imaging multiple colloidal particles by fitting electromagnetic scattering solutions to digital holograms,” J. Quant. Spectrosc. Radiat. Transf. 113(18), 2482–2489 (2012). [CrossRef]

], the same approach has been extended to handle rigid clusters containing up to 6 particles and non-rigid configuration of particles bound to the surface of an emulsion droplet. This method requires initial values for all the model parameters. Despite very good agreement obtained between the recorded hologram and the Mie scattering model, the proposed method is difficult to apply with high concentration of particles [7

7. A. El Mallahi, C. Minetti, and F. Dubois, “Automated three-dimensional detection and classification of living organisms using digital holographic microscopy with partial spatial coherent source: Application to the monitoring of drinking water resources,” Appl. Opt. 52(1), A68–A80 (2013). [CrossRef] [PubMed]

] due to the high number of parameters and a high computation times. Moreover, as mentioned in [23

23. J. Fung, R. W. Perry, T. G. Dimiduk, and V. N. Manoharan, “Imaging multiple colloidal particles by fitting electromagnetic scattering solutions to digital holograms,” J. Quant. Spectrosc. Radiat. Transf. 113(18), 2482–2489 (2012). [CrossRef]

], the algorithm requires the numbers of spheres in the hologram to be known a priori, which is not the case in practical situations.

In this paper, we investigate the case of aggregates of overlapped particles lying in different focus planes appearing during the recordings of digital holograms. For that purpose, we develop a new technique based on a complete analysis of the evolution of the focus planes that permits to partition the aggregate. Our method allows the handling of aggregates composed of objects that have different shapes, and which lie in different focus planes. The assumption that aggregates are composed of objects having one focus plane is done in this study, which is often the case in practical situations. The algorithm extracts the aggregate border and analyzes the variation of the focus plane along the boundary of the aggregate. Thanks to its simplicity, the developed method can be implemented automatically in any particle detection process and is applicable in many cases. Moreover, it does not require any a priori on the parameter cluster (number, sizes or shapes of the constituting objects) before separation. The robustness of the proposed method is quantified. As shown in the following, aggregates with constituting particles having an overlapping area up to 80% can be processed through the proposed method. This separation procedure can considerably increase the amount of detected particles in high concentrated fluxes.

The paper is organized as follows: in section 2, the developed separation procedure is described through a concrete example. The robustness of the technique is demonstrated by simulations in the first part of section 3 while in the second part, experimental results are exposed to demonstrate the applicability of the developed process in practical situations. Conclusions are given in Section 4.

2. Separation of overlapped particles

The developed method consists to separate aggregates into its constituting particles by computing their positions in depth. The determination of the focus plane of a particle is performed thanks to a refocusing criterion [24

24. F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14(13), 5895–5908 (2006). [CrossRef] [PubMed]

-25

25. A. El Mallahi and F. Dubois, “Dependency and precision of the refocusing criterion based on amplitude analysis in digital holographic microscopy,” Opt. Express 19(7), 6684–6698 (2011). [CrossRef] [PubMed]

]. If applied to an aggregate, this criterion will lead to a non-significant value, as there are several focus planes corresponding to the aggregate. To obtain a correct focus plane determination, any application of the refocusing criterion has to be performed on a region containing only one object with a well-defined focus distance. Based on this assumption, the proposed technique consists to generate all around the detected aggregate a set of succeeding regions of interest (ROI) on which the refocusing criterion can be applied. It will result a set of focus planes, one for each ROI, which are merged to provide, by the analysis of the refocus distance distribution, the number of particles constituting the aggregate. The method is described in details in the following section through a concrete example.

2.1 Principle of the developed technique

Consider an aggregate that can be a phase or an amplitude objet. The following analysis can be done in both cases. Figure 1(a)
Fig. 1 (a) Intensity image of a simulated aggregate of 4 particles, overlapping each other with an area of 64%. (b) 3D view of the position of the particles inside the simulated volume. The z axis is parallel to the main viewing direction (optical axis).
illustrates the amplitude of a simulated aggregate of 4 spherical particles of the same size, with an overlapping area (defined as the area between the overlapped particles) of 64%. With respect to the recorded plane, the particles are defocused respectively by distances of 200, 150 100 and 50µm in a clockwise direction (see Section 3.1 for the description of the simulated aggregate). A 3D view is represented on Fig. 1(b) to highlight the way how the aggregate is constituted.

Based on each ROIs, masks are created, as shown in Fig. 2(b), on which the refocusing criterion is computed. It is expected that this criterion will determine correctly the focus planes of the successive ROIs covering the elementary particles. Each ROI is characterized by two parameters: the length and the width. The length is chosen in such a way that the diffraction patterns perpendicular to the border are contained inside the ROI. The width is fixed to recover a small part of the elementary particles. It is also small enough to avoid significant curvature changes when the mask is covering a part of an elementary particle. Tests have been performed to quantify the variation of the computed focus plane as a function of the width of the ROI (for the aggregate of Fig. 2(a)). For very narrow widths (< 5pixels), the diffraction information is not sufficient to reconstruct correctly the focus planes. For large width (> 40pixels), the ROI could recover more than one particle, resulting in a loss of the accuracy of the estimated focus distances. For width between 5 and 30 pixels, the estimated focus distances are acceptable with more accurate results with the smaller width as might be expected. However, the computational time increases with decreasing width. It is then necessary to find some trade-off. In practice, we found that the optimal focus distances are obtained for values of width between 10 and 20 pixels (total image size: 1024x1024 pixels). In Fig. 2(a), the width of the ROI is fixed to 15 and the length to 150 pixels.

Once all the masks are created, the refocusing criterion is computed inside each ROI. As the simulated particles are amplitude objects, the focus plane is reached for the minimum of the criterion [24

24. F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14(13), 5895–5908 (2006). [CrossRef] [PubMed]

]. The evolution of the computed focus plane as a function of the pixel perimeter is then plotted, as illustrated on Fig. 3
Fig. 3 Estimated focus distance as a function of the border segment. The four highlighted horizontal steps correspond to the focus planes of the four simulated spherical particles constituting the aggregate.
.

The four plateaus highlighted on the Fig. 3 correspond to the focus distance of the four simulated spherical particles of the aggregate. Thanks to this representation, the part of the aggregate corresponding to each particle is directly extracted. The computed focus distances between the steps are obtained inside ROIs covering two particles. In those transition regions, the focus distances are thus non-significant and have to be filtered out to determine the number of particles of the under test aggregate. The histogram of the number of border pixels as a function of focus distance can be used to determine the number of particles constituting the aggregate. Their respective focus distances can easily be extracted by a threshold, as shown by Fig. 4
Fig. 4 Number of perimeter pixels corresponding to each computed focus plane.
. In our simulated example, we obtained that the four spherical particles are refocused to respectively 200, 149, 99 and 50µm. The separation of the aggregate into its constituting particles is achieved.

2.2 Determination of the orientation of the generated ROIs

In order to determine the suitable shape of the elementary ROIs, we first derive the classical result that the Kirchhoff-Fresnel propagation is equivalent to a Schrödinger-type equation. Consider the complex amplitude distribution u(x,y,0)located in a planeP(z=0), propagated up to a distancedin a planeP'(z=d). For that purpose, the Kirchhoff-Fresnel free-space propagation operator (FPO) in the paraxial approximation is used. Thanks to the operator formalism described in [27

27. M. Nazarathy and J. Shamir, “Fourier optics described by operator,” J. Opt. Soc. Am. A 70(2), 150–159 (1980). [CrossRef]

], it is expressed by:
u(x',y',d)=R[d]u(x,y,0)=exp(jkd)Fx',y'1Q[λ2d]Fνx,νy+1u(x,y,0)
(1)
WhereQ[λ2d]=exp(jkλ2d2(νx2+νy2))is a quadratic phase factor,u(x,y,d) is the complex amplitude in the plane P'(z=d),k=2π/λ, (x,y,0)and (x',y',d) are the spatial coordinates respectively in the recorded plane and in the propagated plane, (νx,νy)are the spatial frequencies, j=1 and Fα,β±1denotes the direct and inverse two-dimensional continuous Fourier transformations computed at the point (α,β). As the factorexp(jkd)is common for the whole planeP', it does not play a significant role and it can be suppressed in Eq. (1).

Considering a small propagation distanceε, the quadratic phase operator can be developed until the first order and Eq. (1) becomes:
u(x',y',ε)Fx',y'1(1jkλ2ε2(νx2+νy2))Fνx,νy+1u(x,y,0)u(x',y',0)jkλ2ε2Fx',y'1(νx2+νy2)Fνx,νy+1u(x,y,0)
(2)
By rewriting Eq. (2), the partial derivative of the complex amplitude distribution is obtained:
u0zuz|z=0u(x',y',ε)u(x,y,0)εjkλ22Fx',y'1(νx2+νy2)Fνx,νy+1u0(x,y)
(3)
where u(x,y,0)is replaced by u0(x,y)to simplify the notation. Let us now apply the Laplace operator on the complex amplitude field to obtain:
Δu0=2u0=(2πj)2Fx',y'1(νx2+νy2)Fνx,νy+1u0
(4)
By combining the Eq. (3) and Eq. (4), the following Schrödinger Eq. (-)type is obtained:
ju0z=kλ28π2Δu0
(5)
which describes the evolution of the complex amplitude in a plane perpendicular to the optical axis when it propagates along the optical axis [28

28. M. Born and E. Wolf, Principles of Optics-Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge, 1980).

-29

29. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Elsevier, 2006).

].

As a consequence of this Schrödinger equation formulation, the probability conservation equation can be applied to the conserved complex amplitude distributionu0(x,y):
u0z+.(u0v)=0
(6)
This continuity equation describes the transport of the conserved quantityu0moving with a velocityv. The term u0.vrepresents the flux Jof the complex amplitude distribution. By inserting Eq. (5) in Eq. (6), the expression for the complex amplitude flux is obtained:
J=jkλ28π2u0u0
(7)
Equation (7) demonstrates that the flux density is proportional to the gradient of the complex amplitude, and then its evolution direction is perpendicular to the object border during the propagation. This development demonstrates the fact that the ROIs have to be generated with the longer size (length) perpendicular to the border of the aggregate. Concerning the size of the ROI, the width has to be chosen in such a way that the flux densityJinside the ROI keeps the same direction avoiding important curvature change of the boundary. The length is fixed so that the diffraction patterns perpendicular to the border are contained inside the ROI. This can be estimated by a simple computation taking into account the numerical aperture of the microscope lens and the maximum expected defocus distance.

3. Results

3.1 Simulations

Figure 5
Fig. 5 Intensity images of different types of aggregates generated by the cluster generator, composed of (a) 4 spherical particles, (b) 4 prolate ellipsoidal particles (2 rotated by a 45° and 2 by a −45° from the x-axis), (c) 4 cubic particles, (d) 1 spherical, 1 ellipsoidal, and 2 cubic particles (whose one is rotated by a 45° from the x-axis), (e) 2 spherical and 2 cubic particles and (f) 2 spherical (of two different sizes) and 2 ellipsoidal particles (whose one is rotated by a 45° from the x-axis).
shows a non-exhaustive list of several types of aggregates generated by the cluster generator, with different tested combinations of particle type and orientations. For each aggregate, the overlapping area is increased until the separation process reaches its limit, quantifying thereby the robustness of the developed procedure. In Figs. 5(a)5(c) are represented aggregates composed of same particle type, respectively spherical, ellipsoidal and cubic ones. In Figs. 5(d)5(f) aggregates composed with mixed particles are illustrated. For each aggregate, the elementary particles are defocused respectively by 200, 150 100 and 50µm in a clockwise direction. Table 1

Table 1. Reconstructed focus planes as a function of the area between overlapped particlesa

table-icon
View This Table
gives the reconstructed focus planes as a function of the overlapping area for the aggregate of Figs. 5(a)5(c). Those aggregates are composed of same types of particles: spherical, ellipsoidal or cubic. The areas between same types of particles composing one aggregate are made identical for each particle. As shown by the Table 1, the method is able to separate the particles of aggregates with overlapping area up to about 80%. Up to this value, the computed focus distances of each particle are within the depth of field, given a maximum error of 4%. This error is defined by E=|AB|/A whereA is the simulated focus distance andBis the estimated focus distance obtained with the separation procedure. For aggregates with a larger overlap, the error of the reconstructed focal distance is larger than 7µm and is outside our accepted threshold. By simulations, the robustness of the developed separation process is then established for overlapping area up to about 80% for aggregates composed of identical particles.

For mixed particles aggregates of Figs. 5(d)5(f), for which the particles have different shapes, the overlapping area is different for each particle. For example, in the simulated aggregate of Fig. 5(d), the overlapping areas are respectively 32.9%, 60.1%, 41.9% and 30.2% for particles in a clockwise direction starting from the upper left particle. Each of those areas changes differently from the others. For mixed particles aggregates of Figs. 5(d)5(f), each particle is sequentially moved to increase its overlapping area while the others are maintained constant, until the separation method reaches its limit. The robustness is quantified and it has been obtained that a particle of an aggregate is correctly identified if its overlapping area is lower than 75-80%, depending of particles types.

This section demonstrates the capability of the separation procedure to handle different type of simulated aggregates. The robustness of the technique is quantified with respect to the overlapping areas of each particle that can reach up to about 80%.

3.2 Experiments

The developed technique is applied to real holograms to show the capability of the method in actual situations. Tests were performed with both amplitude and phase objects. A first test is achieved by recording opaque polyethylene spherical particles flowing in a micro-channel. The digital holographic setup used in this experiment is a Mach-Zehnder interferometer in a microscope configuration working with a partial spatial coherent source [7

7. A. El Mallahi, C. Minetti, and F. Dubois, “Automated three-dimensional detection and classification of living organisms using digital holographic microscopy with partial spatial coherent source: Application to the monitoring of drinking water resources,” Appl. Opt. 52(1), A68–A80 (2013). [CrossRef] [PubMed]

]. The field of view is 720µm x 720µm recorded on a camera with 1024 x 1024 pixels. The x10 microscope lenses have a numerical aperture of NA = 0.3. The diameters of particles are ranging from 75 to 100µm. The micro-fluidic experimental device consists of a straight micro-channel µ-SlideI0.8Ibidi® (height: 800µm). To perform the flow measurements, we use a programmable KDS Legato® 270P push/pull pump with a user defined program configuration, allowing a wide flow range.

For opaque particles, the detection of the aggregate is performed on the intensity image extracted from the recorded hologram. It has been shown that the focus plane of an amplitude object is reached for the minimum of a refocusing criterion defined in [24

24. F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14(13), 5895–5908 (2006). [CrossRef] [PubMed]

-25

25. A. El Mallahi and F. Dubois, “Dependency and precision of the refocusing criterion based on amplitude analysis in digital holographic microscopy,” Opt. Express 19(7), 6684–6698 (2011). [CrossRef] [PubMed]

]. Figure 6
Fig. 6 Separation method applied on aggregates constituted by opaque polyethylene spherical particles of different sizes. (a) Intensity image of an aggregate of two particles in the recorded plane (b) Automated separation and refocusing of the bottom particle at −370µm (error: 5µm). (c) Automated separation and refocusing of the top particle at 320µm (error: 6µm). (d) Intensity image of an aggregate of three particles in the recorded plane (e) Automated separation and refocusing of the top particle at −135µm (error: 3µm). (f) Automated separation and refocusing of the bottom particle at 95µm (error: 2µm). (g) Intensity image of an aggregate of four particles in the recorded plane (h) Automated separation and refocusing of the top particle at −125µm (error: 2µm). (i) Automated separation and refocusing of the bottom particle at −265µm (error: 4µm).
shows three different aggregates and the corresponding separation into their constituting particles with the separation method. By analyzing the evolution of the focus planes around the aggregate border, different levels are highlighted as shown in Fig. 3, where the focus planes of the different particles can be directly extracted. Figures 6(a), 6(d) and 6(g) show the intensity image of aggregates of respectively two, three and four opaque spherical particles of different sizes. Thanks to the separation method, the focus planes of each particle of the aggregates are computed as shown by Figs. 6(b)6(c) for the first aggregate, by Figs. 6(e)6(f) for the second one and by Figs. 6(h)6(i) for the third one. For real data, as the focus planes are not known a priori, the refocus distance errors on each particle are estimated by computing the standard deviation of the mean recomputed focus planes of all the ROIs recovering the particle. The obtained errors are below our acceptable threshold.

Other tests were performed with red blood cells (RBCs). This problem is of high interest as blood is made of about 50% of RBCs, which means that the volume fraction of RBC in real blood is very high. For this reason, blood must be strongly diluted to access information of individual RBC (typically 0.1% in volume fraction). Even with high dilution, the probability to have an aggregate of RBC is high. Those clusters corrupt the determination of the 3D locations of RBCs. The application of our separation method on RBCs cluster is a first step towards highest concentration monitoring. RBCs are oval and biconcave disks with diameters ranging from 6 to 8µm. The thickness at the thickest location is approximately 2-2.5µm while the thickness in the center is about 1µm.

The optical setup has been set to yield a field of view of 215 µm x 215 µm obtained with a 40x microscope lenses, with NA = 0.6. The resulting DOF is then equal to 1.8µm for this setup. A suspension of RBC is injected in a shear-flow chamber made of two glass plates spaced by 170µm. The bottom disk is fixed while the top one is rotating, creating a linear velocity profile of the fluid inside the channel [31

31. N. Callens, C. Minetti, G. Coupier, M.-A. Mader, F. Dubois, C. Misbah, and T. Podgorski, “Hydrodynamic lift of vesicles under shear flow in microgravity,” Europhys. Lett. 83(2), 24002 (2008). [CrossRef]

]. Holograms are acquired at a frame rate of 24 holograms per second. The main objective of those experiments is to get the depth position of each RBC and the evolution in time of the RBC suspension.

Figures 7(a)
Fig. 7 Cluster of two RBCs in the recorded plane (a) Intensity image (b) Phase image (c) Segmentation of the phase image of the aggregate showing that one big object is detected.
7(b) represent respectively the intensity and the phase image of an aggregate of two RBCs overlapping each other. The detection and segmentation process, as explained in Section 2.1, is performed on the phase image and is illustrated in Fig. 7(c). We can see here that an automatic detection process without separation will consider the aggregate as one big object.

Thanks to the separation method, the RBC on the left is automatically separated from the aggregate and refocused at −24µm of the recorded plane, as illustrated by Figs. 8(a)
Fig. 8 Separation procedure applied to RBCs cluster (a) Automated separation and refocusing of the left particle at −24µm (error: 0.8µm) - Intensity image (b) Automated separation and refocusing of the left particle at −24µm (error: 0.8µm) - Phase image (c) Automated separation and refocusing of the left particle at −76µm (error: 1.5µm) - Intensity image (d) Automated separation and refocusing of the left particle at −76µm (error: 1.5µm) - Phase image.
8(b), while the RBC on the right is refocused at −76µm from the recorded plane, as seen on Figs. 8(c)8(d). The computed errors are in our accepted margin of 1.8 µm. Once the cluster is separated, morphological features of RBCs can be extracted in their focus plane to study their 3D orientation in the channel [32

32. X. Grandchamp, G. Coupier, A. Srivastav, C. Minetti, and T. Podgorski, “Lift and down-gradient shear-induced diffusion in red blood cell suspensions,” Phys. Rev. Lett. (to be published).

-33

33. I. Moon, B. Javidi, F. Yi, D. Boss, and P. Marquet, “Automated statistical quantification of three-dimensional morphology and mean corpuscular hemoglobin of multiple red blood cells,” Opt. Express 20(9), 10295–10309 (2012). [CrossRef] [PubMed]

].

For this cluster, the right cell is deformed and elongated along the flow direction (from bottom to top on the image). Furthermore, this cell lies in a plane parallel to the optical axis and exhibits a prolate ellipsoidal shape, while the other RBC lies in a plane perpendicular to the optical axis. The RBC on the right has then a higher optical thickness than the left one. It is the reason why its error in the refocused z position is higher than the left one. Even in this complex case where the obtained error is slightly above our limit, the estimated z position is acceptable for morphological feature extraction as we can see on Fig. 9(d).

These experiments confirm the capability of the developed separation method in practical situations.

3. Conclusions

In this article, a new method to separate aggregate of particles is proposed in digital holographic microscopy. The developed procedure is based on an accurate analysis of the evolution of the focus plane around the aggregate’s border. Aggregates of amplitude objects as well as phase object can be separated with the proposed technique, which can moreover deal with many types of aggregate shape. Numerical simulations permit to quantify the robustness of the method. It has been demonstrated that the overlapping area can be increased up to a level of around 80% recovering the correct focus planes of the objects inside their depth of field. Experiments were performed and demonstrated that the method can be applied in practical situations.

Acknowledgments

The authors acknowledge financial support from l’Institut Bruxellois pour la Recherche et l’Innovation (IRSIB) in the frame of the Holoflow Impulse project. The authors would like to thank Dr. Christophe Minetti from the Université libre de Bruxelles for providing RBCs holograms and for very helpful comments.

References and links

1.

U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002). [CrossRef]

2.

P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. 42(11), 1938–1946 (2003). [CrossRef] [PubMed]

3.

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30(5), 468–470 (2005). [CrossRef] [PubMed]

4.

F. Dubois, C. Yourassowsky, O. Monnom, J.-C. Legros, O. Debeir, P. Van Ham, R. Kiss, and C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt. 11(5), 054032 (2006). [CrossRef] [PubMed]

5.

B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47(4), A52–A61 (2008). [CrossRef] [PubMed]

6.

D. Allano, M. Malek, F. Walle, F. Corbin, G. Godard, S. Coëtmellec, B. Lecordier, J.-M. Foucaut, and D. Lebrun, “Three-dimensional velocity near-wall measurements by digital in-line holography: calibration and results,” Appl. Opt. 52(1), A9–A17 (2013). [CrossRef] [PubMed]

7.

A. El Mallahi, C. Minetti, and F. Dubois, “Automated three-dimensional detection and classification of living organisms using digital holographic microscopy with partial spatial coherent source: Application to the monitoring of drinking water resources,” Appl. Opt. 52(1), A68–A80 (2013). [CrossRef] [PubMed]

8.

S. Beucher, “The watershed transformation applied to image segmentation,” Scanning Microsc. Suppl. 6, 299–314 (1992).

9.

N. Malpica, C. O. de Solórzano, J. J. Vaquero, A. Santos, I. Vallcorba, J. M. García-Sagredo, and F. del Pozo, “Applying watershed algorithms to the segmentation of clustered nuclei,” Cytometry 28(4), 289–297 (1997). [CrossRef] [PubMed]

10.

F. Long, H. Peng, and E. Myers, “Automatic segmentation of nuclei in 3D microscopy images of C. Elegans,” in Proceedings of IEEE Conference on Biomedical Imaging: From Nano to Macro (IEEE, 2007), pp 536–539. [CrossRef]

11.

A. Pinidiyaarachchi and C. Wählby, “Seeded watersheds for combined segmentation and tracking of cells,” in Proceedings of the 13th international conference on Image Analysis and Processing, (Springer Berlin, 2005), pp. 336–343. [CrossRef]

12.

P. Soille, Morphological Image Analysis: Principle and Applications (Springer, 1999).

13.

J. Cheng and J. C. Rajapakse, “Segmentation of clustered nuclei with shape markers and marking function,” IEEE Trans. Biomed. Eng. 56(3), 741–748 (2009). [CrossRef] [PubMed]

14.

C. Jung and C. Kim, “Segmenting clustered nuclei using H-minima transform-based marker extraction and contour parameterization,” IEEE Trans. Biomed. Eng. 57(10), 2600–2604 (2010). [CrossRef] [PubMed]

15.

P. V. C. Hough, “Method and means for recognizing complex patterns,” U.S. Patent 3 069 654 (1969).

16.

D. H. Ballard, “Generalizing the Hough transform to detect arbitrary shapes,” Pattern Recognit. 13(2), 111–122 (1981). [CrossRef]

17.

M. Smereka and I. Duleba, “Circular object detection using a modified Hough transform,” Int. J. Appl. Math. Comput. Sci. 18(1), 85–91 (2008). [CrossRef]

18.

B. Parvin, Q. Yang, J. Han, H. Chang, B. Rydberg, and M. H. Barcellos-Hoff, “Iterative voting for inference of structural saliency and characterization of subcellular events,” IEEE Trans. Image Process. 16(3), 615–623 (2007). [CrossRef] [PubMed]

19.

Q. Wen, H. Chang, and B. Parvin, “A Delaunay triangulation approach for segmenting clumps of nuclei,” in Proceedings of IEEE Conference on Biomedical Imaging: From Nano to Macro (IEEE, 2009), pp 9–12.

20.

S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express 15(4), 1505–1512 (2007). [CrossRef] [PubMed]

21.

L. Dixon, F. C. Cheong, and D. G. Grier, “Holographic deconvolution microscopy for high-resolution particle tracking,” Opt. Express 19(17), 16410–16417 (2011). [CrossRef] [PubMed]

22.

J. Fung, K. E. Martin, R. W. Perry, D. M. Kaz, R. McGorty, and V. N. Manoharan, “Measuring translational, rotational, and vibrational dynamics in colloids with digital holographic microscopy,” Opt. Express 19(9), 8051–8065 (2011). [CrossRef] [PubMed]

23.

J. Fung, R. W. Perry, T. G. Dimiduk, and V. N. Manoharan, “Imaging multiple colloidal particles by fitting electromagnetic scattering solutions to digital holograms,” J. Quant. Spectrosc. Radiat. Transf. 113(18), 2482–2489 (2012). [CrossRef]

24.

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14(13), 5895–5908 (2006). [CrossRef] [PubMed]

25.

A. El Mallahi and F. Dubois, “Dependency and precision of the refocusing criterion based on amplitude analysis in digital holographic microscopy,” Opt. Express 19(7), 6684–6698 (2011). [CrossRef] [PubMed]

26.

M. Sezgin and B. Sankur, “Survey over image thresholding techniques and quantitative performance evaluation,” J. Electron. Imaging 13, 145–165 (2004).

27.

M. Nazarathy and J. Shamir, “Fourier optics described by operator,” J. Opt. Soc. Am. A 70(2), 150–159 (1980). [CrossRef]

28.

M. Born and E. Wolf, Principles of Optics-Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge, 1980).

29.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Elsevier, 2006).

30.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

31.

N. Callens, C. Minetti, G. Coupier, M.-A. Mader, F. Dubois, C. Misbah, and T. Podgorski, “Hydrodynamic lift of vesicles under shear flow in microgravity,” Europhys. Lett. 83(2), 24002 (2008). [CrossRef]

32.

X. Grandchamp, G. Coupier, A. Srivastav, C. Minetti, and T. Podgorski, “Lift and down-gradient shear-induced diffusion in red blood cell suspensions,” Phys. Rev. Lett. (to be published).

33.

I. Moon, B. Javidi, F. Yi, D. Boss, and P. Marquet, “Automated statistical quantification of three-dimensional morphology and mean corpuscular hemoglobin of multiple red blood cells,” Opt. Express 20(9), 10295–10309 (2012). [CrossRef] [PubMed]

OCIS Codes
(090.0090) Holography : Holography
(100.0100) Image processing : Image processing
(100.2000) Image processing : Digital image processing
(100.6890) Image processing : Three-dimensional image processing
(090.1995) Holography : Digital holography

ToC Category:
Holography

History
Original Manuscript: February 22, 2013
Revised Manuscript: February 27, 2013
Manuscript Accepted: February 27, 2013
Published: March 7, 2013

Virtual Issues
Vol. 8, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Ahmed El Mallahi and Frank Dubois, "Separation of overlapped particles in digital holographic microscopy," Opt. Express 21, 6466-6479 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-6466


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References

  1. U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol.13(9), R85–R101 (2002). [CrossRef]
  2. P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt.42(11), 1938–1946 (2003). [CrossRef] [PubMed]
  3. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett.30(5), 468–470 (2005). [CrossRef] [PubMed]
  4. F. Dubois, C. Yourassowsky, O. Monnom, J.-C. Legros, O. Debeir, P. Van Ham, R. Kiss, and C. Decaestecker, “Digital holographic microscopy for the three-dimensional dynamic analysis of in vitro cancer cell migration,” J. Biomed. Opt.11(5), 054032 (2006). [CrossRef] [PubMed]
  5. B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt.47(4), A52–A61 (2008). [CrossRef] [PubMed]
  6. D. Allano, M. Malek, F. Walle, F. Corbin, G. Godard, S. Coëtmellec, B. Lecordier, J.-M. Foucaut, and D. Lebrun, “Three-dimensional velocity near-wall measurements by digital in-line holography: calibration and results,” Appl. Opt.52(1), A9–A17 (2013). [CrossRef] [PubMed]
  7. A. El Mallahi, C. Minetti, and F. Dubois, “Automated three-dimensional detection and classification of living organisms using digital holographic microscopy with partial spatial coherent source: Application to the monitoring of drinking water resources,” Appl. Opt.52(1), A68–A80 (2013). [CrossRef] [PubMed]
  8. S. Beucher, “The watershed transformation applied to image segmentation,” Scanning Microsc. Suppl.6, 299–314 (1992).
  9. N. Malpica, C. O. de Solórzano, J. J. Vaquero, A. Santos, I. Vallcorba, J. M. García-Sagredo, and F. del Pozo, “Applying watershed algorithms to the segmentation of clustered nuclei,” Cytometry28(4), 289–297 (1997). [CrossRef] [PubMed]
  10. F. Long, H. Peng, and E. Myers, “Automatic segmentation of nuclei in 3D microscopy images of C. Elegans,” in Proceedings of IEEE Conference on Biomedical Imaging: From Nano to Macro (IEEE, 2007), pp 536–539. [CrossRef]
  11. A. Pinidiyaarachchi and C. Wählby, “Seeded watersheds for combined segmentation and tracking of cells,” in Proceedings of the 13th international conference on Image Analysis and Processing, (Springer Berlin, 2005), pp. 336–343. [CrossRef]
  12. P. Soille, Morphological Image Analysis: Principle and Applications (Springer, 1999).
  13. J. Cheng and J. C. Rajapakse, “Segmentation of clustered nuclei with shape markers and marking function,” IEEE Trans. Biomed. Eng.56(3), 741–748 (2009). [CrossRef] [PubMed]
  14. C. Jung and C. Kim, “Segmenting clustered nuclei using H-minima transform-based marker extraction and contour parameterization,” IEEE Trans. Biomed. Eng.57(10), 2600–2604 (2010). [CrossRef] [PubMed]
  15. P. V. C. Hough, “Method and means for recognizing complex patterns,” U.S. Patent 3 069 654 (1969).
  16. D. H. Ballard, “Generalizing the Hough transform to detect arbitrary shapes,” Pattern Recognit.13(2), 111–122 (1981). [CrossRef]
  17. M. Smereka and I. Duleba, “Circular object detection using a modified Hough transform,” Int. J. Appl. Math. Comput. Sci.18(1), 85–91 (2008). [CrossRef]
  18. B. Parvin, Q. Yang, J. Han, H. Chang, B. Rydberg, and M. H. Barcellos-Hoff, “Iterative voting for inference of structural saliency and characterization of subcellular events,” IEEE Trans. Image Process.16(3), 615–623 (2007). [CrossRef] [PubMed]
  19. Q. Wen, H. Chang, and B. Parvin, “A Delaunay triangulation approach for segmenting clumps of nuclei,” in Proceedings of IEEE Conference on Biomedical Imaging: From Nano to Macro (IEEE, 2009), pp 9–12.
  20. S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express15(4), 1505–1512 (2007). [CrossRef] [PubMed]
  21. L. Dixon, F. C. Cheong, and D. G. Grier, “Holographic deconvolution microscopy for high-resolution particle tracking,” Opt. Express19(17), 16410–16417 (2011). [CrossRef] [PubMed]
  22. J. Fung, K. E. Martin, R. W. Perry, D. M. Kaz, R. McGorty, and V. N. Manoharan, “Measuring translational, rotational, and vibrational dynamics in colloids with digital holographic microscopy,” Opt. Express19(9), 8051–8065 (2011). [CrossRef] [PubMed]
  23. J. Fung, R. W. Perry, T. G. Dimiduk, and V. N. Manoharan, “Imaging multiple colloidal particles by fitting electromagnetic scattering solutions to digital holograms,” J. Quant. Spectrosc. Radiat. Transf.113(18), 2482–2489 (2012). [CrossRef]
  24. F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express14(13), 5895–5908 (2006). [CrossRef] [PubMed]
  25. A. El Mallahi and F. Dubois, “Dependency and precision of the refocusing criterion based on amplitude analysis in digital holographic microscopy,” Opt. Express19(7), 6684–6698 (2011). [CrossRef] [PubMed]
  26. M. Sezgin and B. Sankur, “Survey over image thresholding techniques and quantitative performance evaluation,” J. Electron. Imaging13, 145–165 (2004).
  27. M. Nazarathy and J. Shamir, “Fourier optics described by operator,” J. Opt. Soc. Am. A70(2), 150–159 (1980). [CrossRef]
  28. M. Born and E. Wolf, Principles of Optics-Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge, 1980).
  29. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Elsevier, 2006).
  30. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  31. N. Callens, C. Minetti, G. Coupier, M.-A. Mader, F. Dubois, C. Misbah, and T. Podgorski, “Hydrodynamic lift of vesicles under shear flow in microgravity,” Europhys. Lett.83(2), 24002 (2008). [CrossRef]
  32. X. Grandchamp, G. Coupier, A. Srivastav, C. Minetti, and T. Podgorski, “Lift and down-gradient shear-induced diffusion in red blood cell suspensions,” Phys. Rev. Lett. (to be published).
  33. I. Moon, B. Javidi, F. Yi, D. Boss, and P. Marquet, “Automated statistical quantification of three-dimensional morphology and mean corpuscular hemoglobin of multiple red blood cells,” Opt. Express20(9), 10295–10309 (2012). [CrossRef] [PubMed]

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