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Virtual Journal for Biomedical Optics

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  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 1 — Feb. 4, 2013
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On the holographic 3D tracking of in vitro cells characterized by a highly-morphological change

Pasquale Memmolo, Maria Iannone, Maurizio Ventre, Paolo Antonio Netti, Andrea Finizio, Melania Paturzo, and Pietro Ferraro  »View Author Affiliations


Optics Express, Vol. 20, Issue 27, pp. 28485-28493 (2012)
http://dx.doi.org/10.1364/OE.20.028485


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Abstract

Digital Holography (DH) in microscopic configuration is a powerful tool for the imaging of micro-objects contained into a three dimensional (3D) volume, by a single-shot image acquisition. Many studies report on the ability of DH to track particle, microorganism and cells in 3D. However, very few investigations are performed with objects that change severely their morphology during the observation period. Here we study DH as a tool for 3D tracking an osteosarcoma cell line for which extensive changes in cell morphology are associated to cell motion. Due to the great unpredictable morphological change, retrieving cell’s position in 3D can become a complicated issue. We investigate and discuss in this paper how the tridimensional position can be affected by the continuous change of the cells. Moreover we propose and test some strategies to afford the problems and compare it with others approaches. Finally, results on the 3D tracking and comments are reported and illustrated.

© 2012 OSA

1. Introduction

Precise tracking of cells in 3D environments is of great importance in diverse biologic and bio-technologic contexts. 3D cell migration is indeed crucial in embryo morphogenesis [1

1. A. Aman and T. Piotrowski, “Cell migration during morphogenesis,” Dev. Biol. 341(1), 20–33 (2010). [CrossRef] [PubMed]

], immunology [2

2. E. Van Goethem, R. Poincloux, F. Gauffre, I. Maridonneau-Parini, and V. Le Cabec, “Matrix architecture dictates three-dimensional migration modes of human macrophages: differential involvement of proteases and podosome-like structures,” J. Immunol. 184(2), 1049–1061 (2010). [CrossRef] [PubMed]

] and tumor progression [3

3. P. P. Provenzano, K. W. Eliceiri, and P. J. Keely, “Shining new light on 3D cell motility and the metastatic process,” Trends Cell Biol. 19(11), 638–648 (2009). [CrossRef] [PubMed]

]. Moreover, characterizing migration in 3D matrices might be beneficial for the development of more effective prostheses or scaffolds. Migration has been widely studied and characterized in two-dimensional setups, by means of optical microscopy [4

4. D. Guarnieri, A. De Capua, M. Ventre, A. Borzacchiello, C. Pedone, D. Marasco, M. Ruvo, and P. A. Netti, “Covalently immobilized RGD gradient on PEG hydrogel scaffold influences cell migration parameters,” Acta Biomater. 6(7), 2532–2539 (2010). [CrossRef] [PubMed]

, 5

5. M. Ventre, F. Valle, M. Bianchi, F. Biscarini, and P. A. Netti, “Cell fluidics: producing cellular streams on micropatterned synthetic surfaces,” Langmuir 28(1), 714–721 (2012). [CrossRef] [PubMed]

]. Cells, however, display a very different behavior when seeded in 3D matrices like collagen, fibrin or cell derived matrix. Yet, many authors describe 3D cell migration by considering the projection of cell displacements on the focal plane, which might differ considerably from a 3D analysis, especially when long “out-of-focus” displacements occur. Other methods reported so far to track cells in 3D aim at finding the focus of moving cells thus readjusting the focus position at each time point [6

6. Z. N. Demou and L. V. McIntire, “Fully automated three-dimensional tracking of cancer cells in collagen gels: determination of motility phenotypes at the cellular level,” Cancer Res. 62(18), 5301–5307 (2002). [PubMed]

]. Few drawbacks might be associated to this operation. Firstly, it requires continuous real-time mechanical displacements of the imaging lens or a time-consuming scanning along the optical axis with the aim to extract the so-called Extended Focus Image (EFI). Secondly, this method might fail when many objects, at different foci, appears in the same field of view. Through DH, it is possible to reconstruct numerically the complex optical wavefront and thus numerical focusing at various distances [7

7. P. Memmolo, C. Distante, M. Paturzo, A. Finizio, P. Ferraro, and B. Javidi, “Automatic focusing in digital holography and its application to stretched holograms,” Opt. Lett. 36(10), 1945–1947 (2011). [CrossRef] [PubMed]

10

10. 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]

]. Instead, the position of each cell is detected by calculating the center of mass of the cell, usually in the quantitative phase-contrast map. This might be an easy task in the case of cells cultivated on flat surfaces, on which they display a characteristic spread morphology and major changes of this (extension/retraction) occur in the time frame of tens of minutes. In 3D environments, cells possess a spindle like morphology in which highly dynamic membrane processes are continuously projected out cell body in order to scan the pericellular environment eventually forming new adhesions [11

11. G. G. Martins and J. Kolega, “Endothelial cell protrusion and migration in three-dimensional collagen matrices,” Cell Motil. Cytoskeleton 63(2), 101–115 (2006). [CrossRef] [PubMed]

]. Such a dynamic morphology might hamper the assessment of cell position as well as the estimation of its dimensions, that typically are about few microns. Here we investigate an discuss this problematic issue of accurate 3D tracking of an osteosarcoma cell line for which extensive changes in cell morphology are associated to cell motion. However it depends on morphological changes. We also propose some novel strategies and approaches to afford the problem. In particular we tested for the first time a novel approach for estimating the depth coordinate along the optical axis and furthermore we defined established and tested a new strategies for finding transverse coordinate. Comparison with others approaches have been performed and results are discussed.

2. Experimental set-up

The 3D tracking of the osteosarcoma cells in a gelified collagen matrix was performed experimentally by a transmission holographic microscope, based on optical fiber Mach-Zender configuration. The light source is a DPSS laser (150 mW at a wavelength of 532 nm) whose beam is coupled to an optical fiber. The fiber splits the incoming laser light into two beams, (object-beam and reference-beam) by using a fiber splitter (FS) as shown in the optical set-up in Fig. 1
Fig. 1 Set-up of the holographic microscope. FS Fiber Splitter; MI Micro-Incubator; MO Microscope Objective; F Filter; BS Beam Splitter; IP Image Plane; HP Hologram Plane
.

The object-beam impinges on the sample and then is collected by a 10x microscope objective (MO) that provides a focused image on the “image-plane” (IP). The sample is contained inside a micro-incubator (MI) to control both temperature and CO2. A Charge Coupled Device (CCD) camera (1280x1024 square pixels; pixel size: 6.7 μm), is placed at a proper distance from the “image-plane” produced by the imaging microscope objective (MO) objective. Through a beam-splitter (BS), the CCD plane (i.e. the holographic plane, HP) collects both an out-of-focus image of the sample and the reference-beam. On the CCD plane, an interference-pattern (hologram) is generated by the optical interference between the object-beam and the reference-beam. The interference pattern recorded by the CCD contains information about the amplitude as well as the phase of the transmitted wavefront. Time-lapse sequences have been acquired with a frame interval of 5 minutes, for 15 hours total time in order to capture any movements and/or morphological changes of the cells during the experiment. The numerical processing of the hologram allows to evaluating both intensity and phase distribution in each plane between the hologram plane and the image plane.

3. Sample preparation

The MG63 osteosarcoma cell line [12

12. R. T. Franceschi, W. M. James, and G. Zerlauth, “1 alpha, 25-dihydroxyvitamin D3 specific regulation of growth, morphology, and fibronectin in a human osteosarcoma cell line,” J. Cell. Physiol. 123(3), 401–409 (1985). [CrossRef] [PubMed]

] was cultured in Dulbecco’s modified Eagle medium (DMEM) supplemented with 10% fetal bovine serum (FBS) (Biowittaker, Walkersville, MD, USA), 2mM L-glutamine, 100 U/ml penicillin, and 0,1 mg/ml streptomycin (Sigma, St. Louis, MO, USA). MG63 were cultivated in reconstituted bovine collagen gel (Sigma Aldrich St. Louis MO, USA) that was prepared following manufacturer’s procedure. Briefly, 1 part of 10X DMEM (Gibco, Life Technologies) and 10mM Hepes [13

13. K. Schumacher, R. Strehl, U. de Vries, and W. W. Minuth, “Advanced technique for long term culture of epithelia in a continuous luminal-basal medium gradient,” Biomaterials 23(3), 805–815 (2002). [CrossRef] [PubMed]

] (EuroClone) were mixed with 8 parts of collagen (stock solution: 3 mg/ml). The pH of mixture were adjusted to 7.2 adding 0.1 M NaOH. The resulting collagen solution (2.4 mg/ml), was gently mixed with the cells and allowed to gelify for approximately 40 minutes at 37°C, 5% CO2.

4. Approach for detecting the coordinates of the cells

If we consider a coordinate reference volume where XY is the transverse plane while Z is the optical axis of the imaging systems, then the typical approach adopted in DH for the tracking of living cells [14

14. P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14(1), 014018 (2009). [CrossRef] [PubMed]

16

16. P. Memmolo, A. Finizio, M. Paturzo, L. Miccio, and P. Ferraro, “Twin-beams digital holography for 3D tracking and quantitative phase-contrast microscopy in microfluidics,” Opt. Express 19(25), 25833–25842 (2011). [CrossRef] [PubMed]

] consists into estimate the location in 3D, i.e. estimating the X,Y,Z coordinates of the particle by following three conceptual steps:

  • Detection of cells, i.e. identification of the cell from the phase-contrast map.
  • Estimation of the focal plane (i.e. the Z coordinate) on the amplitude reconstruction of the digital hologram, by performing a numerical scanning of the focus (it is important to note that for pure phase objects are in good-focus when they show minimum visibility (see refs [17

    17. 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]

    , 18

    18. 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]

    ].).
  • Estimation of X,Y coordinates are instead determined by the phase reconstruction computed at distance d = Z, i.e. using the Z value computed in the previous step.

Of course different strategies or algorithms have been proposed and can be found in literature for each of the above steps.

4.1 Cell detection

In our investigation, the cell detection is achieved with a simple thresholding filter applied on the phase-contrast map, reconstructed numerically by the digital hologram at the nominal distance, given in the recording step, as shown in Fig. 2
Fig. 2 (a) initial phase map of the tracking sequence reconstructed at the middle plane of the sample volume; (b) labeled cells extracted from (a) with thresholding filter. The white boxes highlight the cells that we will track, identified by (A,B,C).
.

For each detected cell, we use a different color label. Note that a first problem to face with is the fact that detection errors occur when there is a spatial superimposition between two or more cells.

4.2 Estimation of the focal plane

4.3 Estimation of the (X,Y) coordinates

First of all, we try to minimize the contribution of the noise on the phase maps using a novel denoising method described in [23

23. P. Memmolo, I. Esnaola, A. Finizio, M. Paturzo, P. Ferraro, and A. M. Tulino, “SPADEDH: a sparsity-based denoising method of digital holograms without knowing the noise statistics,” Opt. Express 20(15), 17250–17257 (2012). [CrossRef]

]. In this way, the techniques mostly depended on the noise, like maximum phase contrast value and the weighted centroid, that use the phase map values, are put in a better condition for the estimation of (X,Y) position. Instead, the other aforementioned techniques, i.e. the centroid method and the correlation coefficient-based strategy, are principally influenced by morphological changes during the cell motility. In fact, during the migration, the cells can change their morphology without really change the 3D position. In this case, since the centroid method is based on the filtered image in the ROI, the morphological modification without real movement can be produce a different centroid, with a significant error in the 3D tracking. For the same reason, in the correlation coefficient-based method, the maximum value of correlation function, that determine the estimated position, may be in the wrong position. Our idea tries to combine the advantages of these methods in respect to both the noise and the morphological variations introducing the concept of Minimum Boundary Filters (MBF). Our method is described by the following steps.

  • Let consider the ROIs containing the cell under analysis in the frames k and k-1.
  • For both ROIs, computes the thresholding filters used in the centroid method, and the weighted centroids.
  • Translates the (k-1)-th filter on the k-th filter by superimposing the corresponding weighted centroids.
  • The MBF is obtained filtering the result of the last superimposition. The centroid of this new image is the estimated position of the cell.

Obviously, our strategy assumes that the Z variation between two subsequent frames is negligible, like in the correction coefficient-based method.

We report in Fig. 4
Fig. 4 (a,b,c) are the initial frames of the sequence under analysis, (d,e,f) are the 11th, 22nd, and 20th frame respectively.
an example of morphological changes for the three cells under analysis during the migration, and in Fig. 5
Fig. 5 (a,b,c) are the results of the superimposition of 21st and 22nd filters, for the three cells considered in Fig. 1(b). Their corresponding MBFs are reported in (d,e,f) respectively.
the MBF computed at the 22nd frame of the sequence under analysis for the three cells labeled in Fig. 1(b).

5. Discussion and conclusion

Acknowledgments

This work is supported by the Progetto Operativo Nazionale (PON) project MONitoraggio Innovativo per le Coste e l'Ambiente Marino (MONICA) funded by Italian Ministry of Education, University and Research (MIUR).

References and links

1.

A. Aman and T. Piotrowski, “Cell migration during morphogenesis,” Dev. Biol. 341(1), 20–33 (2010). [CrossRef] [PubMed]

2.

E. Van Goethem, R. Poincloux, F. Gauffre, I. Maridonneau-Parini, and V. Le Cabec, “Matrix architecture dictates three-dimensional migration modes of human macrophages: differential involvement of proteases and podosome-like structures,” J. Immunol. 184(2), 1049–1061 (2010). [CrossRef] [PubMed]

3.

P. P. Provenzano, K. W. Eliceiri, and P. J. Keely, “Shining new light on 3D cell motility and the metastatic process,” Trends Cell Biol. 19(11), 638–648 (2009). [CrossRef] [PubMed]

4.

D. Guarnieri, A. De Capua, M. Ventre, A. Borzacchiello, C. Pedone, D. Marasco, M. Ruvo, and P. A. Netti, “Covalently immobilized RGD gradient on PEG hydrogel scaffold influences cell migration parameters,” Acta Biomater. 6(7), 2532–2539 (2010). [CrossRef] [PubMed]

5.

M. Ventre, F. Valle, M. Bianchi, F. Biscarini, and P. A. Netti, “Cell fluidics: producing cellular streams on micropatterned synthetic surfaces,” Langmuir 28(1), 714–721 (2012). [CrossRef] [PubMed]

6.

Z. N. Demou and L. V. McIntire, “Fully automated three-dimensional tracking of cancer cells in collagen gels: determination of motility phenotypes at the cellular level,” Cancer Res. 62(18), 5301–5307 (2002). [PubMed]

7.

P. Memmolo, C. Distante, M. Paturzo, A. Finizio, P. Ferraro, and B. Javidi, “Automatic focusing in digital holography and its application to stretched holograms,” Opt. Lett. 36(10), 1945–1947 (2011). [CrossRef] [PubMed]

8.

M. Paturzo and P. Ferraro, “Creating an extended focus image of a tilted object in Fourier digital holography,” Opt. Express 17(22), 20546–20552 (2009). [CrossRef] [PubMed]

9.

C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Extended focused imaging for digital holograms of macroscopic three-dimensional objects,” Appl. Opt. 47(19), D71–D79 (2008). [CrossRef] [PubMed]

10.

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]

11.

G. G. Martins and J. Kolega, “Endothelial cell protrusion and migration in three-dimensional collagen matrices,” Cell Motil. Cytoskeleton 63(2), 101–115 (2006). [CrossRef] [PubMed]

12.

R. T. Franceschi, W. M. James, and G. Zerlauth, “1 alpha, 25-dihydroxyvitamin D3 specific regulation of growth, morphology, and fibronectin in a human osteosarcoma cell line,” J. Cell. Physiol. 123(3), 401–409 (1985). [CrossRef] [PubMed]

13.

K. Schumacher, R. Strehl, U. de Vries, and W. W. Minuth, “Advanced technique for long term culture of epithelia in a continuous luminal-basal medium gradient,” Biomaterials 23(3), 805–815 (2002). [CrossRef] [PubMed]

14.

P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14(1), 014018 (2009). [CrossRef] [PubMed]

15.

J. Persson, A. Mölder, S. G. Pettersson, and K. Alm, “Cell motility studies using digital holographic microscopy,” in Microscopy: Science, Technology, Applications and Education. Microscopy Series4, 1063–1072 (2010).

16.

P. Memmolo, A. Finizio, M. Paturzo, L. Miccio, and P. Ferraro, “Twin-beams digital holography for 3D tracking and quantitative phase-contrast microscopy in microfluidics,” Opt. Express 19(25), 25833–25842 (2011). [CrossRef] [PubMed]

17.

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]

18.

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]

19.

P. Langehanenberg, B. Kemper, D. Dirksen, and G. von Bally, “Autofocusing in digital holographic phase contrast microscopy on pure phase objects for live cell imaging,” Appl. Opt. 47(19), D176–D182 (2008). [CrossRef] [PubMed]

20.

S. Lee, J. Y. Lee, W. Yang, and D. Y. Kim, “Autofocusing and edge detection schemes in cell volume measurements with quantitative phase microscopy,” Opt. Express 17(8), 6476–6486 (2009). [CrossRef] [PubMed]

21.

Z. Zhang and C.-H. Menq, “Three-dimensional particle tracking with subnanometer resolution using off-focus images,” Appl. Opt. 47(13), 2361–2370 (2008). [CrossRef] [PubMed]

22.

J. F. Restrepo and J. Garcia-Sucerquia, “Automatic three-dimensional tracking of particles with high-numerical-aperture digital lensless holographic microscopy,” Opt. Lett. 37(4), 752–754 (2012). [CrossRef] [PubMed]

23.

P. Memmolo, I. Esnaola, A. Finizio, M. Paturzo, P. Ferraro, and A. M. Tulino, “SPADEDH: a sparsity-based denoising method of digital holograms without knowing the noise statistics,” Opt. Express 20(15), 17250–17257 (2012). [CrossRef]

OCIS Codes
(180.3170) Microscopy : Interference microscopy
(180.6900) Microscopy : Three-dimensional microscopy
(090.1995) Holography : Digital holography

ToC Category:
Microscopy

History
Original Manuscript: October 10, 2012
Revised Manuscript: October 22, 2012
Manuscript Accepted: October 22, 2012
Published: December 7, 2012

Virtual Issues
Vol. 8, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Pasquale Memmolo, Maria Iannone, Maurizio Ventre, Paolo Antonio Netti, Andrea Finizio, Melania Paturzo, and Pietro Ferraro, "On the holographic 3D tracking of in vitro cells characterized by a highly-morphological change," Opt. Express 20, 28485-28493 (2012)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-27-28485


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References

  1. A. Aman and T. Piotrowski, “Cell migration during morphogenesis,” Dev. Biol.341(1), 20–33 (2010). [CrossRef] [PubMed]
  2. E. Van Goethem, R. Poincloux, F. Gauffre, I. Maridonneau-Parini, and V. Le Cabec, “Matrix architecture dictates three-dimensional migration modes of human macrophages: differential involvement of proteases and podosome-like structures,” J. Immunol.184(2), 1049–1061 (2010). [CrossRef] [PubMed]
  3. P. P. Provenzano, K. W. Eliceiri, and P. J. Keely, “Shining new light on 3D cell motility and the metastatic process,” Trends Cell Biol.19(11), 638–648 (2009). [CrossRef] [PubMed]
  4. D. Guarnieri, A. De Capua, M. Ventre, A. Borzacchiello, C. Pedone, D. Marasco, M. Ruvo, and P. A. Netti, “Covalently immobilized RGD gradient on PEG hydrogel scaffold influences cell migration parameters,” Acta Biomater.6(7), 2532–2539 (2010). [CrossRef] [PubMed]
  5. M. Ventre, F. Valle, M. Bianchi, F. Biscarini, and P. A. Netti, “Cell fluidics: producing cellular streams on micropatterned synthetic surfaces,” Langmuir28(1), 714–721 (2012). [CrossRef] [PubMed]
  6. Z. N. Demou and L. V. McIntire, “Fully automated three-dimensional tracking of cancer cells in collagen gels: determination of motility phenotypes at the cellular level,” Cancer Res.62(18), 5301–5307 (2002). [PubMed]
  7. P. Memmolo, C. Distante, M. Paturzo, A. Finizio, P. Ferraro, and B. Javidi, “Automatic focusing in digital holography and its application to stretched holograms,” Opt. Lett.36(10), 1945–1947 (2011). [CrossRef] [PubMed]
  8. M. Paturzo and P. Ferraro, “Creating an extended focus image of a tilted object in Fourier digital holography,” Opt. Express17(22), 20546–20552 (2009). [CrossRef] [PubMed]
  9. C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Extended focused imaging for digital holograms of macroscopic three-dimensional objects,” Appl. Opt.47(19), D71–D79 (2008). [CrossRef] [PubMed]
  10. 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]
  11. G. G. Martins and J. Kolega, “Endothelial cell protrusion and migration in three-dimensional collagen matrices,” Cell Motil. Cytoskeleton63(2), 101–115 (2006). [CrossRef] [PubMed]
  12. R. T. Franceschi, W. M. James, and G. Zerlauth, “1 alpha, 25-dihydroxyvitamin D3 specific regulation of growth, morphology, and fibronectin in a human osteosarcoma cell line,” J. Cell. Physiol.123(3), 401–409 (1985). [CrossRef] [PubMed]
  13. K. Schumacher, R. Strehl, U. de Vries, and W. W. Minuth, “Advanced technique for long term culture of epithelia in a continuous luminal-basal medium gradient,” Biomaterials23(3), 805–815 (2002). [CrossRef] [PubMed]
  14. P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt.14(1), 014018 (2009). [CrossRef] [PubMed]
  15. J. Persson, A. Mölder, S. G. Pettersson, and K. Alm, “Cell motility studies using digital holographic microscopy,” in Microscopy: Science, Technology, Applications and Education. Microscopy Series4, 1063–1072 (2010).
  16. P. Memmolo, A. Finizio, M. Paturzo, L. Miccio, and P. Ferraro, “Twin-beams digital holography for 3D tracking and quantitative phase-contrast microscopy in microfluidics,” Opt. Express19(25), 25833–25842 (2011). [CrossRef] [PubMed]
  17. 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]
  18. 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]
  19. P. Langehanenberg, B. Kemper, D. Dirksen, and G. von Bally, “Autofocusing in digital holographic phase contrast microscopy on pure phase objects for live cell imaging,” Appl. Opt.47(19), D176–D182 (2008). [CrossRef] [PubMed]
  20. S. Lee, J. Y. Lee, W. Yang, and D. Y. Kim, “Autofocusing and edge detection schemes in cell volume measurements with quantitative phase microscopy,” Opt. Express17(8), 6476–6486 (2009). [CrossRef] [PubMed]
  21. Z. Zhang and C.-H. Menq, “Three-dimensional particle tracking with subnanometer resolution using off-focus images,” Appl. Opt.47(13), 2361–2370 (2008). [CrossRef] [PubMed]
  22. J. F. Restrepo and J. Garcia-Sucerquia, “Automatic three-dimensional tracking of particles with high-numerical-aperture digital lensless holographic microscopy,” Opt. Lett.37(4), 752–754 (2012). [CrossRef] [PubMed]
  23. P. Memmolo, I. Esnaola, A. Finizio, M. Paturzo, P. Ferraro, and A. M. Tulino, “SPADEDH: a sparsity-based denoising method of digital holograms without knowing the noise statistics,” Opt. Express20(15), 17250–17257 (2012). [CrossRef]

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