Abstract

The number of colloidal particles per unit of volume that can be imaged correctly with digital lensless holographic microscopy (DLHM) is determined numerically. Typical in-line DLHM holograms with controlled concentration are modeled and reconstructed numerically. By quantifying the ratio of the retrieved particles from the reconstructed hologram to the number of the seeding particles in the modeled intensity, the limit of concentration of the colloidal suspensions up to which DLHM can operate successfully is found numerically. A new shadow density parameter for spherical illumination is defined. The limit of performance of DLHM is determined from a graph of the shadow density versus the efficiency of the microscope.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  35. H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouv. Rev. Opt. 5, 87–93 (1974).
    [CrossRef]
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    [CrossRef]
  37. S. Kim and S. Lee, “Effect of particle number density in in-line digital holographic particle velocimetry,” Exp. Fluids 44, 623–631 (2008).
    [CrossRef]
  38. F. C. Cheong, B. Krishnatreya, and D. G. Grier, “Strategies for three-dimensional particle tracking with holographic video microscopy,” Opt. Express 18, 13563–13573 (2010).
    [CrossRef]

2012 (2)

2011 (2)

2010 (4)

2008 (2)

S. Kim and S. Lee, “Effect of particle number density in in-line digital holographic particle velocimetry,” Exp. Fluids 44, 623–631 (2008).
[CrossRef]

M. Antkowiak, N. Callens, C. Yourassowsky, and F. Dubois, “Extended focused imaging of a microparticle field with digital holographic microscopy,” Opt. Lett. 33, 1626–1628 (2008).
[CrossRef]

2007 (1)

2006 (3)

2004 (1)

2003 (1)

2002 (2)

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography of microspheres,” Appl. Opt. 41, 5367–5375 (2002).
[CrossRef]

P. T. Korda, M. B. Taylor, and D. G. Grier, “Kinetically locked-in colloidal transport in an array of optical tweezers,” Phys. Rev. Lett. 89, 128301 (2002).
[CrossRef]

2001 (1)

2000 (3)

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition,” Science 287, 627–631 (2000).
[CrossRef]

M. D. Ediger, “Movies of the glass transition,” Science 287, 604–605 (2000).
[CrossRef]

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, and D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef]

1996 (1)

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

1988 (1)

J. Barton, “Photoelectron holography,” Phys. Rev. Lett. 61, 1356–1359 (1988).
[CrossRef]

1979 (1)

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man Cybern. 9, 62–66 (1979).
[CrossRef]

1974 (1)

H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouv. Rev. Opt. 5, 87–93 (1974).
[CrossRef]

1951 (1)

D. Gabor, “Microscopy by reconstructed wave fronts: II,” Proc. Phys. Soc. London Sect. B 64, 449–469 (1951).
[CrossRef]

1949 (1)

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 197, 454–487 (1949).
[CrossRef]

Abboud, M.

Allano, D.

Alvarez-Palacio, D. C.

D. C. Alvarez-Palacio and J. Garcia-Sucerquia, “Lensless microscopy technique for static and dynamic colloidal systems,” J. Colloid Interface Sci. 349, 637–640 (2010).
[CrossRef]

Antkowiak, M.

Atlan, M.

Barton, J.

J. Barton, “Photoelectron holography,” Phys. Rev. Lett. 61, 1356–1359 (1988).
[CrossRef]

Bhattacharje, S.

J. Masliyah and S. Bhattacharje, Electrokinetic and Colloid Transport Phenomena (Wiley, 2006).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2002).

Bun, P.

Callens, N.

Casanova, H.

D. Hincapie, C. Restrepo, H. Casanova, H. J. Kreuzer, and J. Garcia-Sucerquia, “Colloidal stability evaluation via digital in-line holographic microscopy,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2008), paper DTuC7.

Chapin, S.

Cheong, F. C.

Coëtmellec, S.

Coppey-Moisan, M.

Crocker, J. C.

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, and D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef]

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition,” Science 287, 627–631 (2000).
[CrossRef]

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

Desbiolles, P.

Dinsmore, A.

Dubois, F.

Dufresne, E.

Ediger, M. D.

M. D. Ediger, “Movies of the glass transition,” Science 287, 604–605 (2000).
[CrossRef]

Fung, J.

Gabor, D.

D. Gabor, “Microscopy by reconstructed wave fronts: II,” Proc. Phys. Soc. London Sect. B 64, 449–469 (1951).
[CrossRef]

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 197, 454–487 (1949).
[CrossRef]

Garcia-Sucerquia, J.

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

J. F. Restrepo and J. Garcia-Sucerquia, “Diffraction-based modeling of high-numerical-aperture in-line lensless holograms,” Appl. Opt. 50, 1745–1752 (2011).
[CrossRef]

D. C. Alvarez-Palacio and J. Garcia-Sucerquia, “Lensless microscopy technique for static and dynamic colloidal systems,” J. Colloid Interface Sci. 349, 637–640 (2010).
[CrossRef]

J. Garcia-Sucerquia, W. Xu, P. Kagles, S. M. Jericho, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836–850 (2006).
[CrossRef]

D. Hincapie, C. Restrepo, H. Casanova, H. J. Kreuzer, and J. Garcia-Sucerquia, “Colloidal stability evaluation via digital in-line holographic microscopy,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2008), paper DTuC7.

Germain, V.

Gisler, T.

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, and D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef]

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Grier, D.

Grier, D. G.

F. C. Cheong, B. Krishnatreya, and D. G. Grier, “Strategies for three-dimensional particle tracking with holographic video microscopy,” Opt. Express 18, 13563–13573 (2010).
[CrossRef]

F. C. Cheong, B. Krishnatreya, and D. G. Grier, “Strategies for three-dimensional particle tracking with holographic video microscopy,” Opt. Express 18, 13563–13573 (2010).
[CrossRef]

P. T. Korda, M. B. Taylor, and D. G. Grier, “Kinetically locked-in colloidal transport in an array of optical tweezers,” Phys. Rev. Lett. 89, 128301 (2002).
[CrossRef]

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

Gross, M.

Hincapie, D.

D. Hincapie, C. Restrepo, H. Casanova, H. J. Kreuzer, and J. Garcia-Sucerquia, “Colloidal stability evaluation via digital in-line holographic microscopy,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2008), paper DTuC7.

Jericho, M. H.

J. Garcia-Sucerquia, W. Xu, P. Kagles, S. M. Jericho, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836–850 (2006).
[CrossRef]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography of microspheres,” Appl. Opt. 41, 5367–5375 (2002).
[CrossRef]

M. H. Jericho and H. J. Kreuzer, “Point source digital in-line holographic microscopy,” in Coherent Light Microscopy, P. P. Ferraro, A. Wax, and Z. Zalevvsky, eds., Springer Series in Surface Sciences (Springer, 2011), pp. 3–30.

Jericho, S. M.

Joud, F.

Kagles, P.

Kaplan, P. D.

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, and D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef]

Kaz, D.

Kim, M.

M. Kim, Digital Holographic Microscopy: Principles, Techniques, and Applications, 1st ed. (Springer, 2011).

Kim, M. W.

Kim, S.

Kim, Y.

Kompenhans, J.

Y. Zhang, G. Shen, A. Schroder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

Korda, P. T.

P. T. Korda, M. B. Taylor, and D. G. Grier, “Kinetically locked-in colloidal transport in an array of optical tweezers,” Phys. Rev. Lett. 89, 128301 (2002).
[CrossRef]

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH Verlag, 2005).

Kreuzer, H. J.

J. Garcia-Sucerquia, W. Xu, P. Kagles, S. M. Jericho, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836–850 (2006).
[CrossRef]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography of microspheres,” Appl. Opt. 41, 5367–5375 (2002).
[CrossRef]

D. Hincapie, C. Restrepo, H. Casanova, H. J. Kreuzer, and J. Garcia-Sucerquia, “Colloidal stability evaluation via digital in-line holographic microscopy,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2008), paper DTuC7.

H. J. Kreuzer, “Holographic microscope and method of hologram reconstruction,” U.S. patent6,411,406 (25June2002).

M. H. Jericho and H. J. Kreuzer, “Point source digital in-line holographic microscopy,” in Coherent Light Microscopy, P. P. Ferraro, A. Wax, and Z. Zalevvsky, eds., Springer Series in Surface Sciences (Springer, 2011), pp. 3–30.

Krishnatreya, B.

Lebrun, D.

Lee, S.

Levitt, A.

Levitt, A. C.

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition,” Science 287, 627–631 (2000).
[CrossRef]

Malek, M.

Manoharan, V.

Martin, K.

Masliyah, J.

J. Masliyah and S. Bhattacharje, Electrokinetic and Colloid Transport Phenomena (Wiley, 2006).

McGorty, R.

Meinertzhagen, I. A.

Meng, H.

Otsu, N.

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man Cybern. 9, 62–66 (1979).
[CrossRef]

Park, H.

Park, Y.

Perry, R.

Pluta, M.

M. Pluta, Advanced Light Microscopy, Principles and Basic Properties (Elsevier Science, 1988).

Prasad, V.

Pu, Y.

Restrepo, C.

D. Hincapie, C. Restrepo, H. Casanova, H. J. Kreuzer, and J. Garcia-Sucerquia, “Colloidal stability evaluation via digital in-line holographic microscopy,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2008), paper DTuC7.

Restrepo, J. F.

Roichman, Y.

Royer, H.

H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouv. Rev. Opt. 5, 87–93 (1974).
[CrossRef]

Schofield, A.

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition,” Science 287, 627–631 (2000).
[CrossRef]

Schramm, L. L.

L. L. Schramm, Emulsions, Foams, and Suspensions: Fundamentals and Applications (WILEY-VCH Verlag, 2005).

Schroder, A.

Y. Zhang, G. Shen, A. Schroder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

Shen, G.

Y. Zhang, G. Shen, A. Schroder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

Taylor, M. B.

P. T. Korda, M. B. Taylor, and D. G. Grier, “Kinetically locked-in colloidal transport in an array of optical tweezers,” Phys. Rev. Lett. 89, 128301 (2002).
[CrossRef]

Tessier, G.

Valentine, M. T.

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, and D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef]

van Blaaderen, A.

van Oostrum, P.

Warnasooriya, N.

Weeks, E.

Weeks, E. R.

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition,” Science 287, 627–631 (2000).
[CrossRef]

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, and D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef]

Weitz, D.

Weitz, D. A.

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition,” Science 287, 627–631 (2000).
[CrossRef]

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, and D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2002).

Xu, W.

Yang, S.

Yi, G.

Yodh, A. G.

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, and D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef]

Yourassowsky, C.

Yu, H.

Zhang, Y.

Y. Zhang, G. Shen, A. Schroder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

Appl. Opt. (4)

Exp. Fluids (1)

S. Kim and S. Lee, “Effect of particle number density in in-line digital holographic particle velocimetry,” Exp. Fluids 44, 623–631 (2008).
[CrossRef]

IEEE Trans. Syst. Man Cybern. (1)

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man Cybern. 9, 62–66 (1979).
[CrossRef]

J. Colloid Interface Sci. (2)

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[CrossRef]

D. C. Alvarez-Palacio and J. Garcia-Sucerquia, “Lensless microscopy technique for static and dynamic colloidal systems,” J. Colloid Interface Sci. 349, 637–640 (2010).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nouv. Rev. Opt. (1)

H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouv. Rev. Opt. 5, 87–93 (1974).
[CrossRef]

Opt. Eng. (1)

Y. Zhang, G. Shen, A. Schroder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

Opt. Express (7)

Opt. Lett. (3)

Phys. Rev. Lett. (3)

J. Barton, “Photoelectron holography,” Phys. Rev. Lett. 61, 1356–1359 (1988).
[CrossRef]

J. C. Crocker, M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, and D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85, 888–891 (2000).
[CrossRef]

P. T. Korda, M. B. Taylor, and D. G. Grier, “Kinetically locked-in colloidal transport in an array of optical tweezers,” Phys. Rev. Lett. 89, 128301 (2002).
[CrossRef]

Proc. Phys. Soc. London Sect. B (1)

D. Gabor, “Microscopy by reconstructed wave fronts: II,” Proc. Phys. Soc. London Sect. B 64, 449–469 (1951).
[CrossRef]

Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. (1)

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 197, 454–487 (1949).
[CrossRef]

Science (2)

E. R. Weeks, J. C. Crocker, A. C. Levitt, A. Schofield, and D. A. Weitz, “Three-dimensional direct imaging of structural relaxation near the colloidal glass transition,” Science 287, 627–631 (2000).
[CrossRef]

M. D. Ediger, “Movies of the glass transition,” Science 287, 604–605 (2000).
[CrossRef]

Other (10)

J. Masliyah and S. Bhattacharje, Electrokinetic and Colloid Transport Phenomena (Wiley, 2006).

L. L. Schramm, Emulsions, Foams, and Suspensions: Fundamentals and Applications (WILEY-VCH Verlag, 2005).

M. Pluta, Advanced Light Microscopy, Principles and Basic Properties (Elsevier Science, 1988).

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Figures (5)

Fig. 1.
Fig. 1.

DLHM conceptual setup. In this illustration, the point source illuminates a colloidal suspension.

Fig. 2.
Fig. 2.

Illustration of the automatic tracking algorithm. (a) Modeled in-line contrast hologram of three particles. The axial projection image, X-Y plane of (b) is obtained by the use of Eq. (6) on 40 reconstructed images; the CROIs are found and labeled. The CROIs are axially backprojected to produce the VOIs, the truncate cones in (c) Profiles along the maximum intensities inside the VOIs with the corresponding SSE values are plotted in (d). The three Gaussian type curves, correspond to the intensity profiles along the VOI # 1, 3, and 4, in that order starting from the left-hand side. The exponential decaying type curve, illustrates the intensity inside the VOI # 2. CROI #2 was intentionally added without particle to show the performance of the method.

Fig. 3.
Fig. 3.

Example of the results for modeling and tracking. While (a) shows the diffraction-like modeled contrast hologram, (b) presents the same obtained with the point-like method. (c) Seeding (circles) and retrieved (squares) scatters obtained from the point-like modeled in-line hologram.

Fig. 4.
Fig. 4.

Analysis of results of the seeding-retrieved scatters shown in Fig. 3(c). The histogram of the absolute error on the seeding-retrieved positions is shown in (a). The red circles in (b) represent the absolute retrieved positions in comparison with the locations of the seeding scatters placed along the blue line.

Fig. 5.
Fig. 5.

Performance of DLHM as for the efficiency of reconstruction versus the shadow parameter. The performance is evaluated for different numerical apertures; see inset for the values; the point-like and diffraction-like modeling methods are used.

Equations (7)

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H(r)=(A0eik|r||r|+n=1Np[Ascat(n)(rn)eik|rrn||rrn|])(A0eik|r||r|+n=1Np[Ascat(n)(rn)eik|rrn||rrn|])*.
H˜(r)=H(r)(A0|r|)2=|A0eik|r||r|+n=1Np[Ascat(n)(rn)eik|rrn||rrn|]|2(A0|r|)2.
Ascat(rn)=i2λScreenH˜(r)A0eik|r||r|exp[ik|rrn|]|rrn|(1+cosχ)dr,
Ascat(rn)=ScreenH˜(r)exp[i2πλ(rn·r|r|)]dr.
Ascat(sΔx,tΔy,z)=ΔxΔyexp[ik(s2ΔxΔx+t2ΔyΔy)2L]m=M/2(M/2)1n=N/2(N/2)1H˜(mΔx,nΔy)×exp[ik(m2ΔxΔx+n2ΔyΔy)2L]exp[ik((sm)2ΔxΔx+(tn)2ΔyΔy)2L].
Im,n=r=1P(Im,nrk=1Ml=1NIk,lr).
ssd=i=1Np(2rpLzi)2W2.

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