Abstract

In-line holographic optical imaging has the unique capability of high speed imaging in three dimensions at rates limited only by the imaging rate of the camera used. In this technique the 3D data is recorded on the detector in a form of a hologram generated by diffraction between the scattered and unscattered light passing through the sample. For dilute samples of single particles or a small cluster of particles, this technique was shown to result in particle tracking with spatial positioning accuracy of a few nanometers. For dense suspension only approximate reconstruction were achieved with systematic axial positioning errors. We propose a scheme to extend accurate holographic microscopy to dense suspensions, by calibrating the Rayleigh-Sommerfeld reconstruction algorithm against Lorentz-Mie scattering theory. We perform this calibration both numerically and experimentally and define the parameter space in which accurate imaging is achieved, and in which numerical calibration holds. We demonstrate the validity of our approach by imaging two attached particles and measuring the distance between their centers with 36 nm accuracy. A difference of 50 nm in particle diameter is easily measured.

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  1. G. Bolognesi, S. Bianchi, and R. D. Leonardo, “Digital holographic tracking of microprobes for multipoint viscosity measurements,” Opt. Express19, 19245–19254 (2011).
    [CrossRef] [PubMed]
  2. J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt.45, 836–850 (2006).
    [CrossRef] [PubMed]
  3. W. Xu, M. H. Jericho, H. J. Kreuzer, and I. A. Meinertzhagen, “Tracking particles in four dimensions with in-line holographic microscopy,” Opt. Lett.28, 164–166 (2003).
    [CrossRef] [PubMed]
  4. L. Dixon, F. C. Cheong, and D. G. Grier, “Holographic deconvolution microscopy for high-resolution particle tracking,” Opt. Express19, 16410–16417 (2011).
    [CrossRef] [PubMed]
  5. J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt.45, 3893–3901 (2006).
    [CrossRef] [PubMed]
  6. F. C. Cheong, B. J. Krishnatreya, and D. G. Grier, “Strategies for three-dimensional particle tracking with holographic video microscopy,” Opt. Express18, 13563–13573 (2010).
    [CrossRef] [PubMed]
  7. 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, 8051–8065 (2011).
    [CrossRef] [PubMed]
  8. F. C. Cheong and D. G. Grier, “Rotational and translational diffusion of copper oxide nanorods measured with holographic video microscopy,” Opt. Express18, 6555–6562 (2010).
    [CrossRef] [PubMed]
  9. J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci.179, 298 – 310 (1996).
    [CrossRef]
  10. Y.-S. Choi and S.-J. Lee, “High-accuracy three-dimensional position measurement of tens of micrometers size transparent microspheres using digital in-line holographic microscopy,” Opt. Lett.36, 4167–4169 (2011).
    [CrossRef] [PubMed]
  11. L. Cavallini, G. Bolognesi, and R. D. Leonardo, “Real-time digital holographic microscopy of multiple and arbitrarily oriented planes,” Opt. Lett.36, 3491–3493 (2011).
    [CrossRef] [PubMed]
  12. T. Savin and P. S. Doyle, “Role of a finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E71, 041106 (2005).
    [CrossRef]
  13. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2005).
  14. S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express15, 1505–1512 (2007).
    [CrossRef] [PubMed]
  15. Y. Roichman, I. Cholis, and D. G. Grier, “Volumetric imaging of holographic optical traps,” Opt. Express14, 10907–10912 (2006).
    [CrossRef] [PubMed]
  16. S. D. A. Russel, W. B. Schowalter, and W. R. Schowalter, Colloidal Dispersions (Cambridge University Press, 1989).
    [CrossRef]

2011

2010

2007

2006

2005

T. Savin and P. S. Doyle, “Role of a finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E71, 041106 (2005).
[CrossRef]

2003

1996

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

Bianchi, S.

Bolognesi, G.

Cavallini, L.

Cheong, F. C.

Choi, Y.-S.

Cholis, I.

Crocker, J. C.

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

Dixon, L.

Doyle, P. S.

T. Savin and P. S. Doyle, “Role of a finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E71, 041106 (2005).
[CrossRef]

Fung, J.

Garcia-Sucerquia, J.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2005).

Grier, D. G.

Jericho, M. H.

Jericho, S. K.

Katz, J.

Kaz, D. M.

Klages, P.

Kreuzer, H. J.

Krishnatreya, B. J.

Lee, S.-H.

Lee, S.-J.

Leonardo, R. D.

Malkiel, E.

Manoharan, V. N.

Martin, K. E.

McGorty, R.

Meinertzhagen, I. A.

Perry, R. W.

Roichman, Y.

Russel, S. D. A.

S. D. A. Russel, W. B. Schowalter, and W. R. Schowalter, Colloidal Dispersions (Cambridge University Press, 1989).
[CrossRef]

Savin, T.

T. Savin and P. S. Doyle, “Role of a finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E71, 041106 (2005).
[CrossRef]

Schowalter, W. B.

S. D. A. Russel, W. B. Schowalter, and W. R. Schowalter, Colloidal Dispersions (Cambridge University Press, 1989).
[CrossRef]

Schowalter, W. R.

S. D. A. Russel, W. B. Schowalter, and W. R. Schowalter, Colloidal Dispersions (Cambridge University Press, 1989).
[CrossRef]

Sheng, J.

Xu, W.

Appl. Opt.

J. Colloid Interface Sci.

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

Opt. Express

Opt. Lett.

Phys. Rev. E

T. Savin and P. S. Doyle, “Role of a finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E71, 041106 (2005).
[CrossRef]

Other

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2005).

S. D. A. Russel, W. B. Schowalter, and W. R. Schowalter, Colloidal Dispersions (Cambridge University Press, 1989).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Numerical calibration of Rayleigh-Sommerfeld reconstruction against Lorentz-Mie (LM) scattering theory. Calibration graph of polystyrene sphere’s effective focal length Δz = zLMzRS in TE buffer, (a) as a function of the sphere’s size, and (b) as a function of field 0 of-view size. The focal length varies across the sphere’s height and is more significant for larger particles due to the decrease in the number of diffration ring in the field-of-view.

Fig. 2
Fig. 2

Digital holographic microscope (green) combined with holographic optical trapping (HOT) [14] (red). A collimated laser beam (532nm) is expanded to overfill the field of view of a 100x objective lens of an Olympus IX71 microscope instead of its convention bright field illumination. A second laser beam (750nm) is expanded to overfill the face of a special light modulator (SLM) and relayed to the back focal plane of the same objective lens. The light pattern imprinted on the beam by the SLM focuses in the sample plane to form optical traps.

Fig. 3
Fig. 3

Tracking results of a Polystyrene particle, ap = 1.025μm, trapped with holographic optical tweezers at different heights. (a) Particle trajectory (Lorentz-Mie fitting (blue dots)), average height (Lorentz-Mie fitting (black line)), average height (Rayleigh-Sommerfeld reconstruction (red line), height by volumetric imaging (green line). (b) Correlation between zLM and zRS in the lowest trap. (c) Distribution of residuals after correction for systematic difference between zLM and zRS in the lowest trap.

Fig. 4
Fig. 4

Comparing numerical and experimental calibration of Rayleigh-Sommerfeld reconstruction against Lorentz-Mie (LM) fitting. Polystyrene colloids, ap = 0.55 μm, diffusing in TE buffer close (a) and far (b) from the microscope objective’s focal plane.

Fig. 5
Fig. 5

(a) Trajectory of a silica bead suspended in water and floating above a glass floor extracted by Lorentz-Mie fitting (green) and numerically calibrated Rayleigh-Sommerfeld reconstruction (blue). (b) The height probability distribution of the sphere extracted by both methods and shifted so that the maximal values coincide, and confirm theoretical prediction.

Fig. 6
Fig. 6

Center-to-center distance (3D) between a 1 μm and a 2 μm diameter polystyrene attached beads diffusing in water, extracted from their Rayleigh-Sommerfeld reconstructed trajectories. Washed particles without (a) and with (b) calibration. DNA coated particles without (c) and with (d) calibration.

Equations (10)

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E 0 ( r , z ) = E 0 ( r ) e i k z ε ^ 0 E s ( r , z ) = E s ( r , z ) ε ^ ( r , z )
I ( r ) = | E 0 ( r , z ) + E s ( r , z ) | 2 = E 0 2 ( r ) + 2 Re { E 0 ( r ) E s ( r , z ) ε ^ 0 * ε ^ ( r , z ) } + | E s ( r , z ) | 2
b ( r ) I ( r ) I 0 ( r ) 1 2 Re { E S ( r , 0 ) }
E S ( r , z ) = E S ( r , 0 ) h ( r , z )
E S ( r , z ) e i k z 4 π 2 B ( q ) H ( q , z ) e i q r d 2 q
I ˜ D ( ρ ) = I ˜ R ( ρ ) K ˜ ( ρ ) + χ
E s ( r , 0 ) = E 0 ( r p ) f s ( k ( r r p ) )
f s ( k r ) = n = 1 n c i n ( 2 n + 1 ) n ( n + 1 ) [ i a n N e 1 n ( 3 ) ( k r ) b n M o 1 n ( 3 ) ( k r ) ]
B ( r ) I ( r ) I 0 ( r ) 1 + 2 Re { f s ( k ( r r p ) ) ε ^ 0 } + | f s ( k ( r r p ) ) | 2
Pr ( z ) = e E grav + E elect K B T E grav + E elect K B T = 4 π a p 3 Δ ρ g 3 k B T z Q 2 e κ ε κ 2 a p 3 ( z a p )

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