Abstract

We present a way to measure the positions and instantaneous velocities of micrometer-scale colloidal spheres using a single holographic snapshot obtained through in-line holographic video microscopy. This method builds on previous quantitative analyses of colloidal holograms by accounting for blurring that occurs as a sphere moves during the camera’s exposure time. The angular variance of a blurred hologram’s radial intensity profile yields both the magnitude and direction of a sphere’s in-plane velocity. At sufficiently low speeds, the same hologram also can be used to characterize other properties, such as the sphere’s radius and refractive index.

© 2011 Optical Society of America

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References

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  1. R. J. Adrian, “Particle-imaging techniques for experimental fluid-mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
    [CrossRef]
  2. M. Raffel, C. E. Willert, S. T. Wereley, and J. Kompenhans, Particle Image Velocimetry: A Practical Guide (Springer, 2007).
  3. S.-H. Lee, Y. Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 15, 18275–18282 (2007).
    [CrossRef] [PubMed]
  4. F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17, 13071–13079 (2009).
    [CrossRef] [PubMed]
  5. F. C. Cheong, B. J. Krishnatreya, and D. G. Grier, “Strategies for three-dimensional particle tracking with holographic video microscopy,” Opt. Express 18, 13563–13573 (2010).
    [CrossRef] [PubMed]
  6. S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express 15, 1505–1512 (2007).
    [CrossRef] [PubMed]
  7. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).
  8. F. C. Cheong, K. Xiao, and D. G. Grier, “Characterization of individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (2009).
    [CrossRef]
  9. P. E. Dimotakis, F. D. Debussy, and M. M. Koochesfahani, “Particle streak velocity field measurements in a two-dimensional mixing layer,” Phys. Fluids 24, 995–999 (1981).
    [CrossRef]
  10. J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45(16), 3893–3901 (2006).
    [CrossRef] [PubMed]

2010

2009

F. C. Cheong, K. Xiao, and D. G. Grier, “Characterization of individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (2009).
[CrossRef]

F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17, 13071–13079 (2009).
[CrossRef] [PubMed]

2007

2006

1991

R. J. Adrian, “Particle-imaging techniques for experimental fluid-mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
[CrossRef]

1981

P. E. Dimotakis, F. D. Debussy, and M. M. Koochesfahani, “Particle streak velocity field measurements in a two-dimensional mixing layer,” Phys. Fluids 24, 995–999 (1981).
[CrossRef]

Adrian, R. J.

R. J. Adrian, “Particle-imaging techniques for experimental fluid-mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
[CrossRef]

Amato-Grill, J.

Cheong, F. C.

Debussy, F. D.

P. E. Dimotakis, F. D. Debussy, and M. M. Koochesfahani, “Particle streak velocity field measurements in a two-dimensional mixing layer,” Phys. Fluids 24, 995–999 (1981).
[CrossRef]

Dimotakis, P. E.

P. E. Dimotakis, F. D. Debussy, and M. M. Koochesfahani, “Particle streak velocity field measurements in a two-dimensional mixing layer,” Phys. Fluids 24, 995–999 (1981).
[CrossRef]

Dixon, L.

Dreyfus, R.

Grier, D. G.

Katz, J.

Kim, S.-H.

Koochesfahani, M. M.

P. E. Dimotakis, F. D. Debussy, and M. M. Koochesfahani, “Particle streak velocity field measurements in a two-dimensional mixing layer,” Phys. Fluids 24, 995–999 (1981).
[CrossRef]

Krishnatreya, B. J.

Lee, S.-H.

Malkiel, E.

Roichman, Y.

Sheng, J.

Sun, B.

van Blaaderen, A.

van Oostrum, P.

Xiao, K.

F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17, 13071–13079 (2009).
[CrossRef] [PubMed]

F. C. Cheong, K. Xiao, and D. G. Grier, “Characterization of individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (2009).
[CrossRef]

Yang, S.-M.

Yi, G.-R.

Annu. Rev. Fluid Mech.

R. J. Adrian, “Particle-imaging techniques for experimental fluid-mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
[CrossRef]

Appl. Opt.

J. Dairy Sci.

F. C. Cheong, K. Xiao, and D. G. Grier, “Characterization of individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (2009).
[CrossRef]

Opt. Express

Phys. Fluids

P. E. Dimotakis, F. D. Debussy, and M. M. Koochesfahani, “Particle streak velocity field measurements in a two-dimensional mixing layer,” Phys. Fluids 24, 995–999 (1981).
[CrossRef]

Other

M. Raffel, C. E. Willert, S. T. Wereley, and J. Kompenhans, Particle Image Velocimetry: A Practical Guide (Springer, 2007).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).

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Figures (5)

Fig. 1
Fig. 1

In-line holographic video microscope. Objects illuminated by a collimated laser beam scatter some of the light to the microscope’s focal plane, where it interferes with the unscattered portion of the beam. The interference pattern is magnified and its intensity pattern recorded by a video camera. Each particle’s holographic image can fit to Lorenz-Mie theory to obtain the particle’s position, size and refractive index. The images show a typical hologram of a 1.5 μm diameter polystyrene sphere in water together with such a fit.

Fig. 2
Fig. 2

Holographic velocimetry. (a) Computed holograms I(r) for (i) a stationary sphere, (ii) a sphere moving by one wavelength along and (iii) a sphere moving diagonally by one wavelength. (b) The integrand of S(t) for the holograms in (a), together with the sin(2θ) mask. (c) The integrand of C(t) for the holograms in (a), together with the cos(2θ) mask.

Fig. 3
Fig. 3

Measurement error in calculated (a) speed and (b) angle for simulated motion-blurred holograms. Accurate results are obtained for displacements larger than one wavelength of light during the exposure time.

Fig. 4
Fig. 4

Details from a sequence of holograms of a moving sphere recorded at 1/6 s intervals. Cropped images are placed in the original coordinate system of the camera, so that overlayed velocity vectors anticipate the position of the sphere’s center in consecutive frames.

Fig. 5
Fig. 5

Distribution of estimated instantaneous speeds as a function of trajectory-averaged speed obtaind from 6,500 snapshots of 1,500 polystyrene spheres flowing down a microfluidic channel. The dashed line of slope 1 is a guide to the eye.

Equations (7)

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I ( r , t ) = | E 0 ( z z p ( t ) ) + E S ( r r p ( t ) ) | 2
I τ ( r , t ) = 0 τ I ( r , t + t ) d t .
I τ ( r , t | v ( t ) ) = I ( r , t ) [ 1 ( v ( t ) v 0 ( τ ) ) cos 2 ( θ + ϕ ( t ) 2 ) ] ,
S ( t ) = I ( r , v , t ) sin ( 2 θ ) d r d θ and
C ( t ) = I ( r , v , t ) cos ( 2 θ ) d r d θ ,
v ( t ) = v 0 S 2 ( t ) + C 2 ( t ) and
ϕ ( t ) = arctan ( S ( t ) C ( t ) ) .

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