Abstract

Digital in-line holographic microscopy has a strong potential in measuring various three-dimensional (3D) microscale flow phenomena. However, the axial elongation problem in reconstructing particles severely degrades the measurement accuracy along the light propagation direction. In this Letter, we utilize the lenslike characteristic of tens of micrometers size transparent spherical particles to extract their 3D position. A sharp intensity peak is observed in the reconstructed wave field, resulting from the light-focusing effect of the particle. As a result, the depth-of-focus constraint caused by the particle size is eliminated and the measurement accuracy is drastically improved up to submicrometer resolution.

© 2011 Optical Society of America

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References

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  1. H. A. Stone, A. D. Stroock, and A. Ajdari, Annu. Rev. Fluid Mech. 36, 381 (2004).
    [CrossRef]
  2. J. Sheng, E. Malkiel, and J. Katz, Appl. Opt. 45, 3893 (2006).
    [CrossRef] [PubMed]
  3. S. Kim and S. J. Lee, Exp. Fluids 46, 255 (2009).
    [CrossRef]
  4. T. A. Ooms, R. Lindken, and J. Westerweel, Exp. Fluids 47, 941 (2009).
    [CrossRef]
  5. Y. S. Choi, K. W. Seo, and S. J. Lee, Lab Chip 11, 460 (2011).
    [CrossRef]
  6. H. Meng, G. Pan, Y. Pu, and S. H. Woodward, Meas. Sci. Technol. 15, 673 (2004).
    [CrossRef]
  7. W. Yang, A. B. Kostinski, and R. A. Shaw, Opt. Lett. 30, 1303 (2005).
    [CrossRef] [PubMed]
  8. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  9. M. K. Kim, L. Yu, and J. M. Christopher, J. Opt. A 8, S518 (2006).
    [CrossRef]

2011 (1)

Y. S. Choi, K. W. Seo, and S. J. Lee, Lab Chip 11, 460 (2011).
[CrossRef]

2009 (2)

S. Kim and S. J. Lee, Exp. Fluids 46, 255 (2009).
[CrossRef]

T. A. Ooms, R. Lindken, and J. Westerweel, Exp. Fluids 47, 941 (2009).
[CrossRef]

2006 (2)

J. Sheng, E. Malkiel, and J. Katz, Appl. Opt. 45, 3893 (2006).
[CrossRef] [PubMed]

M. K. Kim, L. Yu, and J. M. Christopher, J. Opt. A 8, S518 (2006).
[CrossRef]

2005 (1)

2004 (2)

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, Meas. Sci. Technol. 15, 673 (2004).
[CrossRef]

H. A. Stone, A. D. Stroock, and A. Ajdari, Annu. Rev. Fluid Mech. 36, 381 (2004).
[CrossRef]

Ajdari, A.

H. A. Stone, A. D. Stroock, and A. Ajdari, Annu. Rev. Fluid Mech. 36, 381 (2004).
[CrossRef]

Choi, Y. S.

Y. S. Choi, K. W. Seo, and S. J. Lee, Lab Chip 11, 460 (2011).
[CrossRef]

Christopher, J. M.

M. K. Kim, L. Yu, and J. M. Christopher, J. Opt. A 8, S518 (2006).
[CrossRef]

Goodman, J. W.

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

Katz, J.

Kim, M. K.

M. K. Kim, L. Yu, and J. M. Christopher, J. Opt. A 8, S518 (2006).
[CrossRef]

Kim, S.

S. Kim and S. J. Lee, Exp. Fluids 46, 255 (2009).
[CrossRef]

Kostinski, A. B.

Lee, S. J.

Y. S. Choi, K. W. Seo, and S. J. Lee, Lab Chip 11, 460 (2011).
[CrossRef]

S. Kim and S. J. Lee, Exp. Fluids 46, 255 (2009).
[CrossRef]

Lindken, R.

T. A. Ooms, R. Lindken, and J. Westerweel, Exp. Fluids 47, 941 (2009).
[CrossRef]

Malkiel, E.

Meng, H.

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, Meas. Sci. Technol. 15, 673 (2004).
[CrossRef]

Ooms, T. A.

T. A. Ooms, R. Lindken, and J. Westerweel, Exp. Fluids 47, 941 (2009).
[CrossRef]

Pan, G.

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, Meas. Sci. Technol. 15, 673 (2004).
[CrossRef]

Pu, Y.

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, Meas. Sci. Technol. 15, 673 (2004).
[CrossRef]

Seo, K. W.

Y. S. Choi, K. W. Seo, and S. J. Lee, Lab Chip 11, 460 (2011).
[CrossRef]

Shaw, R. A.

Sheng, J.

Stone, H. A.

H. A. Stone, A. D. Stroock, and A. Ajdari, Annu. Rev. Fluid Mech. 36, 381 (2004).
[CrossRef]

Stroock, A. D.

H. A. Stone, A. D. Stroock, and A. Ajdari, Annu. Rev. Fluid Mech. 36, 381 (2004).
[CrossRef]

Westerweel, J.

T. A. Ooms, R. Lindken, and J. Westerweel, Exp. Fluids 47, 941 (2009).
[CrossRef]

Woodward, S. H.

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, Meas. Sci. Technol. 15, 673 (2004).
[CrossRef]

Yang, W.

Yu, L.

M. K. Kim, L. Yu, and J. M. Christopher, J. Opt. A 8, S518 (2006).
[CrossRef]

Annu. Rev. Fluid Mech. (1)

H. A. Stone, A. D. Stroock, and A. Ajdari, Annu. Rev. Fluid Mech. 36, 381 (2004).
[CrossRef]

Appl. Opt. (1)

Exp. Fluids (2)

S. Kim and S. J. Lee, Exp. Fluids 46, 255 (2009).
[CrossRef]

T. A. Ooms, R. Lindken, and J. Westerweel, Exp. Fluids 47, 941 (2009).
[CrossRef]

J. Opt. A (1)

M. K. Kim, L. Yu, and J. M. Christopher, J. Opt. A 8, S518 (2006).
[CrossRef]

Lab Chip (1)

Y. S. Choi, K. W. Seo, and S. J. Lee, Lab Chip 11, 460 (2011).
[CrossRef]

Meas. Sci. Technol. (1)

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, Meas. Sci. Technol. 15, 673 (2004).
[CrossRef]

Opt. Lett. (1)

Other (1)

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

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic diagram of the rays passing through a transparent spherical particle. (b) DIHM setup employed in this study: L, laser; NDF, neutral density filter; SF, spatial filter; CL, collimation lens; MO, microscope objective.

Fig. 2
Fig. 2

Comparison of the reconstructed intensity field for transparent and opaque spheres having a similar diameter. The spheres are positioned at the axial distance z = 300 μm from the hologram plane. (a), (b) Microscope image of the transparent sphere ( d = 30.1 μm ) and its hologram. (c), (d) Microscope image of the opaque sphere ( d = 27.7 μm ) and its hologram. (e), (f) Spatial intensity distributions reconstructed from (b) and (d) on an axial plane passing through the center of each sphere. (g) Comparison of the axial intensity profiles for (e) and (f) along the center of each sphere.

Fig. 3
Fig. 3

Comparison of the intensity peak profiles for a sphere of d = 49.7 μm along the (a) x and (b) z axes. (c) Measured z positions of the sphere attached on a slide glass by varying the z position.

Fig. 4
Fig. 4

(a) 3D trajectory of a sphere ( d = 49.7 μm ) moving in a micropipe. The micropipe is tilted at an arbitrary angle. The particle moves up along the bottom surface because of the pressure gradient. (b) Variation of the three measured velocity components.

Equations (3)

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τ p d 2 / λ ,
f = d 2 + ( 2 n o n i ) d 4 ( n i n o ) ,
Γ ( x , y ; z ) = I 1 [ I { h ( x 0 , y 0 ; 0 ) } exp ( i k z z ) ] ,

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