Abstract

We describe a simple holographic method that has enabled us to capture as a single data set the trajectories of micrometer-sized objects suspended in water. By subtracting consecutive holograms of a particle suspension and then adding these difference holograms, we constructed a final data set that contains the time evolution of the particle trajectories free from spurious background interference effects. The method is illustrated by a recording of the motion of 510µm diameter algae in water.

© 2003 Optical Society of America

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  1. R. B. Owen and A. A. Zozulya, Opt. Eng. 39, 2187 (2000).
    [CrossRef]
  2. E. Malkiel, O. Alquaddoomi, and J. Katz, Meas. Sci. Technol. 10, 1142 (1999).
    [CrossRef]
  3. P. R. Hobson and J. Watson, Meas. Sci. Technol. 10, 1153 (1999).
    [CrossRef]
  4. H. Hinrichs, K. D. Hinsch, J. Kickstein, and M. Boehmer, Exp. Fluids 24, 333 (1998).
    [CrossRef]
  5. E. R. Dufresne, D. Altman, and D. G. Grier, Europhys. Lett. 53, 264 (2001).
    [CrossRef]
  6. J. C. Crocker and D. G. Grier, J. Colloid Interface Sci. 179, 298 (1995).
    [CrossRef]
  7. W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, Proc. Natl. Acad. Sci. USA 98, 11301 (2001).
    [CrossRef]
  8. W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, Appl. Opt. 41, 5367 (2002).
    [CrossRef] [PubMed]
  9. H. J. Kreuzer, M. H. Jericho, I. A. Meinertzhagen, and W. B. Xu, J. Phys. Condens. Matter 13, 10, 729 (2001).
    [CrossRef]
  10. H. J. Kreuzer and R. A. Pawlitzek, LEEPS, Version 1.2, a software package for the simulation and reconstruction of Low-Energy Electron Point source images and other holograms (1993–1998) available from the authors.
  11. A film of the motion of Tetraselmis can be viewed at http://www.physics.dal.ca/~kreuzer (click on DIH and proceed).

2002

2001

E. R. Dufresne, D. Altman, and D. G. Grier, Europhys. Lett. 53, 264 (2001).
[CrossRef]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, Proc. Natl. Acad. Sci. USA 98, 11301 (2001).
[CrossRef]

H. J. Kreuzer, M. H. Jericho, I. A. Meinertzhagen, and W. B. Xu, J. Phys. Condens. Matter 13, 10, 729 (2001).
[CrossRef]

2000

R. B. Owen and A. A. Zozulya, Opt. Eng. 39, 2187 (2000).
[CrossRef]

1999

E. Malkiel, O. Alquaddoomi, and J. Katz, Meas. Sci. Technol. 10, 1142 (1999).
[CrossRef]

P. R. Hobson and J. Watson, Meas. Sci. Technol. 10, 1153 (1999).
[CrossRef]

1998

H. Hinrichs, K. D. Hinsch, J. Kickstein, and M. Boehmer, Exp. Fluids 24, 333 (1998).
[CrossRef]

1995

J. C. Crocker and D. G. Grier, J. Colloid Interface Sci. 179, 298 (1995).
[CrossRef]

Alquaddoomi, O.

E. Malkiel, O. Alquaddoomi, and J. Katz, Meas. Sci. Technol. 10, 1142 (1999).
[CrossRef]

Altman, D.

E. R. Dufresne, D. Altman, and D. G. Grier, Europhys. Lett. 53, 264 (2001).
[CrossRef]

Boehmer, M.

H. Hinrichs, K. D. Hinsch, J. Kickstein, and M. Boehmer, Exp. Fluids 24, 333 (1998).
[CrossRef]

Crocker, J. C.

J. C. Crocker and D. G. Grier, J. Colloid Interface Sci. 179, 298 (1995).
[CrossRef]

Dufresne, E. R.

E. R. Dufresne, D. Altman, and D. G. Grier, Europhys. Lett. 53, 264 (2001).
[CrossRef]

Grier, D. G.

E. R. Dufresne, D. Altman, and D. G. Grier, Europhys. Lett. 53, 264 (2001).
[CrossRef]

J. C. Crocker and D. G. Grier, J. Colloid Interface Sci. 179, 298 (1995).
[CrossRef]

Hinrichs, H.

H. Hinrichs, K. D. Hinsch, J. Kickstein, and M. Boehmer, Exp. Fluids 24, 333 (1998).
[CrossRef]

Hinsch, K. D.

H. Hinrichs, K. D. Hinsch, J. Kickstein, and M. Boehmer, Exp. Fluids 24, 333 (1998).
[CrossRef]

Hobson, P. R.

P. R. Hobson and J. Watson, Meas. Sci. Technol. 10, 1153 (1999).
[CrossRef]

Jericho, M. H.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, Appl. Opt. 41, 5367 (2002).
[CrossRef] [PubMed]

H. J. Kreuzer, M. H. Jericho, I. A. Meinertzhagen, and W. B. Xu, J. Phys. Condens. Matter 13, 10, 729 (2001).
[CrossRef]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, Proc. Natl. Acad. Sci. USA 98, 11301 (2001).
[CrossRef]

Katz, J.

E. Malkiel, O. Alquaddoomi, and J. Katz, Meas. Sci. Technol. 10, 1142 (1999).
[CrossRef]

Kickstein, J.

H. Hinrichs, K. D. Hinsch, J. Kickstein, and M. Boehmer, Exp. Fluids 24, 333 (1998).
[CrossRef]

Kreuzer, H. J.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, Appl. Opt. 41, 5367 (2002).
[CrossRef] [PubMed]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, Proc. Natl. Acad. Sci. USA 98, 11301 (2001).
[CrossRef]

H. J. Kreuzer, M. H. Jericho, I. A. Meinertzhagen, and W. B. Xu, J. Phys. Condens. Matter 13, 10, 729 (2001).
[CrossRef]

H. J. Kreuzer and R. A. Pawlitzek, LEEPS, Version 1.2, a software package for the simulation and reconstruction of Low-Energy Electron Point source images and other holograms (1993–1998) available from the authors.

Malkiel, E.

E. Malkiel, O. Alquaddoomi, and J. Katz, Meas. Sci. Technol. 10, 1142 (1999).
[CrossRef]

Meinertzhagen, I. A.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, Appl. Opt. 41, 5367 (2002).
[CrossRef] [PubMed]

H. J. Kreuzer, M. H. Jericho, I. A. Meinertzhagen, and W. B. Xu, J. Phys. Condens. Matter 13, 10, 729 (2001).
[CrossRef]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, Proc. Natl. Acad. Sci. USA 98, 11301 (2001).
[CrossRef]

Owen, R. B.

R. B. Owen and A. A. Zozulya, Opt. Eng. 39, 2187 (2000).
[CrossRef]

Pawlitzek, R. A.

H. J. Kreuzer and R. A. Pawlitzek, LEEPS, Version 1.2, a software package for the simulation and reconstruction of Low-Energy Electron Point source images and other holograms (1993–1998) available from the authors.

Watson, J.

P. R. Hobson and J. Watson, Meas. Sci. Technol. 10, 1153 (1999).
[CrossRef]

Xu, W.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, Appl. Opt. 41, 5367 (2002).
[CrossRef] [PubMed]

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, Proc. Natl. Acad. Sci. USA 98, 11301 (2001).
[CrossRef]

Xu, W. B.

H. J. Kreuzer, M. H. Jericho, I. A. Meinertzhagen, and W. B. Xu, J. Phys. Condens. Matter 13, 10, 729 (2001).
[CrossRef]

Zozulya, A. A.

R. B. Owen and A. A. Zozulya, Opt. Eng. 39, 2187 (2000).
[CrossRef]

Appl. Opt.

Europhys. Lett.

E. R. Dufresne, D. Altman, and D. G. Grier, Europhys. Lett. 53, 264 (2001).
[CrossRef]

Exp. Fluids

H. Hinrichs, K. D. Hinsch, J. Kickstein, and M. Boehmer, Exp. Fluids 24, 333 (1998).
[CrossRef]

J. Colloid Interface Sci.

J. C. Crocker and D. G. Grier, J. Colloid Interface Sci. 179, 298 (1995).
[CrossRef]

J. Phys. Condens. Matter

H. J. Kreuzer, M. H. Jericho, I. A. Meinertzhagen, and W. B. Xu, J. Phys. Condens. Matter 13, 10, 729 (2001).
[CrossRef]

LEEPS, Version 1.2

H. J. Kreuzer and R. A. Pawlitzek, LEEPS, Version 1.2, a software package for the simulation and reconstruction of Low-Energy Electron Point source images and other holograms (1993–1998) available from the authors.

Meas. Sci. Technol.

E. Malkiel, O. Alquaddoomi, and J. Katz, Meas. Sci. Technol. 10, 1142 (1999).
[CrossRef]

P. R. Hobson and J. Watson, Meas. Sci. Technol. 10, 1153 (1999).
[CrossRef]

Opt. Eng.

R. B. Owen and A. A. Zozulya, Opt. Eng. 39, 2187 (2000).
[CrossRef]

Proc. Natl. Acad. Sci. USA

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, Proc. Natl. Acad. Sci. USA 98, 11301 (2001).
[CrossRef]

Other

A film of the motion of Tetraselmis can be viewed at http://www.physics.dal.ca/~kreuzer (click on DIH and proceed).

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Figures (2)

Fig. 1
Fig. 1

Holograms and reconstructed trajectories of the alga Tetraselmis in seawater. A, single hologram of three algae (T1–T3); inset, bright-field image of a single alga, showing flagella (arrowhead). (Zeiss, Plan-Neofluar 100×/1.30 oil.) B, Sum of 10 difference holograms (from a total of 20) of the trajectories of the algae in A. C, Reconstruction of summed hologram B in one plane with the trajectory of alga T1 in focus. D, Reconstruction from hologram B in the plane 500 µm above that in C. Arrows indicate the directions of algal motion. (Blue laser; 1µm pinhole; source-to-sample distance, 2.5 mm; source-to-CCD camera distance, 20 mm.)

Fig. 2
Fig. 2

Reconstructed trajectories of the alga Tetraselmis in seawater from four individual holograms. A, Arrows mark three algae that are in sharp focus in a plane that was 2.4 mm from the pinhole. B, Arrows mark four algae in sharp focus in a plane 6.7 mm from the pinhole. In both A and B several less sharply reconstructed algae trajectories are visible. Sets of closely spaced reconstruction planes thus permit the determination of algae density throughout volumes several cubic centimeters in size. Analysis of the sample through multiple reconstructions showed that this sample contained 96 algae in a volume of 1 mm3 of seawater. (Blue laser; 1µm pinhole; source-to-CCD camera distance, 3.05 cm; reconstruction area, 1 mm×1 mm.)

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Kr=Sd3ξI˜ξexp2πiξ·r/λξ,

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