Abstract

Poor axial precision caused, in part, by large depth of focus (τ) has been a vexing problem in extraction of particle position from digital in-line holograms. A simple method is proposed to combat this depth-of-focus difficulty. The method is based on decoupling of size and position information. With d,Δ, and λ being particle diameter, CCD pixel size, and the wavelength, respectively, our main theoretical result is the reduction of τ from τd2λ to τΔ2λ for particles of known size. This result is confirmed in laboratory experiments with holograms of calibrated glass spheres.

© 2005 Optical Society of America

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References

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  1. K. D. Hinsch, Meas. Sci. Technol. 13, R61 (2002).
    [CrossRef]
  2. H. Meng, G. Pan, Y. Pu, and S. H. Woodward, Meas. Sci. Technol. 15, 673 (2004).
    [CrossRef]
  3. D. Gabor, in Nobel Lectures, Physics 1971–1980, S. Lundqvist, ed. (World Scientific, Singapore, 1992).
  4. B. J. Thomson, Proc. SPIE 1136, 308 (1989).
    [CrossRef]
  5. C. S. Vikram, Particle Field Holography (Cambridge U. Press, Cambridge, UK, 1992).
    [CrossRef]
  6. J. P. Fugal, R. A. Shaw, E. W. Saw, and A. V. Sergeyev, Appl. Opt. 43, 5987 (2004).
    [CrossRef] [PubMed]
  7. C. S. Vikram and M. L. Billet, Appl. Phys. B 33, 149 (1984).
    [CrossRef]
  8. L. Onural and M. T. Özgen, J. Opt. Soc. Am. A 9, 252 (1992).
    [CrossRef]
  9. L. Onural, Opt. Lett. 18, 846 (1993).
    [CrossRef]
  10. C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, Opt. Lasers Eng. 33, 409 (2000).
    [CrossRef]
  11. S. Coëtmellec, D. Lebrun, and C. Özkul, Appl. Opt. 41, 312 (2002)
    [CrossRef]
  12. S. Murata and N. Yasuda, Opt. Laser Technol. 32, 567 (2000).
    [CrossRef]
  13. R. B. Owen and A. A. Zozulya, Opt. Eng. 39, 2187 (2000).
    [CrossRef]
  14. G. Pan and H. Meng, Appl. Opt. 42, 827 (2003).
    [CrossRef] [PubMed]
  15. C. Fournier, C. Ducottet, and T. Fournel, Meas. Sci. Technol. 15, 686 (2004).
    [CrossRef]
  16. F. Liu and F. Hussain, Opt. Lett. 23, 132 (1998).
    [CrossRef]
  17. J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, Boston, Mass., 1996).
  18. T. Kreis, Opt. Eng. 41, 1829 (2002).
    [CrossRef]
  19. J. Zhang, B. Tao, and J. Katz, Exp. Fluids 23, 373 (1997).
    [CrossRef]
  20. J. Sheng, E. Malkiel, and J. Katz, Appl. Opt. 42, 235 (2003).
    [CrossRef] [PubMed]

2004

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

J. P. Fugal, R. A. Shaw, E. W. Saw, and A. V. Sergeyev, Appl. Opt. 43, 5987 (2004).
[CrossRef] [PubMed]

C. Fournier, C. Ducottet, and T. Fournel, Meas. Sci. Technol. 15, 686 (2004).
[CrossRef]

2003

2002

T. Kreis, Opt. Eng. 41, 1829 (2002).
[CrossRef]

S. Coëtmellec, D. Lebrun, and C. Özkul, Appl. Opt. 41, 312 (2002)
[CrossRef]

K. D. Hinsch, Meas. Sci. Technol. 13, R61 (2002).
[CrossRef]

2000

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, Opt. Lasers Eng. 33, 409 (2000).
[CrossRef]

S. Murata and N. Yasuda, Opt. Laser Technol. 32, 567 (2000).
[CrossRef]

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

1998

1997

J. Zhang, B. Tao, and J. Katz, Exp. Fluids 23, 373 (1997).
[CrossRef]

1993

1992

1989

B. J. Thomson, Proc. SPIE 1136, 308 (1989).
[CrossRef]

1984

C. S. Vikram and M. L. Billet, Appl. Phys. B 33, 149 (1984).
[CrossRef]

Billet, M. L.

C. S. Vikram and M. L. Billet, Appl. Phys. B 33, 149 (1984).
[CrossRef]

Buraga-Lefebvre, C.

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, Opt. Lasers Eng. 33, 409 (2000).
[CrossRef]

Coëtmellec, S.

S. Coëtmellec, D. Lebrun, and C. Özkul, Appl. Opt. 41, 312 (2002)
[CrossRef]

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, Opt. Lasers Eng. 33, 409 (2000).
[CrossRef]

Ducottet, C.

C. Fournier, C. Ducottet, and T. Fournel, Meas. Sci. Technol. 15, 686 (2004).
[CrossRef]

Fournel, T.

C. Fournier, C. Ducottet, and T. Fournel, Meas. Sci. Technol. 15, 686 (2004).
[CrossRef]

Fournier, C.

C. Fournier, C. Ducottet, and T. Fournel, Meas. Sci. Technol. 15, 686 (2004).
[CrossRef]

Fugal, J. P.

Gabor, D.

D. Gabor, in Nobel Lectures, Physics 1971–1980, S. Lundqvist, ed. (World Scientific, Singapore, 1992).

Goodman, J.

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

Hinsch, K. D.

K. D. Hinsch, Meas. Sci. Technol. 13, R61 (2002).
[CrossRef]

Hussain, F.

Katz, J.

J. Sheng, E. Malkiel, and J. Katz, Appl. Opt. 42, 235 (2003).
[CrossRef] [PubMed]

J. Zhang, B. Tao, and J. Katz, Exp. Fluids 23, 373 (1997).
[CrossRef]

Kreis, T.

T. Kreis, Opt. Eng. 41, 1829 (2002).
[CrossRef]

Lebrun, D.

S. Coëtmellec, D. Lebrun, and C. Özkul, Appl. Opt. 41, 312 (2002)
[CrossRef]

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, Opt. Lasers Eng. 33, 409 (2000).
[CrossRef]

Liu, F.

Malkiel, E.

Meng, H.

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

G. Pan and H. Meng, Appl. Opt. 42, 827 (2003).
[CrossRef] [PubMed]

Murata, S.

S. Murata and N. Yasuda, Opt. Laser Technol. 32, 567 (2000).
[CrossRef]

Onural, L.

Owen, R. B.

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

Özgen, M. T.

Özkul, C.

S. Coëtmellec, D. Lebrun, and C. Özkul, Appl. Opt. 41, 312 (2002)
[CrossRef]

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, Opt. Lasers Eng. 33, 409 (2000).
[CrossRef]

Pan, G.

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

G. Pan and H. Meng, Appl. Opt. 42, 827 (2003).
[CrossRef] [PubMed]

Pu, Y.

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

Saw, E. W.

Sergeyev, A. V.

Shaw, R. A.

Sheng, J.

Tao, B.

J. Zhang, B. Tao, and J. Katz, Exp. Fluids 23, 373 (1997).
[CrossRef]

Thomson, B. J.

B. J. Thomson, Proc. SPIE 1136, 308 (1989).
[CrossRef]

Vikram, C. S.

C. S. Vikram and M. L. Billet, Appl. Phys. B 33, 149 (1984).
[CrossRef]

C. S. Vikram, Particle Field Holography (Cambridge U. Press, Cambridge, UK, 1992).
[CrossRef]

Woodward, S. H.

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

Yasuda, N.

S. Murata and N. Yasuda, Opt. Laser Technol. 32, 567 (2000).
[CrossRef]

Zhang, J.

J. Zhang, B. Tao, and J. Katz, Exp. Fluids 23, 373 (1997).
[CrossRef]

Zozulya, A. A.

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

Appl. Opt.

Appl. Phys. B

C. S. Vikram and M. L. Billet, Appl. Phys. B 33, 149 (1984).
[CrossRef]

Exp. Fluids

J. Zhang, B. Tao, and J. Katz, Exp. Fluids 23, 373 (1997).
[CrossRef]

J. Opt. Soc. Am. A

Meas. Sci. Technol.

K. D. Hinsch, Meas. Sci. Technol. 13, R61 (2002).
[CrossRef]

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

C. Fournier, C. Ducottet, and T. Fournel, Meas. Sci. Technol. 15, 686 (2004).
[CrossRef]

Opt. Eng.

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

T. Kreis, Opt. Eng. 41, 1829 (2002).
[CrossRef]

Opt. Laser Technol.

S. Murata and N. Yasuda, Opt. Laser Technol. 32, 567 (2000).
[CrossRef]

Opt. Lasers Eng.

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, Opt. Lasers Eng. 33, 409 (2000).
[CrossRef]

Opt. Lett.

Proc. SPIE

B. J. Thomson, Proc. SPIE 1136, 308 (1989).
[CrossRef]

Other

C. S. Vikram, Particle Field Holography (Cambridge U. Press, Cambridge, UK, 1992).
[CrossRef]

D. Gabor, in Nobel Lectures, Physics 1971–1980, S. Lundqvist, ed. (World Scientific, Singapore, 1992).

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

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Figures (2)

Fig. 1
Fig. 1

Simulations of the depth-of-focus improvement. The dashed and dashed–dotted curves are the on-axis normalized intensity profiles for the reconstructed fields of a 40- and a 30 - μ m particle before filtering, respectively; the solid curve with a 170 - μ m depth of focus is the common profile obtained after the filters are applied.

Fig. 2
Fig. 2

Experimental demonstration of the depth-of-focus improvement. The top and bottom images in (a) show the normalized intensity distribution on the x z longitude cross-section plane of reconstructed field of a 30 - μ m particle, before and after filtering, respectively. The dashed–dotted and solid curves in (b) show the on-axis normalized intensity profile before and after filtering in the reconstruction, respectively. The improvement of the depth of focus illustrated in Fig. 1 has basically been achieved.

Equations (6)

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τ d 2 λ ,
e z ( u , v ) = [ 1 i ( s , t ) ] h z ( u s , v t ) d s d t ,
e z ( u , v ) = F 1 { [ δ ( η , ξ ) I ( η , ξ ) ] H z ( η , ξ ) } ,
e z ( u , v ) = F 1 { δ ( η , ξ ) I ( η , ξ ) P ( η , ξ ) H z ( η , ξ ) } .
e z ( u , v ) F 1 { H z 0 z ( η , ξ ) } = 1 j λ ( z 0 z ) exp { j π ( u 2 + v 2 ) [ λ ( z 0 z ) ] } .
F ( η , ξ ) = { 1 P ( η , ξ ) P ( η , ξ ) > threshold 0 otherwise } .

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