Abstract

We used a real-time joint transform correlation technique for sizing opaque particles. The scheme can be used to estimate the size of both nonspherical and spherical particles. Computer simulation results are presented to illustrate the performance of this technique.

© 1997 Optical Society of America

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References

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  1. M. E. Milham, D. H. Anderson, “Obscuration sciences smoke data compendium: standard smokes,” (U.S. Army Aberdeen Proving Ground, Maryland, 1983).
  2. J. C. Liljegren, W. E. Dunn, G. E. Devaull, A. J. Policasto, “Field study of fog-oil smokes (University of Illinois, Urbana, Ill., 1986).
  3. J. Cairns, K. L. Dickson, P. Pryfogle, S. P. Almeida, S. K. Case, J. M. Fournier, H. Fujii, “Determining the accuracy of coherent optical identification of diatoms,” Water Res. Bull. 15, 1770–1775 (1979).
    [CrossRef]
  4. S. P. Almeida, S. K. Case, J. M. Fournier, H. Junii, J. Cairns, K. L. Dickson, P. Pryfogle, “Analysis of algae using coherent optical processing,” in Proceedings of ICO-11 Conference, (International Commission for Optics, Madrid, Spain, 1978), pp. 351–354.
  5. E. D. Hirleman, P. A. Dellenback, “Adaptive Fraunhofer diffraction particle sizing instrument using a spatial light modulator,” Appl. Opt. 28, 4870–4878 (1989).
    [CrossRef] [PubMed]
  6. E. D. Hirleman, “Particle sizing by optical nonimaging techniques,” in Liquid Particle Size Techniques, STP 484, J. M. Tishkoff, R. D. Ingebo, J. B. Kennedy, eds. (American Society for Testing and Materials, Philadelphia, Pa., 1984), pp. 35–60.
    [CrossRef]
  7. B. J. Thompson, “Droplet characteristics with conventional and holographic techniques,” in Liquid Particle Size Measurement Techniques, STP 848, J. M. Tishkoff, R. D. Ingeho, J. B. Kennedy, eds. (American Society for Testing and Materials, Philadelphia, Pa., 1985), pp. 111–122.
  8. S. D. Coston, N. George, “Particle sizing by inversion of the optical transform pattern,” Appl. Opt. 30, 4785–4794 (1991).
    [CrossRef] [PubMed]
  9. D. A. Ross, “Focused laser beam effects in optical particle sizing by dynamic light scattering,” Appl. Opt. 30, 4882–4888 (1991).
    [CrossRef] [PubMed]
  10. K. A. Kusters, J. G. Wiljers, P. Thoenes, “Particle sizing by laser diffraction spectrometry in the anomalous region,” Appl. Opt. 30, 4839–4847 (1991).
    [CrossRef] [PubMed]
  11. D. D. Cooke, M. Kerker, “Response calculations for light scattering aerosol particle counters,” Appl. Opt. 14, 734–739 (1975).
    [CrossRef] [PubMed]
  12. M. S. Marshall, R. E. Benner, “Spherical particle sizing based on the VanderLugt correlator,” Appl. Opt. 30, 4848–4853 (1991).
    [CrossRef] [PubMed]
  13. C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  14. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  15. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 7.

1991 (4)

1989 (1)

1979 (1)

J. Cairns, K. L. Dickson, P. Pryfogle, S. P. Almeida, S. K. Case, J. M. Fournier, H. Fujii, “Determining the accuracy of coherent optical identification of diatoms,” Water Res. Bull. 15, 1770–1775 (1979).
[CrossRef]

1975 (1)

1966 (1)

Almeida, S. P.

J. Cairns, K. L. Dickson, P. Pryfogle, S. P. Almeida, S. K. Case, J. M. Fournier, H. Fujii, “Determining the accuracy of coherent optical identification of diatoms,” Water Res. Bull. 15, 1770–1775 (1979).
[CrossRef]

S. P. Almeida, S. K. Case, J. M. Fournier, H. Junii, J. Cairns, K. L. Dickson, P. Pryfogle, “Analysis of algae using coherent optical processing,” in Proceedings of ICO-11 Conference, (International Commission for Optics, Madrid, Spain, 1978), pp. 351–354.

Anderson, D. H.

M. E. Milham, D. H. Anderson, “Obscuration sciences smoke data compendium: standard smokes,” (U.S. Army Aberdeen Proving Ground, Maryland, 1983).

Benner, R. E.

Cairns, J.

J. Cairns, K. L. Dickson, P. Pryfogle, S. P. Almeida, S. K. Case, J. M. Fournier, H. Fujii, “Determining the accuracy of coherent optical identification of diatoms,” Water Res. Bull. 15, 1770–1775 (1979).
[CrossRef]

S. P. Almeida, S. K. Case, J. M. Fournier, H. Junii, J. Cairns, K. L. Dickson, P. Pryfogle, “Analysis of algae using coherent optical processing,” in Proceedings of ICO-11 Conference, (International Commission for Optics, Madrid, Spain, 1978), pp. 351–354.

Case, S. K.

J. Cairns, K. L. Dickson, P. Pryfogle, S. P. Almeida, S. K. Case, J. M. Fournier, H. Fujii, “Determining the accuracy of coherent optical identification of diatoms,” Water Res. Bull. 15, 1770–1775 (1979).
[CrossRef]

S. P. Almeida, S. K. Case, J. M. Fournier, H. Junii, J. Cairns, K. L. Dickson, P. Pryfogle, “Analysis of algae using coherent optical processing,” in Proceedings of ICO-11 Conference, (International Commission for Optics, Madrid, Spain, 1978), pp. 351–354.

Cooke, D. D.

Coston, S. D.

Dellenback, P. A.

Devaull, G. E.

J. C. Liljegren, W. E. Dunn, G. E. Devaull, A. J. Policasto, “Field study of fog-oil smokes (University of Illinois, Urbana, Ill., 1986).

Dickson, K. L.

J. Cairns, K. L. Dickson, P. Pryfogle, S. P. Almeida, S. K. Case, J. M. Fournier, H. Fujii, “Determining the accuracy of coherent optical identification of diatoms,” Water Res. Bull. 15, 1770–1775 (1979).
[CrossRef]

S. P. Almeida, S. K. Case, J. M. Fournier, H. Junii, J. Cairns, K. L. Dickson, P. Pryfogle, “Analysis of algae using coherent optical processing,” in Proceedings of ICO-11 Conference, (International Commission for Optics, Madrid, Spain, 1978), pp. 351–354.

Dunn, W. E.

J. C. Liljegren, W. E. Dunn, G. E. Devaull, A. J. Policasto, “Field study of fog-oil smokes (University of Illinois, Urbana, Ill., 1986).

Fournier, J. M.

J. Cairns, K. L. Dickson, P. Pryfogle, S. P. Almeida, S. K. Case, J. M. Fournier, H. Fujii, “Determining the accuracy of coherent optical identification of diatoms,” Water Res. Bull. 15, 1770–1775 (1979).
[CrossRef]

S. P. Almeida, S. K. Case, J. M. Fournier, H. Junii, J. Cairns, K. L. Dickson, P. Pryfogle, “Analysis of algae using coherent optical processing,” in Proceedings of ICO-11 Conference, (International Commission for Optics, Madrid, Spain, 1978), pp. 351–354.

Fujii, H.

J. Cairns, K. L. Dickson, P. Pryfogle, S. P. Almeida, S. K. Case, J. M. Fournier, H. Fujii, “Determining the accuracy of coherent optical identification of diatoms,” Water Res. Bull. 15, 1770–1775 (1979).
[CrossRef]

George, N.

Goodman, J. W.

Hirleman, E. D.

E. D. Hirleman, P. A. Dellenback, “Adaptive Fraunhofer diffraction particle sizing instrument using a spatial light modulator,” Appl. Opt. 28, 4870–4878 (1989).
[CrossRef] [PubMed]

E. D. Hirleman, “Particle sizing by optical nonimaging techniques,” in Liquid Particle Size Techniques, STP 484, J. M. Tishkoff, R. D. Ingebo, J. B. Kennedy, eds. (American Society for Testing and Materials, Philadelphia, Pa., 1984), pp. 35–60.
[CrossRef]

Junii, H.

S. P. Almeida, S. K. Case, J. M. Fournier, H. Junii, J. Cairns, K. L. Dickson, P. Pryfogle, “Analysis of algae using coherent optical processing,” in Proceedings of ICO-11 Conference, (International Commission for Optics, Madrid, Spain, 1978), pp. 351–354.

Kerker, M.

Kusters, K. A.

Liljegren, J. C.

J. C. Liljegren, W. E. Dunn, G. E. Devaull, A. J. Policasto, “Field study of fog-oil smokes (University of Illinois, Urbana, Ill., 1986).

Marshall, M. S.

Milham, M. E.

M. E. Milham, D. H. Anderson, “Obscuration sciences smoke data compendium: standard smokes,” (U.S. Army Aberdeen Proving Ground, Maryland, 1983).

Policasto, A. J.

J. C. Liljegren, W. E. Dunn, G. E. Devaull, A. J. Policasto, “Field study of fog-oil smokes (University of Illinois, Urbana, Ill., 1986).

Pryfogle, P.

J. Cairns, K. L. Dickson, P. Pryfogle, S. P. Almeida, S. K. Case, J. M. Fournier, H. Fujii, “Determining the accuracy of coherent optical identification of diatoms,” Water Res. Bull. 15, 1770–1775 (1979).
[CrossRef]

S. P. Almeida, S. K. Case, J. M. Fournier, H. Junii, J. Cairns, K. L. Dickson, P. Pryfogle, “Analysis of algae using coherent optical processing,” in Proceedings of ICO-11 Conference, (International Commission for Optics, Madrid, Spain, 1978), pp. 351–354.

Ross, D. A.

Thoenes, P.

Thompson, B. J.

B. J. Thompson, “Droplet characteristics with conventional and holographic techniques,” in Liquid Particle Size Measurement Techniques, STP 848, J. M. Tishkoff, R. D. Ingeho, J. B. Kennedy, eds. (American Society for Testing and Materials, Philadelphia, Pa., 1985), pp. 111–122.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Weaver, C. S.

Wiljers, J. G.

Appl. Opt. (7)

Water Res. Bull. (1)

J. Cairns, K. L. Dickson, P. Pryfogle, S. P. Almeida, S. K. Case, J. M. Fournier, H. Fujii, “Determining the accuracy of coherent optical identification of diatoms,” Water Res. Bull. 15, 1770–1775 (1979).
[CrossRef]

Other (7)

S. P. Almeida, S. K. Case, J. M. Fournier, H. Junii, J. Cairns, K. L. Dickson, P. Pryfogle, “Analysis of algae using coherent optical processing,” in Proceedings of ICO-11 Conference, (International Commission for Optics, Madrid, Spain, 1978), pp. 351–354.

E. D. Hirleman, “Particle sizing by optical nonimaging techniques,” in Liquid Particle Size Techniques, STP 484, J. M. Tishkoff, R. D. Ingebo, J. B. Kennedy, eds. (American Society for Testing and Materials, Philadelphia, Pa., 1984), pp. 35–60.
[CrossRef]

B. J. Thompson, “Droplet characteristics with conventional and holographic techniques,” in Liquid Particle Size Measurement Techniques, STP 848, J. M. Tishkoff, R. D. Ingeho, J. B. Kennedy, eds. (American Society for Testing and Materials, Philadelphia, Pa., 1985), pp. 111–122.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 7.

M. E. Milham, D. H. Anderson, “Obscuration sciences smoke data compendium: standard smokes,” (U.S. Army Aberdeen Proving Ground, Maryland, 1983).

J. C. Liljegren, W. E. Dunn, G. E. Devaull, A. J. Policasto, “Field study of fog-oil smokes (University of Illinois, Urbana, Ill., 1986).

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Figures (6)

Fig. 1
Fig. 1

Real-time joint transform correlator.

Fig. 2
Fig. 2

Spherical particle sizing method: (a) measured values of input spherical particle pattern radii versus their actual values when the reference radius is 200 µm and (b) the normalized deviation values versus the radii.

Fig. 3
Fig. 3

Measured radii of spherical particle patterns versus the actual radii of particles obtained with the nonspherical particle sizing technique when the reference particle patterns have radii of (a) 150, (b) 200, and (c) 250 µm.

Fig. 4
Fig. 4

Normalized deviation values versus the radii obtained with the nonspherical particle sizing technique when the reference particle patterns have radii of (a) 150, (b) 200, and (c) 250 µm.

Fig. 5
Fig. 5

Measured areas of nonspherical particle patterns versus the actual areas of particles when the reference particle patterns have radii of (a) 150, (b) 200, and (c) 250 µm.

Fig. 6
Fig. 6

Normalized deviation values versus the areas for nonspherical particles when the reference particle patterns have radii of (a) 150, (b) 200, and (c) 250 µm.

Equations (14)

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I=fx, yf*x, y+gx, yg*x, y+f*x, ygx, yδx+2a+fx, yg*x, yδx-2a,
Ip=fx, yg*x, yδx±2a2.
gx, y=gr=circr/r1,
fx, y=fr=circr/r0,
I=2πcircr/r1circr/r0rdr2.
I=Ip/Ip0=r1/r04.
r1=r0Ip/Ip01/4.
gx, y=1,x, yS0,x, yS.
I=gx, y2dxdy=Sdxdy=S.
I=S+πr02.
k=2πr02S+πr02.
S=2k-1πr02.
r=r02k-11/2.
D=expected value-measured valueexpected value.

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