Abstract

The analysis of coherent light scattering patterns, under certain conditions, for inference of the number of scatterers in each of several possible types is examined in terms of statistical parameter estimation theory. From the spatial autocorrelation of the patterns a criterion is established for reducing to negligible values the variances in estimates caused by spatial irradiance fluctuations. On the basis of these considerations a rationale for the use of optical processing to effect minimumvariance linear unbiased estimates of particle numbers is given.

© 1980 Optical Society of America

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  1. W. L. Anderson, "Particle counting and sizing by Fourier-plane measurements of scattered light," J. Opt. Soc. Am. 58, 1566–1567A (1968).
  2. W. L. Anderson and R. E. Beissner, "Counting and classifying small objects by far-field light scattering," Appl. Opt. 10, 1503–1508 (1971).
  3. S. Y. Shen and W. L. Anderson, "Small-object counting and classification by scattered light," J. Opt. Soc. Am. 64, 1399A (1974).
  4. H. Stark and B. Dimitriadis, "Minimum-bias spectral estimation with a coherent optical spectrum analyzer," J. Opt. Soc. Am. 65, 425–431/973E (1975).
  5. H. Stark, D. Lee, and B. Dimitriadis, "Smoothing of irradiance spectra with finite-bandwidth windows, with application to particle-size analysis," J. Opt. Soc. Am. 65, 1436–1442 (1975).
  6. H. Stark, D. Lee, and B. W. Koo, "Counting quasicircular particles by an optical-digital method," Appl. Opt. 15, 2246–2249 (1976).
  7. H. Stark and G. Shao, "Design considerations in counting particles by size with an optical-digital training method," Appl. Opt. 16, 1670–1674 (1977).
  8. H. Stark, "Diffraction patterns of nonoverlapping circular grains," J. Opt. Soc. Am. 67, 700–703 (1977).
  9. J. W. Goodman, "Some Effects of Target-Induced Scintillation on Optical Radar Performance," Proc. IEEE 53, 1688–1700 (1965).
  10. R. Barakat, "First-Order Probability Densities of Laser Speckle Patterns Observed through Finite-Size Scanning Apertures," Opt. Acta 20, 729–740 (1973).
  11. J. W. Goodman, "Some fundamental properties of speckle," J. Opt. Soc. Am. 66, 1145–1149 (1976).
  12. T. O. Lewis and P. L. Odell, Estimation in Linear Models (Prentice- Hall, Englewood Cliffs, N. J., 1971), pp. 52–55.
  13. J. H. Ward, "Determination of particle-size distributions from composite diffraction-pattern data," J. Opt. Soc. Am. 58, 1566A (1968).
  14. F. P. Carlson and C. K. Lee, "An Adaptive Coherent Optical Processor for Cell Recognition and Counting," IEEE Trans. BioMed. Engr. BME-25, 361–367 (1978).
  15. H. L. van Trees, Detection, Estimation and Modulation Theory, Part I, (Wiley, New York, 1968), p. 76.

1978 (1)

F. P. Carlson and C. K. Lee, "An Adaptive Coherent Optical Processor for Cell Recognition and Counting," IEEE Trans. BioMed. Engr. BME-25, 361–367 (1978).

1977 (2)

1976 (2)

1975 (2)

1974 (1)

S. Y. Shen and W. L. Anderson, "Small-object counting and classification by scattered light," J. Opt. Soc. Am. 64, 1399A (1974).

1973 (1)

R. Barakat, "First-Order Probability Densities of Laser Speckle Patterns Observed through Finite-Size Scanning Apertures," Opt. Acta 20, 729–740 (1973).

1971 (1)

1968 (2)

J. H. Ward, "Determination of particle-size distributions from composite diffraction-pattern data," J. Opt. Soc. Am. 58, 1566A (1968).

W. L. Anderson, "Particle counting and sizing by Fourier-plane measurements of scattered light," J. Opt. Soc. Am. 58, 1566–1567A (1968).

Anderson, W. L.

S. Y. Shen and W. L. Anderson, "Small-object counting and classification by scattered light," J. Opt. Soc. Am. 64, 1399A (1974).

W. L. Anderson and R. E. Beissner, "Counting and classifying small objects by far-field light scattering," Appl. Opt. 10, 1503–1508 (1971).

W. L. Anderson, "Particle counting and sizing by Fourier-plane measurements of scattered light," J. Opt. Soc. Am. 58, 1566–1567A (1968).

Barakat, R.

R. Barakat, "First-Order Probability Densities of Laser Speckle Patterns Observed through Finite-Size Scanning Apertures," Opt. Acta 20, 729–740 (1973).

Beissner, R. E.

Carlson, F. P.

F. P. Carlson and C. K. Lee, "An Adaptive Coherent Optical Processor for Cell Recognition and Counting," IEEE Trans. BioMed. Engr. BME-25, 361–367 (1978).

Dimitriadis, B.

Goodman, J. W.

J. W. Goodman, "Some fundamental properties of speckle," J. Opt. Soc. Am. 66, 1145–1149 (1976).

J. W. Goodman, "Some Effects of Target-Induced Scintillation on Optical Radar Performance," Proc. IEEE 53, 1688–1700 (1965).

Koo, B. W.

Lee, C. K.

F. P. Carlson and C. K. Lee, "An Adaptive Coherent Optical Processor for Cell Recognition and Counting," IEEE Trans. BioMed. Engr. BME-25, 361–367 (1978).

Lee, D.

Lewis, T. O.

T. O. Lewis and P. L. Odell, Estimation in Linear Models (Prentice- Hall, Englewood Cliffs, N. J., 1971), pp. 52–55.

Odell, P. L.

T. O. Lewis and P. L. Odell, Estimation in Linear Models (Prentice- Hall, Englewood Cliffs, N. J., 1971), pp. 52–55.

Shao, G.

Shen, S. Y.

S. Y. Shen and W. L. Anderson, "Small-object counting and classification by scattered light," J. Opt. Soc. Am. 64, 1399A (1974).

Stark, H.

van Trees, H. L.

H. L. van Trees, Detection, Estimation and Modulation Theory, Part I, (Wiley, New York, 1968), p. 76.

Ward, J. H.

J. H. Ward, "Determination of particle-size distributions from composite diffraction-pattern data," J. Opt. Soc. Am. 58, 1566A (1968).

Appl. Opt. (3)

IEEE Trans. BioMed. Engr. (1)

F. P. Carlson and C. K. Lee, "An Adaptive Coherent Optical Processor for Cell Recognition and Counting," IEEE Trans. BioMed. Engr. BME-25, 361–367 (1978).

J. Opt. Soc. Am. (7)

H. Stark, "Diffraction patterns of nonoverlapping circular grains," J. Opt. Soc. Am. 67, 700–703 (1977).

J. H. Ward, "Determination of particle-size distributions from composite diffraction-pattern data," J. Opt. Soc. Am. 58, 1566A (1968).

H. Stark and B. Dimitriadis, "Minimum-bias spectral estimation with a coherent optical spectrum analyzer," J. Opt. Soc. Am. 65, 425–431/973E (1975).

H. Stark, D. Lee, and B. Dimitriadis, "Smoothing of irradiance spectra with finite-bandwidth windows, with application to particle-size analysis," J. Opt. Soc. Am. 65, 1436–1442 (1975).

J. W. Goodman, "Some fundamental properties of speckle," J. Opt. Soc. Am. 66, 1145–1149 (1976).

W. L. Anderson, "Particle counting and sizing by Fourier-plane measurements of scattered light," J. Opt. Soc. Am. 58, 1566–1567A (1968).

S. Y. Shen and W. L. Anderson, "Small-object counting and classification by scattered light," J. Opt. Soc. Am. 64, 1399A (1974).

Opt. Acta (1)

R. Barakat, "First-Order Probability Densities of Laser Speckle Patterns Observed through Finite-Size Scanning Apertures," Opt. Acta 20, 729–740 (1973).

Other (3)

T. O. Lewis and P. L. Odell, Estimation in Linear Models (Prentice- Hall, Englewood Cliffs, N. J., 1971), pp. 52–55.

J. W. Goodman, "Some Effects of Target-Induced Scintillation on Optical Radar Performance," Proc. IEEE 53, 1688–1700 (1965).

H. L. van Trees, Detection, Estimation and Modulation Theory, Part I, (Wiley, New York, 1968), p. 76.

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