Abstract

We describe an efficient algorithm for the sizing of single microspheres having a known index of refraction as a function of wavelength. The algorithm employs a peak-detection routine that determines several resonant frequencies in the radiation scattered from the particle. These measured resonances are then compared with entries from a library of stored resonance locations in order to determine a few neighborhoods within which the size of the particle is likely to lie. A final step finds a local minimum of the cost function within each neighborhood, and the size estimate is determined by selecting the smallest of these local minima. The algorithm has modest computational and memory requirements, and it requires no analysis of complicated features of the resonance spectrum that would call for human intervention. Hence it could be automated for nearly real-time operation using a microprocessor. When applied to the measured resonance spectrum of a fluorescent polystyrene sphere, the algorithm finds the radius with an accuracy limited only by such factors as surface roughness, asphericity, and imperfect knowledge of the refractive index. The algorithm is currently limited to use with first-order resonances.

© 1984 Optical Society of America

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  1. P. Chylek, “Partial-wave resonances and the ripple structure in the Mie normalized cross section,”J. Opt. Soc. Am. 66, 285–287 (1976).
    [CrossRef]
  2. P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
    [CrossRef]
  3. G. J. Rosasco, H. S. Bennett, “Internal field resonance structure: implications for optical absorption and scattering by microspheric particles,”J. Opt. Soc. Am. 68, 1242–1250 (1978).
    [CrossRef]
  4. P. Chylek, J. T. Kiehl, M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978).
    [CrossRef] [PubMed]
  5. R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phy. Rev. Let. 44, 475–478 (1980).
    [CrossRef]
  6. P. R. Conwell, P. W. Barber, C. K. Rushforth, “Resonant spectra of dielectric spheres,” J. Opt. Soc. Am. A 1, 62–67 (1984).
    [CrossRef]
  7. P. W. Barber, J. F. Owen, R. K. Chang, “Resonant scattering for characterization of axisymmetric dielectric objects,”IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
    [CrossRef]
  8. P. Chylek, V. Ramaswamy, A. Ashkin, J. M. Dziedzic, “Simultaneous determination of refractive index and size of spherical dielectric particles from light scattering data,” Appl. Opt. 22, 2302–2307 (1983).
    [CrossRef] [PubMed]
  9. A. J. Wilson, C. I. Franks, I. L. Freeston, “Algorithms for the detection of breaths from respiratory waveform recordings of infants,” Med. Biol. Eng. Comput. 20, 286–292 (1982).
    [CrossRef] [PubMed]
  10. K. S. Fu, Syntactic Pattern Recognition and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1982), pp. 411–444.
  11. J. T. Tou, ed., Software Engineering: Proceedings of the Third Symposium on Computer and Information Sciences (Academic, New York, 1971), pp. 183–202.
  12. T. Pavlidis, Structural Pattern Recognition (Springer-Verlag, New York, 1977), pp. 13–15.
  13. S. C. Hill, R. E. Benner, C. K. Rushforth, P. R. Conwell, “Structural resonances observed in the fluorescence emission from small spheres on substrates,” Appl. Opt. 23, 1680–1683 (1984).
    [CrossRef] [PubMed]

1984 (2)

1983 (1)

1982 (2)

A. J. Wilson, C. I. Franks, I. L. Freeston, “Algorithms for the detection of breaths from respiratory waveform recordings of infants,” Med. Biol. Eng. Comput. 20, 286–292 (1982).
[CrossRef] [PubMed]

P. W. Barber, J. F. Owen, R. K. Chang, “Resonant scattering for characterization of axisymmetric dielectric objects,”IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[CrossRef]

1980 (1)

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phy. Rev. Let. 44, 475–478 (1980).
[CrossRef]

1978 (3)

1976 (1)

Ashkin, A.

Barber, P. W.

P. R. Conwell, P. W. Barber, C. K. Rushforth, “Resonant spectra of dielectric spheres,” J. Opt. Soc. Am. A 1, 62–67 (1984).
[CrossRef]

P. W. Barber, J. F. Owen, R. K. Chang, “Resonant scattering for characterization of axisymmetric dielectric objects,”IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[CrossRef]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phy. Rev. Let. 44, 475–478 (1980).
[CrossRef]

Benner, R. E.

S. C. Hill, R. E. Benner, C. K. Rushforth, P. R. Conwell, “Structural resonances observed in the fluorescence emission from small spheres on substrates,” Appl. Opt. 23, 1680–1683 (1984).
[CrossRef] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phy. Rev. Let. 44, 475–478 (1980).
[CrossRef]

Bennett, H. S.

Chang, R. K.

P. W. Barber, J. F. Owen, R. K. Chang, “Resonant scattering for characterization of axisymmetric dielectric objects,”IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[CrossRef]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phy. Rev. Let. 44, 475–478 (1980).
[CrossRef]

Chylek, P.

Conwell, P. R.

Dziedzic, J. M.

Franks, C. I.

A. J. Wilson, C. I. Franks, I. L. Freeston, “Algorithms for the detection of breaths from respiratory waveform recordings of infants,” Med. Biol. Eng. Comput. 20, 286–292 (1982).
[CrossRef] [PubMed]

Freeston, I. L.

A. J. Wilson, C. I. Franks, I. L. Freeston, “Algorithms for the detection of breaths from respiratory waveform recordings of infants,” Med. Biol. Eng. Comput. 20, 286–292 (1982).
[CrossRef] [PubMed]

Fu, K. S.

K. S. Fu, Syntactic Pattern Recognition and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1982), pp. 411–444.

Hill, S. C.

Kiehl, J. T.

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978).
[CrossRef] [PubMed]

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

Ko, M. K. W.

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978).
[CrossRef] [PubMed]

Owen, J. F.

P. W. Barber, J. F. Owen, R. K. Chang, “Resonant scattering for characterization of axisymmetric dielectric objects,”IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[CrossRef]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phy. Rev. Let. 44, 475–478 (1980).
[CrossRef]

Pavlidis, T.

T. Pavlidis, Structural Pattern Recognition (Springer-Verlag, New York, 1977), pp. 13–15.

Ramaswamy, V.

Rosasco, G. J.

Rushforth, C. K.

Wilson, A. J.

A. J. Wilson, C. I. Franks, I. L. Freeston, “Algorithms for the detection of breaths from respiratory waveform recordings of infants,” Med. Biol. Eng. Comput. 20, 286–292 (1982).
[CrossRef] [PubMed]

Appl. Opt. (3)

IEEE Trans. Antennas Propag. (1)

P. W. Barber, J. F. Owen, R. K. Chang, “Resonant scattering for characterization of axisymmetric dielectric objects,”IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Med. Biol. Eng. Comput. (1)

A. J. Wilson, C. I. Franks, I. L. Freeston, “Algorithms for the detection of breaths from respiratory waveform recordings of infants,” Med. Biol. Eng. Comput. 20, 286–292 (1982).
[CrossRef] [PubMed]

Phy. Rev. Let. (1)

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phy. Rev. Let. 44, 475–478 (1980).
[CrossRef]

Phys. Rev. A (1)

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

Other (3)

K. S. Fu, Syntactic Pattern Recognition and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1982), pp. 411–444.

J. T. Tou, ed., Software Engineering: Proceedings of the Third Symposium on Computer and Information Sciences (Academic, New York, 1971), pp. 183–202.

T. Pavlidis, Structural Pattern Recognition (Springer-Verlag, New York, 1977), pp. 13–15.

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