Abstract

An algorithm for determining the size of dielectric spheres and cylinders by aligning measured and computed resonance locations is presented. The orders of the resonance locations need not be known a priori. The algorithm is applicable to several types of scattering and emission spectra of spheres and cylinders if the index of refraction including dispersion is known and uniform, or nearly uniform, throughout the sphere or cylinder. The algorithm performs well when tested with groups of computed resonance locations of spheres (synthetic data) and with measured fluorescence emission spectra of spheres exhibiting as many as 5 orders of resonance.

© 1985 Optical Society of America

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  1. A. Ashkin, J. M. Dziedzic, “Observations of Resonances in the Radiation Pressure on Dielectric Spheres,” Phys. Rev. Lett. 38, 1351 (1977).
    [CrossRef]
  2. P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial-Wave Resonances,” Phys. Rev. A 18, 2229 (1978).
    [CrossRef]
  3. A. Ashkin, J. M. Dziedzic, “Observations of Optical Resonances of Dielectric Spheres by Light Scattering,” Appl. Opt. 20, 1803 (1981).
    [CrossRef] [PubMed]
  4. 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 (1983).
    [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,” Phys. Rev. Lett. 44, 475 (1980).
    [CrossRef]
  6. 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 (1984).
    [CrossRef] [PubMed]
  7. R. Thurn, W. Kiefer, “Raman-Microsampling Technique Applying Optical Levitation by Radiation Pressure,” Appl. Spectrosc. 38, 78 (1984).
    [CrossRef]
  8. J. B. Snow, S.-X. Qian, R. K. Chang, “Stimulated Raman Scattering from Individual Water and Ethanol Droplets at Morphology-Dependent Resonances,” Opt. Lett. 10, 37 (1985).
    [CrossRef] [PubMed]
  9. J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, “Determination of Optical-Fiber Diameter from Resonances in the Elastic Scattering Spectrum,” Opt. Lett. 6, 272 (1981).
    [CrossRef] [PubMed]
  10. A. Ashkin, J. M. Dziedzic, R. H. Stolen, “Outer Diameter Measurement of Low Birefringence Optical Fibers by a New Resonant Backscatter Technique,” Appl. Opt. 20, 2299 (1981).
    [CrossRef] [PubMed]
  11. J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-Dependent Resonances in Raman Scattering, Fluorescence Emission, and Elastic Scattering from Microparticles,” Aerosol Sci. Technol. 1, 293 (1982).
    [CrossRef]
  12. P. W. Barber, J. F. Owen, R. K. Chang, “Resonant Scattering for Characterization of Axisymmetric Dielectric Objects,” IEEE Trans Antennas Propag. AP-30, 168 (1982).
    [CrossRef]
  13. P. R. Conwell, C. K. Rushforth, R. E. Benner, S. C. Hill, “An Efficient Automated Algorithm for the Sizing of Dielectric Microspheres Using the Resonance Spectrum,” J. Opt. Soc. Am. A 1, 1181 (1984).
    [CrossRef]
  14. H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and Fluorescent Scattering by Molecules Embedded in Small Particles,” Phys. Rev. A 13, 396 (1976).
    [CrossRef]
  15. M. Kerker, S. D. Druger, “Raman and Fluorescent Scattering by Molecules Embedded in Spheres with Radii Up to Several Multiples of the Wavelength,” Appl. Opt. 18, 1172 (1979).
    [CrossRef] [PubMed]
  16. P. R. Conwell, P. W. Barber, C. K. Rushforth, “Resonant Spectra of Dielectric Spheres,” J. Opt. Soc. Am. A 1, 62 (1984). The order of a resonance refers to a particular solution of the characteristic equation of the scatterer (or, equivalently, to a particular pole in a coefficient of the field). In this paper, the lowest frequency resonances that are sharp enough to be distinguished from the background in a computed elastic scattering spectrum are termed the first-order resonances.
    [CrossRef]
  17. H.-M. Tzeng, K. F. Wall, M. B. Long, R. K. Chang, “Laser Emission from Individual Droplets at Wavelengths Corresponding to Morphology-Dependent Resonances,” Opt. Lett. 9, 499 (1984).
    [CrossRef] [PubMed]
  18. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 554–557.
  19. R. Fuchs, K. L. Kliewer, “Optical Modes of Vibration in an Ionic Crystal Sphere,” J. Opt. Soc. Am. 58, 319 (1968).
    [CrossRef]
  20. J. S. Kim, S. S. Lee, “Scattering of Laser Beams and the Optical Potential Well for a Homogeneous Sphere,” J. Opt. Soc. Am. 73, 303 (1983).
    [CrossRef]
  21. H. Chew, D.-S. Wang, M. Kerker, “Elastic Scattering of Evanescent Electromagnetic Waves,” Appl. Opt. 18, 2679 (1979).
    [CrossRef] [PubMed]
  22. M. Kerker, “Resonances in Electromagnetic Scattering by Objects with Negative Absorbtion,” Appl. Opt. 18, 1180 (1979). The analysis is for cylinders; the same arguments hold for spheres.
    [CrossRef] [PubMed]
  23. 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 (1982).
    [CrossRef] [PubMed]
  24. M. A. Fischler, R. A. Elschlager, “The Representation and Matching of Pictorial Structures,” IEEE Trans. Comput. C-22, 67 (1973).
    [CrossRef]
  25. R. W. Christiansen, C. K. Rushforth, “Detecting and Locating Key Words in Continuous Speech Using Linear Predictive Coding,” IEEE Trans. Acoust. Speech Signal Process. ASSP-25, 361 (1977).
    [CrossRef]
  26. We use x = 2πr/λ to facilitate the presentation. In the actual implementation of the algorithm, the medium surrounding the sphere is assumed to have a linear dispersion. See note at end of Appendix B.
  27. R. H. Boundy, R. F. Boyer, S. M. Stoesser, Eds., Styrene: its Polymers, Copolymers and Derivatives (Reinhold, New York, 1952), p. 524.
  28. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Interscience, New York, 1983).
  29. H.-M. Tzeng, K. F. Wall, M. B. Long, R. K. Chang, “Evaporation and Condensation Rates of Liquid Droplets Deduced from Structure Resonances in the Fluorescence Spectra,” Opt. Lett. 9, 273 (1984).
    [CrossRef] [PubMed]
  30. J. V. Dave, “Scattering of Electromagnetic Radiation by a Large, Absorbing Sphere,” IBM J. Res. Dev. 13, 302 (1969).
    [CrossRef]
  31. O. B. Toon, T. P. Ackerman, “Algorithms for the Calculation of Scattering by Stratified Spheres,” Appl. Opt. 20, 3657 (1981).
    [CrossRef] [PubMed]
  32. G. W. Kattawar, G. N. Plass, “Electromagnetic Scattering from Absorbing Spheres,” Appl. Opt. 6, 1377 (1967).
    [CrossRef] [PubMed]

1985

1984

P. R. Conwell, P. W. Barber, C. K. Rushforth, “Resonant Spectra of Dielectric Spheres,” J. Opt. Soc. Am. A 1, 62 (1984). The order of a resonance refers to a particular solution of the characteristic equation of the scatterer (or, equivalently, to a particular pole in a coefficient of the field). In this paper, the lowest frequency resonances that are sharp enough to be distinguished from the background in a computed elastic scattering spectrum are termed the first-order resonances.
[CrossRef]

P. R. Conwell, C. K. Rushforth, R. E. Benner, S. C. Hill, “An Efficient Automated Algorithm for the Sizing of Dielectric Microspheres Using the Resonance Spectrum,” J. Opt. Soc. Am. A 1, 1181 (1984).
[CrossRef]

H.-M. Tzeng, K. F. Wall, M. B. Long, R. K. Chang, “Evaporation and Condensation Rates of Liquid Droplets Deduced from Structure Resonances in the Fluorescence Spectra,” Opt. Lett. 9, 273 (1984).
[CrossRef] [PubMed]

H.-M. Tzeng, K. F. Wall, M. B. Long, R. K. Chang, “Laser Emission from Individual Droplets at Wavelengths Corresponding to Morphology-Dependent Resonances,” Opt. Lett. 9, 499 (1984).
[CrossRef] [PubMed]

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 (1984).
[CrossRef] [PubMed]

R. Thurn, W. Kiefer, “Raman-Microsampling Technique Applying Optical Levitation by Radiation Pressure,” Appl. Spectrosc. 38, 78 (1984).
[CrossRef]

1983

1982

J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-Dependent Resonances in Raman Scattering, Fluorescence Emission, and Elastic Scattering from Microparticles,” Aerosol Sci. Technol. 1, 293 (1982).
[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 (1982).
[CrossRef]

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 (1982).
[CrossRef] [PubMed]

1981

1980

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structure Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

1979

1978

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial-Wave Resonances,” Phys. Rev. A 18, 2229 (1978).
[CrossRef]

1977

A. Ashkin, J. M. Dziedzic, “Observations of Resonances in the Radiation Pressure on Dielectric Spheres,” Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

R. W. Christiansen, C. K. Rushforth, “Detecting and Locating Key Words in Continuous Speech Using Linear Predictive Coding,” IEEE Trans. Acoust. Speech Signal Process. ASSP-25, 361 (1977).
[CrossRef]

1976

H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and Fluorescent Scattering by Molecules Embedded in Small Particles,” Phys. Rev. A 13, 396 (1976).
[CrossRef]

1973

M. A. Fischler, R. A. Elschlager, “The Representation and Matching of Pictorial Structures,” IEEE Trans. Comput. C-22, 67 (1973).
[CrossRef]

1969

J. V. Dave, “Scattering of Electromagnetic Radiation by a Large, Absorbing Sphere,” IBM J. Res. Dev. 13, 302 (1969).
[CrossRef]

1968

1967

Ackerman, T. P.

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 (1984). The order of a resonance refers to a particular solution of the characteristic equation of the scatterer (or, equivalently, to a particular pole in a coefficient of the field). In this paper, the lowest frequency resonances that are sharp enough to be distinguished from the background in a computed elastic scattering spectrum are termed the first-order resonances.
[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 (1982).
[CrossRef]

J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-Dependent Resonances in Raman Scattering, Fluorescence Emission, and Elastic Scattering from Microparticles,” Aerosol Sci. Technol. 1, 293 (1982).
[CrossRef]

J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, “Determination of Optical-Fiber Diameter from Resonances in the Elastic Scattering Spectrum,” Opt. Lett. 6, 272 (1981).
[CrossRef] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structure Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Benner, R. E.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Interscience, New York, 1983).

Chang, R. K.

Chew, H.

H. Chew, D.-S. Wang, M. Kerker, “Elastic Scattering of Evanescent Electromagnetic Waves,” Appl. Opt. 18, 2679 (1979).
[CrossRef] [PubMed]

H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and Fluorescent Scattering by Molecules Embedded in Small Particles,” Phys. Rev. A 13, 396 (1976).
[CrossRef]

Christiansen, R. W.

R. W. Christiansen, C. K. Rushforth, “Detecting and Locating Key Words in Continuous Speech Using Linear Predictive Coding,” IEEE Trans. Acoust. Speech Signal Process. ASSP-25, 361 (1977).
[CrossRef]

Chylek, P.

Conwell, P. R.

Dave, J. V.

J. V. Dave, “Scattering of Electromagnetic Radiation by a Large, Absorbing Sphere,” IBM J. Res. Dev. 13, 302 (1969).
[CrossRef]

Druger, S. D.

Dziedzic, J. M.

Elschlager, R. A.

M. A. Fischler, R. A. Elschlager, “The Representation and Matching of Pictorial Structures,” IEEE Trans. Comput. C-22, 67 (1973).
[CrossRef]

Fischler, M. A.

M. A. Fischler, R. A. Elschlager, “The Representation and Matching of Pictorial Structures,” IEEE Trans. Comput. C-22, 67 (1973).
[CrossRef]

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 (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 (1982).
[CrossRef] [PubMed]

Fuchs, R.

Hill, S. C.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Interscience, New York, 1983).

Kattawar, G. W.

Kerker, M.

Kiefer, W.

Kiehl, J. T.

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial-Wave Resonances,” Phys. Rev. A 18, 2229 (1978).
[CrossRef]

Kim, J. S.

Kliewer, K. L.

Ko, M. K. W.

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial-Wave Resonances,” Phys. Rev. A 18, 2229 (1978).
[CrossRef]

Lee, S. S.

Long, M. B.

McNulty, P. J.

H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and Fluorescent Scattering by Molecules Embedded in Small Particles,” Phys. Rev. A 13, 396 (1976).
[CrossRef]

Messinger, B. J.

Owen, J. F.

J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-Dependent Resonances in Raman Scattering, Fluorescence Emission, and Elastic Scattering from Microparticles,” Aerosol Sci. Technol. 1, 293 (1982).
[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 (1982).
[CrossRef]

J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, “Determination of Optical-Fiber Diameter from Resonances in the Elastic Scattering Spectrum,” Opt. Lett. 6, 272 (1981).
[CrossRef] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structure Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Plass, G. N.

Qian, S.-X.

Ramaswamy, V.

Rushforth, C. K.

Snow, J. B.

Stolen, R. H.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 554–557.

Thurn, R.

Toon, O. B.

Tzeng, H.-M.

Wall, K. F.

Wang, D.-S.

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 (1982).
[CrossRef] [PubMed]

Aerosol Sci. Technol.

J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-Dependent Resonances in Raman Scattering, Fluorescence Emission, and Elastic Scattering from Microparticles,” Aerosol Sci. Technol. 1, 293 (1982).
[CrossRef]

Appl. Opt.

G. W. Kattawar, G. N. Plass, “Electromagnetic Scattering from Absorbing Spheres,” Appl. Opt. 6, 1377 (1967).
[CrossRef] [PubMed]

M. Kerker, S. D. Druger, “Raman and Fluorescent Scattering by Molecules Embedded in Spheres with Radii Up to Several Multiples of the Wavelength,” Appl. Opt. 18, 1172 (1979).
[CrossRef] [PubMed]

M. Kerker, “Resonances in Electromagnetic Scattering by Objects with Negative Absorbtion,” Appl. Opt. 18, 1180 (1979). The analysis is for cylinders; the same arguments hold for spheres.
[CrossRef] [PubMed]

H. Chew, D.-S. Wang, M. Kerker, “Elastic Scattering of Evanescent Electromagnetic Waves,” Appl. Opt. 18, 2679 (1979).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observations of Optical Resonances of Dielectric Spheres by Light Scattering,” Appl. Opt. 20, 1803 (1981).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, R. H. Stolen, “Outer Diameter Measurement of Low Birefringence Optical Fibers by a New Resonant Backscatter Technique,” Appl. Opt. 20, 2299 (1981).
[CrossRef] [PubMed]

O. B. Toon, T. P. Ackerman, “Algorithms for the Calculation of Scattering by Stratified Spheres,” Appl. Opt. 20, 3657 (1981).
[CrossRef] [PubMed]

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 (1984).
[CrossRef] [PubMed]

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 (1983).
[CrossRef] [PubMed]

Appl. Spectrosc.

IBM J. Res. Dev.

J. V. Dave, “Scattering of Electromagnetic Radiation by a Large, Absorbing Sphere,” IBM J. Res. Dev. 13, 302 (1969).
[CrossRef]

IEEE Trans Antennas Propag.

P. W. Barber, J. F. Owen, R. K. Chang, “Resonant Scattering for Characterization of Axisymmetric Dielectric Objects,” IEEE Trans Antennas Propag. AP-30, 168 (1982).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process.

R. W. Christiansen, C. K. Rushforth, “Detecting and Locating Key Words in Continuous Speech Using Linear Predictive Coding,” IEEE Trans. Acoust. Speech Signal Process. ASSP-25, 361 (1977).
[CrossRef]

IEEE Trans. Comput.

M. A. Fischler, R. A. Elschlager, “The Representation and Matching of Pictorial Structures,” IEEE Trans. Comput. C-22, 67 (1973).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Med. Biol. Eng. Comput.

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 (1982).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial-Wave Resonances,” Phys. Rev. A 18, 2229 (1978).
[CrossRef]

H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and Fluorescent Scattering by Molecules Embedded in Small Particles,” Phys. Rev. A 13, 396 (1976).
[CrossRef]

Phys. Rev. Lett.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structure Resonances in the Fluorescence Spectra from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

A. Ashkin, J. M. Dziedzic, “Observations of Resonances in the Radiation Pressure on Dielectric Spheres,” Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

Other

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 554–557.

We use x = 2πr/λ to facilitate the presentation. In the actual implementation of the algorithm, the medium surrounding the sphere is assumed to have a linear dispersion. See note at end of Appendix B.

R. H. Boundy, R. F. Boyer, S. M. Stoesser, Eds., Styrene: its Polymers, Copolymers and Derivatives (Reinhold, New York, 1952), p. 524.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Interscience, New York, 1983).

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