Abstract

The diameter and refractive index of micrometer sized spherical dielectric particles are simultaneously deduced using the wavelength dependence of backscattering data from optically levitated particles. The accuracy of the results is set by experimental errors in the determination of the wavelength of backscatter resonance peaks and the ratio of slopes of specified peaks. At present the refractive index and diameter can be deduced with relative errors of 5 × 10−5. This represents the most accurate determination of absolute size and refractive index yet made by light scattering. A reduction of these errors by an order of magnitude is possible. We assume a priori knowledge of diameter and refractive index with accuracy of 10−1 and 5 × 10−3, respectively.

© 1983 Optical Society of America

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References

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  1. A. Ashkin, Science 210, 1081 (1980).
    [CrossRef] [PubMed]
  2. A. Ashkin, J. M. Dziedzic, Appl. Opt. 20, 1803 (1981).
    [CrossRef] [PubMed]
  3. A. Ashkin, J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
    [CrossRef]
  4. P. Chylek, J. Opt. Soc. Am. 66, 285 (1976).
    [CrossRef]
  5. P. Chylek, J. T. Kiehl, M. K. W. Ko, Phys. Rev. A 18, 2229 (1978).
    [CrossRef]
  6. P. Chylek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles, D. Schuerman, Ed. (Plenum, New York, 1980).
  7. G. J. Rosasco, H. S. Bennett, J. Opt. Soc. Am. 68, 1598 (1978).
    [CrossRef]
  8. R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
    [CrossRef]
  9. J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, Opt. Lett. 6, 272 (1981).
    [CrossRef] [PubMed]
  10. A. Ashkin, J. M. Dziedzic, R. H. Stolen, Appl. Opt. 20, 2299 (1981).
    [CrossRef] [PubMed]

1981 (3)

1980 (2)

A. Ashkin, Science 210, 1081 (1980).
[CrossRef] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

1978 (2)

P. Chylek, J. T. Kiehl, M. K. W. Ko, Phys. Rev. A 18, 2229 (1978).
[CrossRef]

G. J. Rosasco, H. S. Bennett, J. Opt. Soc. Am. 68, 1598 (1978).
[CrossRef]

1977 (1)

A. Ashkin, J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

1976 (1)

Ashkin, A.

A. Ashkin, J. M. Dziedzic, Appl. Opt. 20, 1803 (1981).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, R. H. Stolen, Appl. Opt. 20, 2299 (1981).
[CrossRef] [PubMed]

A. Ashkin, Science 210, 1081 (1980).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

P. Chylek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles, D. Schuerman, Ed. (Plenum, New York, 1980).

Barber, P. W.

J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, Opt. Lett. 6, 272 (1981).
[CrossRef] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Benner, R. E.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Bennett, H. S.

G. J. Rosasco, H. S. Bennett, J. Opt. Soc. Am. 68, 1598 (1978).
[CrossRef]

Chang, R. K.

J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, Opt. Lett. 6, 272 (1981).
[CrossRef] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Chylek, P.

P. Chylek, J. T. Kiehl, M. K. W. Ko, Phys. Rev. A 18, 2229 (1978).
[CrossRef]

P. Chylek, J. Opt. Soc. Am. 66, 285 (1976).
[CrossRef]

P. Chylek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles, D. Schuerman, Ed. (Plenum, New York, 1980).

Dziedzic, J. M.

Kiehl, J. T.

P. Chylek, J. T. Kiehl, M. K. W. Ko, Phys. Rev. A 18, 2229 (1978).
[CrossRef]

P. Chylek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles, D. Schuerman, Ed. (Plenum, New York, 1980).

Ko, M. K. W.

P. Chylek, J. T. Kiehl, M. K. W. Ko, Phys. Rev. A 18, 2229 (1978).
[CrossRef]

P. Chylek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles, D. Schuerman, Ed. (Plenum, New York, 1980).

Messinger, B. J.

Owen, J. F.

J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, Opt. Lett. 6, 272 (1981).
[CrossRef] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Rosasco, G. J.

G. J. Rosasco, H. S. Bennett, J. Opt. Soc. Am. 68, 1598 (1978).
[CrossRef]

Stolen, R. H.

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

P. Chylek, J. Opt. Soc. Am. 66, 285 (1976).
[CrossRef]

G. J. Rosasco, H. S. Bennett, J. Opt. Soc. Am. 68, 1598 (1978).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

P. Chylek, J. T. Kiehl, M. K. W. Ko, Phys. Rev. A 18, 2229 (1978).
[CrossRef]

Phys. Rev. Lett. (2)

A. Ashkin, J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Science (1)

A. Ashkin, Science 210, 1081 (1980).
[CrossRef] [PubMed]

Other (1)

P. Chylek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles, D. Schuerman, Ed. (Plenum, New York, 1980).

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Figures (10)

Fig. 1
Fig. 1

Basic optical levitation apparatus and feedback stabilization apparatus used for measuring the wavelength dependence of Mie light scattering from ∼10-μm oil droplets.

Fig. 2
Fig. 2

Backscattering measurement of relative intensity of a small silicone oil droplet. Because of a narrow acceptance angle the backscattered relative intensity reaches an almost zero value between groups of peaks. Note that the group of peaks denoted 1 has a secondary peak superimposed on the long-wavelength side of the main peak of this group. The group of peaks denoted 2 has a shoulder (instead of a secondary peak) superimposed on the long λ side of the main peak. This fact is used to identify an and bn resonances responsible for the peaks in the backscattering.

Fig. 3
Fig. 3

Calculated normalized backscattering cross section Qback as a function of size parameter x for the case of refractive indices n = 1.398 and n = 1.400 and for the range of size parameter 64 ≤ x ≤ 71. The solid curve represents the contribution from the third- and higher-order resonances. The first- and second-order resonances are marked by arrows. Notice the transition between the peaks and shoulders superimposed on the small x size (long λ side) of the main peaks around 64 < x < 66.

Fig. 4
Fig. 4

Same as Fig. 3 but for n = 1.402, 1.404, and 1.406.

Fig. 5
Fig. 5

Enlarged section of the Qback for the case of n = 1.400. Notice that the shoulder superimposed on the a 72 3 peak is caused by the b 68 4 resonance, while the secondary peak superimposed on the a 73 3 peak is caused by a 69 4 resonance. The ratio of the slopes (defined as slopes of tangents at inflection points) of the shoulder and the secondary peak is a sensitive function of refractive index n.

Fig. 6
Fig. 6

Shoulder-to-peak transition a 73 3 a 72 3 (n = 1.400) is followed by at least three groups of resonances with a shoulder superimposed on the main peak in agreement with the measurements (Fig. 2). The case of n = 1.406 with the shoulder-to-peak transition a 72 3 a 71 3 is in discrepancy with the measurements.

Fig. 7
Fig. 7

Enlarged section of measured backscattered intensity. The error of experimental determination of the ratio of slopes at the inflection point between the main and the secondary peak in group 1 and at the inflection point of the shoulder in group 2 limits the accuracy of the proposed method for simultaneous determination of the refractive index and the size of a droplet.

Fig. 8
Fig. 8

Ratio R of the slopes is a sensitive function of refractive index n.

Fig. 9
Fig. 9

Numerical calculation of the real part of a 73 3 resonance for several values of refractive index n. The position of the peak is a sensitive function of refractive index.

Fig. 10
Fig. 10

Numerically calculated position of the a 73 3 peak in the backscattering as a function of the refractive index n.

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