Abstract

Intensities of light scattered in the planes parallel and perpendicular to the polarization plane of the incident light are used to determine the size, refractive index, and dispersion of a single droplet suspended in an electrodynamic balance. Wavelengths of TE- and TM-mode resonances are determined independently with high precision when a ring dye laser is scanned. Resonating wavelengths are matched with theoretical intensity peaks to determine the constants of a dispersion formula and the size that minimizes the difference between observed and calculated wavelengths. The procedure permits the determination of the size and refractive index with relative errors of 3 × 10−5 and dispersion with an absolute error of 2 × 10−5 over the experimental spectral range.

© 1994 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  26. P. R. Conwell, P. W. Barber, C. K. Rushforth, “Resonant spectra of dielectric spheres,” J. Opt. Soc. Am. A 1, 62–67 (1984).
    [CrossRef]
  27. H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. I. Direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969).
    [CrossRef]
  28. P. Chýlek, “Partial-wave resonance and the ripple structure in the Mie normalized extinction cross section,” J. Opt. Soc. Am. 66, 285–287 (1975).
    [CrossRef]
  29. P. Chýlek, “Resonance structure of Mie scattering: distance between resonances,” J. Opt. Soc. Am. A 7, 1609–1613 (1990).
    [CrossRef]
  30. J. L. Huckaby, “Elastic and inelastic light scattering by microdroplets,” Ph.D. dissertation (University of Kentucky, Lexington, Ky., 1991).
  31. R. C. Weast, ed., CRC Handbook of Chemistry and Physics (CRC, Boca Raton, Florida, 1985), Sec. E, p. 370.
  32. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 95–96.
  33. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).
  34. L. W. Tilton, J. K. Taylor, “Refractive index and dispersion of distilled water for visible radiation, at temperatures 0 to 60 °C,” J. Res. Natl. Bur. Stand. 20, 419–442 (1938).
    [CrossRef]

1991 (2)

1990 (4)

H. B. Lin, J. D. Eversole, A. J. Campillo, “Identification of morphology-dependent resonances in stimulated Raman scattering from microdroplets,” Opt. Commun. 77, 407–410 (1990).
[CrossRef]

H.-B. Lin, A. L. Huston, J. D. Eversole, A. J. Campillo, “Double-resonance stimulated Raman scattering from micrometer-sized droplets,” J. Opt. Soc. Am. B 7, 2079–2089 (1990).
[CrossRef]

G. Schweiger, “Observation of morphology-dependent resonances caused by the input field in the Raman spectrum of microdroplets,” J. Raman Spectrosc. 21, 165–168 (1990).
[CrossRef]

P. Chýlek, “Resonance structure of Mie scattering: distance between resonances,” J. Opt. Soc. Am. A 7, 1609–1613 (1990).
[CrossRef]

1989 (2)

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

A. K. Ray, R. D. Johnson, A. Souyri, “Dynamic behavior of single glycerol droplets in humid air streams,” Langmuir 5, 133–140 (1989).
[CrossRef]

1988 (1)

D. C. Taflin, S. H. Zhang, T. Allen, E. J. Davis, “Measurements of droplet Interfacial phenomena by light-scattering techniques,” AIChE J. 34, 1310–1320 (1988).
[CrossRef]

1986 (1)

1985 (3)

1984 (3)

1983 (1)

1981 (1)

1980 (1)

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, 475–478 (1980).
[CrossRef]

1977 (1)

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

1975 (1)

1973 (1)

1969 (1)

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. I. Direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969).
[CrossRef]

1968 (1)

1938 (1)

L. W. Tilton, J. K. Taylor, “Refractive index and dispersion of distilled water for visible radiation, at temperatures 0 to 60 °C,” J. Res. Natl. Bur. Stand. 20, 419–442 (1938).
[CrossRef]

Allen, T.

D. C. Taflin, S. H. Zhang, T. Allen, E. J. Davis, “Measurements of droplet Interfacial phenomena by light-scattering techniques,” AIChE J. 34, 1310–1320 (1988).
[CrossRef]

Allen, T. M.

Armstrong, R. L.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

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]

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, 475–478 (1980).
[CrossRef]

Benner, R. E.

Biswas, A.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Interscience, New York, 1983), Chap. 4, pp. 100–113.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 95–96.

Bryant, H. C.

Campillo, A. J.

H.-B. Lin, A. L. Huston, J. D. Eversole, A. J. Campillo, “Double-resonance stimulated Raman scattering from micrometer-sized droplets,” J. Opt. Soc. Am. B 7, 2079–2089 (1990).
[CrossRef]

H. B. Lin, J. D. Eversole, A. J. Campillo, “Identification of morphology-dependent resonances in stimulated Raman scattering from microdroplets,” Opt. Commun. 77, 407–410 (1990).
[CrossRef]

Chang, R. K.

J. B. Snow, S.-X. Qian, R. K. Chang, “Stimulated Raman scattering from individual water and ethanol droplets at morphological-dependent resonances,” Opt. Lett. 10, 37–39 (1985).
[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, 475–478 (1980).
[CrossRef]

Chýlek, P.

Conwell, P. R.

Davis, E. J.

A. K. Ray, A. Souyri, E. J. Davis, T. M. Allen, “Precision of light scattering techniques for measuring optical parameters of microspheres,” Appl. Opt. 30, 3974–3983 (1991).
[CrossRef] [PubMed]

D. C. Taflin, S. H. Zhang, T. Allen, E. J. Davis, “Measurements of droplet Interfacial phenomena by light-scattering techniques,” AIChE J. 34, 1310–1320 (1988).
[CrossRef]

Dziedzic, J. M.

Eversole, J. D.

H. B. Lin, J. D. Eversole, A. J. Campillo, “Identification of morphology-dependent resonances in stimulated Raman scattering from microdroplets,” Opt. Commun. 77, 407–410 (1990).
[CrossRef]

H.-B. Lin, A. L. Huston, J. D. Eversole, A. J. Campillo, “Double-resonance stimulated Raman scattering from micrometer-sized droplets,” J. Opt. Soc. Am. B 7, 2079–2089 (1990).
[CrossRef]

Fahlen, T. S.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Hightower, R. L.

Hill, S. C.

Huckaby, J. L.

J. L. Huckaby, “Elastic and inelastic light scattering by microdroplets,” Ph.D. dissertation (University of Kentucky, Lexington, Ky., 1991).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Interscience, New York, 1983), Chap. 4, pp. 100–113.

Huston, A. L.

Johnson, R. D.

A. K. Ray, R. D. Johnson, A. Souyri, “Dynamic behavior of single glycerol droplets in humid air streams,” Langmuir 5, 133–140 (1989).
[CrossRef]

Jones, D. S.

D. S. Jones, Acoustic and Electromagnetic Waves (Oxford U. Press, Oxford, 1986), Chap. 8, pp. 452–454.

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1983), Chap. 3, pp. 46–50.

Kiefer, W.

Latifi, H.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

Lin, H. B.

H. B. Lin, J. D. Eversole, A. J. Campillo, “Identification of morphology-dependent resonances in stimulated Raman scattering from microdroplets,” Opt. Commun. 77, 407–410 (1990).
[CrossRef]

Lin, H.-B.

Nussenzveig, H. M.

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. I. Direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969).
[CrossRef]

Owen, J. F.

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, 475–478 (1980).
[CrossRef]

Pigg, A. L.

Pinnick, R. G.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Probert-Jones, J. R.

Qian, S.-X.

Ramaswamy, V.

Ray, A. K.

A. K. Ray, A. Souyri, E. J. Davis, T. M. Allen, “Precision of light scattering techniques for measuring optical parameters of microspheres,” Appl. Opt. 30, 3974–3983 (1991).
[CrossRef] [PubMed]

A. K. Ray, R. D. Johnson, A. Souyri, “Dynamic behavior of single glycerol droplets in humid air streams,” Langmuir 5, 133–140 (1989).
[CrossRef]

Richardson, C. B.

Rushforth, C. K.

Schweiger, G.

G. Schweiger, “Raman scattering on microdroplets: size dependence,” J. Opt. Soc. Am. B 8, 1770–1778 (1991).
[CrossRef]

G. Schweiger, “Observation of morphology-dependent resonances caused by the input field in the Raman spectrum of microdroplets,” J. Raman Spectrosc. 21, 165–168 (1990).
[CrossRef]

Snow, J. B.

Souyri, A.

A. K. Ray, A. Souyri, E. J. Davis, T. M. Allen, “Precision of light scattering techniques for measuring optical parameters of microspheres,” Appl. Opt. 30, 3974–3983 (1991).
[CrossRef] [PubMed]

A. K. Ray, R. D. Johnson, A. Souyri, “Dynamic behavior of single glycerol droplets in humid air streams,” Langmuir 5, 133–140 (1989).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Chap. 9, pp. 554–556.

Taflin, D. C.

D. C. Taflin, S. H. Zhang, T. Allen, E. J. Davis, “Measurements of droplet Interfacial phenomena by light-scattering techniques,” AIChE J. 34, 1310–1320 (1988).
[CrossRef]

Taylor, J. K.

L. W. Tilton, J. K. Taylor, “Refractive index and dispersion of distilled water for visible radiation, at temperatures 0 to 60 °C,” J. Res. Natl. Bur. Stand. 20, 419–442 (1938).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Thurn, R.

Tilton, L. W.

L. W. Tilton, J. K. Taylor, “Refractive index and dispersion of distilled water for visible radiation, at temperatures 0 to 60 °C,” J. Res. Natl. Bur. Stand. 20, 419–442 (1938).
[CrossRef]

van de Hulst, H. C.

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

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 95–96.

Zhang, S. H.

D. C. Taflin, S. H. Zhang, T. Allen, E. J. Davis, “Measurements of droplet Interfacial phenomena by light-scattering techniques,” AIChE J. 34, 1310–1320 (1988).
[CrossRef]

AIChE J. (1)

D. C. Taflin, S. H. Zhang, T. Allen, E. J. Davis, “Measurements of droplet Interfacial phenomena by light-scattering techniques,” AIChE J. 34, 1310–1320 (1988).
[CrossRef]

Appl. Opt. (6)

J. Math. Phys. (1)

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. I. Direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (4)

J. Opt. Soc. Am. B (2)

J. Raman Spectrosc. (1)

G. Schweiger, “Observation of morphology-dependent resonances caused by the input field in the Raman spectrum of microdroplets,” J. Raman Spectrosc. 21, 165–168 (1990).
[CrossRef]

J. Res. Natl. Bur. Stand. (1)

L. W. Tilton, J. K. Taylor, “Refractive index and dispersion of distilled water for visible radiation, at temperatures 0 to 60 °C,” J. Res. Natl. Bur. Stand. 20, 419–442 (1938).
[CrossRef]

Langmuir (1)

A. K. Ray, R. D. Johnson, A. Souyri, “Dynamic behavior of single glycerol droplets in humid air streams,” Langmuir 5, 133–140 (1989).
[CrossRef]

Opt. Commun. (1)

H. B. Lin, J. D. Eversole, A. J. Campillo, “Identification of morphology-dependent resonances in stimulated Raman scattering from microdroplets,” Opt. Commun. 77, 407–410 (1990).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

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, 475–478 (1980).
[CrossRef]

Other (9)

J. L. Huckaby, “Elastic and inelastic light scattering by microdroplets,” Ph.D. dissertation (University of Kentucky, Lexington, Ky., 1991).

R. C. Weast, ed., CRC Handbook of Chemistry and Physics (CRC, Boca Raton, Florida, 1985), Sec. E, p. 370.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 95–96.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Chap. 9, pp. 554–556.

D. S. Jones, Acoustic and Electromagnetic Waves (Oxford U. Press, Oxford, 1986), Chap. 8, pp. 452–454.

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

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1983), Chap. 3, pp. 46–50.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Interscience, New York, 1983), Chap. 4, pp. 100–113.

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Figures (8)

Fig. 1
Fig. 1

Theoretical scattered intensity spectra for various angles in the plane parallel to the plane of polarization.

Fig. 2
Fig. 2

Position of the intensity extremum that is due to scattering coefficient b24021 as a function of the scattering angle: Squares represent peaks and circles represent troughs.

Fig. 3
Fig. 3

Schematic of the experimental setup.

Fig. 4
Fig. 4

Comparisons between observed scattering spectra and spectra calculated for optimum parameters at scattering angles θTE = 90.48° and θTM = 90.88°.

Fig. 5
Fig. 5

Results from alignments of scattering coefficient peaks with observed intensity peaks.

Fig. 6
Fig. 6

Comparisons between observed scattering spectra and spectra calculated for optimum parameters at scattering angles θTE = 90.70° and θTM = 90.05°.

Fig. 7
Fig. 7

Intensity peak-alignment errors versus droplet radius for detector angles θTE = 90.48° and θTM = 90.88°.

Fig. 8
Fig. 8

Comparisons between the observed (mobs) and calculated (mcal) refractive-index differences droplets 1 and 2 under identical conditions.

Tables (4)

Tables Icon

Table 1 Observed Peak Locations of Wave Numbers in Dry Air

Tables Icon

Table 2 Results from Alignments of Theoretical Intensity Peaks with Observed Peaks

Tables Icon

Table 3 Results of Analyses of Data Subsets of Droplet 1

Tables Icon

Table 4 Summary of Results for Droplets 1 and 2 under Identical Conditions

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

I 1 = I i λ 2 4 π 2 r 2 [ n = 1 2 n + 1 n ( n + 1 ) ( a n π n + b n τ n ) ] 2 ,
I 2 = I i λ 2 4 π 2 r 2 [ n = 1 2 n + 1 n ( n + 1 ) ( b n π n + a n τ n ) ] 2 ,
π n = P n 1 ( cos θ ) sin θ ,             τ n = d d θ P n 1 ( cos θ ) ,
a n = A n ( x , m ) A n ( x , m ) + i C n ( x , m ) ,
b n = B n ( x , m ) B n ( x , m ) + i D n ( x , m ) ,
A n ( x , m ) = ψ n ( x ) ψ n ( m x ) - m ψ n ( m x ) ψ n ( x ) ,
B n ( x , m ) = m ψ n ( x ) ψ n ( m x ) - ψ n ( m x ) ψ n ( x ) ,
C n ( x , m ) = χ n ( x ) ψ n ( m x ) - m ψ n ( m x ) χ n ( x ) ,
D n ( x , m ) = m χ n ( x ) ψ n ( m x ) - ψ n ( m x ) χ n ( x ) ,
Δ x x n , l = - K ( m , x ) Δ m m ,
Δ x 0 = x n , l + 1 - x n , l π ρ ,
Δ x m = x n + 1 , l - x n , l tan - 1 ρ ρ .
Δ x m = x n + 1 , l - x n , l x tan - 1 [ ( m x / n ) 2 - 1 ] 1 / 2 n [ ( m x / n ) 2 - 1 ] 1 / 2 .
Δ x π ρ - tan - 1 ρ .
I 1 ( θ π / 2 ) I i λ 2 4 π 2 r 2 ( n = 1 2 n + 1 n ( n + 1 ) b n τ n ( θ ) ) 2 ,
I 2 ( θ π / 2 ) I i λ 2 4 π 2 r 2 ( n = 1 2 n + 1 n ( n + 1 ) a n τ n ( θ ) ) 2 .
ϕ = i = 1 N pts ( ν i , o - ν i , c ) 2 ,
ν i , c = ν i , c ( a , m , θ TE             or             θ TM ) ,
m ( ν ) = A + B ν 2 + C ν 4 .
χ 2 ( a , A , B , C ) = i = 1 N pts ( ν i , o - ν i , c 0 ) 2 σ i , o 2 + σ i , c 2 ,
ϕ j k 0 ( a ) = i = 1 N pts { ν i , o - ν i j k 0 [ m ( ν i j k 0 ) , a ] } 2 ,
m ( ν ) = 1.5367071 + 7.60005 × 10 - 11 ν 2 + 3.56782 × 10 - 20 ν 4 .
m ( ν ) = 1.4962803 + 4.83055 × 10 - 10 ν 2 - 1.32931 × 10 - 18 ν 4 + 1.525 × 10 - 27 ν 6 , a = 20.5799 μ m ,             ϕ min = 0.0157 cm - 2 .
m ( ν ) = ( 2.4693693 - 1.39416 × 10 7 ν 2 + 2.75402 × 10 - 11 ν 2 1 - 1.9001 × 10 - 9 ν 2 ) 1 / 2 , a = 20.5800 μ m ,             ϕ min = 0.0157 cm - 2 .
m ( ν ) = ( 2.6364309 - 8.91047 × 10 7 ν 2 - 9.2470 × 10 15 ν 4 - 2.62384 × 10 - 16 ν 2 1 - 3.4570 × 10 - 9 ν 2 ) 1 / 2 , a = 20.5798 μ m ,             ϕ min = 0.0147 cm - 2 .
m = 1.5317895 + 7.77150 × 10 - 11 ν 2 + 2.82659 × 10 - 20 ν 4 .

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