Abstract

The polar nephelometer of Tohoku University has been improved so that it can be used to measure the scattering matrix element D 21. Polar nephelometer observations were conducted at Tohoku University in the suburbs of Sendai, Japan, from 12 October to 10 December 1988. A method presented in an earlier publication [Appl. Opt. 36, 7992 (1997)] is applied to determine the complex index of refraction and size distribution of aerosols simultaneously. It is shown that the accuracy of the determined quantities is reasonable.

© 1999 Optical Society of America

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References

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  1. F. Zhao, Z. Gong, H. Hu, M. Tanaka, T. Hayasaka, “Simultaneous determination of the aerosol complex index of refraction and size distribution from scattering measurements of polarized light,” Appl. Opt. 36, 7992–8001 (1997).
    [CrossRef]
  2. M. Tanaka, T. Nakamura, T. Nakajima, “Refractive Index and size distribution of aerosols as estimated from light scattering measurements,” J. Clim. Appl. Meteorol. 22, 1253–1261 (1983).
    [CrossRef]
  3. F. Zhao, “A method of the determination of the complex index of refraction and size distribution from the measurements of scattered light,” Ph.D dissertation (Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, China, 1989).
  4. D. L. Phillips, “A technique for the numerical solution of certain integral equations of the first kind,” J. Assoc. Comput. Mach. 9, 84–97 (1962).
    [CrossRef]
  5. S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963).
    [CrossRef]
  6. E. M. Patterson, D. A. Gillette, “Commonalities in measures size distributions for aerosols having a soil-derived component,” J. Geophys. Res. 82, 2074–2082 (1977).
    [CrossRef]
  7. G. M. Sverdrup, K. T. Whitby, W. E. Clark, “Characterization of California aerosols. 2: aerosol size distribution in the Mojave Desert,” Atmos. Environ. 8, 438–494 (1975).
  8. Y. Kim, H. Sievering, J. F. Boatman, “Airborne measurements of atmospheric aerosol particles in the lower troposphere over the central United States,” J. Geophys. Res. 93, 12,631–12,644 (1988).

1997

1988

Y. Kim, H. Sievering, J. F. Boatman, “Airborne measurements of atmospheric aerosol particles in the lower troposphere over the central United States,” J. Geophys. Res. 93, 12,631–12,644 (1988).

1983

M. Tanaka, T. Nakamura, T. Nakajima, “Refractive Index and size distribution of aerosols as estimated from light scattering measurements,” J. Clim. Appl. Meteorol. 22, 1253–1261 (1983).
[CrossRef]

1977

E. M. Patterson, D. A. Gillette, “Commonalities in measures size distributions for aerosols having a soil-derived component,” J. Geophys. Res. 82, 2074–2082 (1977).
[CrossRef]

1975

G. M. Sverdrup, K. T. Whitby, W. E. Clark, “Characterization of California aerosols. 2: aerosol size distribution in the Mojave Desert,” Atmos. Environ. 8, 438–494 (1975).

1963

S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963).
[CrossRef]

1962

D. L. Phillips, “A technique for the numerical solution of certain integral equations of the first kind,” J. Assoc. Comput. Mach. 9, 84–97 (1962).
[CrossRef]

Boatman, J. F.

Y. Kim, H. Sievering, J. F. Boatman, “Airborne measurements of atmospheric aerosol particles in the lower troposphere over the central United States,” J. Geophys. Res. 93, 12,631–12,644 (1988).

Clark, W. E.

G. M. Sverdrup, K. T. Whitby, W. E. Clark, “Characterization of California aerosols. 2: aerosol size distribution in the Mojave Desert,” Atmos. Environ. 8, 438–494 (1975).

Gillette, D. A.

E. M. Patterson, D. A. Gillette, “Commonalities in measures size distributions for aerosols having a soil-derived component,” J. Geophys. Res. 82, 2074–2082 (1977).
[CrossRef]

Gong, Z.

Hayasaka, T.

Hu, H.

Kim, Y.

Y. Kim, H. Sievering, J. F. Boatman, “Airborne measurements of atmospheric aerosol particles in the lower troposphere over the central United States,” J. Geophys. Res. 93, 12,631–12,644 (1988).

Nakajima, T.

M. Tanaka, T. Nakamura, T. Nakajima, “Refractive Index and size distribution of aerosols as estimated from light scattering measurements,” J. Clim. Appl. Meteorol. 22, 1253–1261 (1983).
[CrossRef]

Nakamura, T.

M. Tanaka, T. Nakamura, T. Nakajima, “Refractive Index and size distribution of aerosols as estimated from light scattering measurements,” J. Clim. Appl. Meteorol. 22, 1253–1261 (1983).
[CrossRef]

Patterson, E. M.

E. M. Patterson, D. A. Gillette, “Commonalities in measures size distributions for aerosols having a soil-derived component,” J. Geophys. Res. 82, 2074–2082 (1977).
[CrossRef]

Phillips, D. L.

D. L. Phillips, “A technique for the numerical solution of certain integral equations of the first kind,” J. Assoc. Comput. Mach. 9, 84–97 (1962).
[CrossRef]

Sievering, H.

Y. Kim, H. Sievering, J. F. Boatman, “Airborne measurements of atmospheric aerosol particles in the lower troposphere over the central United States,” J. Geophys. Res. 93, 12,631–12,644 (1988).

Sverdrup, G. M.

G. M. Sverdrup, K. T. Whitby, W. E. Clark, “Characterization of California aerosols. 2: aerosol size distribution in the Mojave Desert,” Atmos. Environ. 8, 438–494 (1975).

Tanaka, M.

F. Zhao, Z. Gong, H. Hu, M. Tanaka, T. Hayasaka, “Simultaneous determination of the aerosol complex index of refraction and size distribution from scattering measurements of polarized light,” Appl. Opt. 36, 7992–8001 (1997).
[CrossRef]

M. Tanaka, T. Nakamura, T. Nakajima, “Refractive Index and size distribution of aerosols as estimated from light scattering measurements,” J. Clim. Appl. Meteorol. 22, 1253–1261 (1983).
[CrossRef]

Twomey, S.

S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963).
[CrossRef]

Whitby, K. T.

G. M. Sverdrup, K. T. Whitby, W. E. Clark, “Characterization of California aerosols. 2: aerosol size distribution in the Mojave Desert,” Atmos. Environ. 8, 438–494 (1975).

Zhao, F.

F. Zhao, Z. Gong, H. Hu, M. Tanaka, T. Hayasaka, “Simultaneous determination of the aerosol complex index of refraction and size distribution from scattering measurements of polarized light,” Appl. Opt. 36, 7992–8001 (1997).
[CrossRef]

F. Zhao, “A method of the determination of the complex index of refraction and size distribution from the measurements of scattered light,” Ph.D dissertation (Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, China, 1989).

Appl. Opt.

Atmos. Environ.

G. M. Sverdrup, K. T. Whitby, W. E. Clark, “Characterization of California aerosols. 2: aerosol size distribution in the Mojave Desert,” Atmos. Environ. 8, 438–494 (1975).

J. Assoc. Comput. Mach.

D. L. Phillips, “A technique for the numerical solution of certain integral equations of the first kind,” J. Assoc. Comput. Mach. 9, 84–97 (1962).
[CrossRef]

S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963).
[CrossRef]

J. Clim. Appl. Meteorol.

M. Tanaka, T. Nakamura, T. Nakajima, “Refractive Index and size distribution of aerosols as estimated from light scattering measurements,” J. Clim. Appl. Meteorol. 22, 1253–1261 (1983).
[CrossRef]

J. Geophys. Res.

E. M. Patterson, D. A. Gillette, “Commonalities in measures size distributions for aerosols having a soil-derived component,” J. Geophys. Res. 82, 2074–2082 (1977).
[CrossRef]

Y. Kim, H. Sievering, J. F. Boatman, “Airborne measurements of atmospheric aerosol particles in the lower troposphere over the central United States,” J. Geophys. Res. 93, 12,631–12,644 (1988).

Other

F. Zhao, “A method of the determination of the complex index of refraction and size distribution from the measurements of scattered light,” Ph.D dissertation (Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, China, 1989).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the polar nephelometer.

Fig. 2
Fig. 2

Schematic diagram of the optical arrangement of the improved polar nephelometer. The and directions refer to the parallel and perpendicular components in the transverse plane of light as referenced to the scattering plane.

Fig. 3
Fig. 3

Normalized molecular scattering: (1) vertical component of scattered light, (2) parallel component of scattered light, (3) scattered light at β = 45°. The solid curves are theoretically calculated values.

Fig. 4
Fig. 4

Example of retrieved aerosol volume spectra: circles, retrieved from the measured data shown in Table 1; solid curve, the log-nomal distributions fitted to the retrieved values.

Fig. 5
Fig. 5

Isolines of the δ (in percent) hypersurface for the data measured at (a) 09:23–09:56, 17 October 1988; (b) 08:41–09:14, 20 October 1988; (c) 15:36–16:09, 17 October 1988. The + corresponds to the minimum value of the standard deviation.

Fig. 6
Fig. 6

Comparisons of the retrieved aerosol volume spectra averaged for weekdays and Sundays for different relative humidities: (a) 65% and (b) 37%.

Tables (4)

Tables Icon

Table 1 Examples of Measured and Reconstructed Scattering Matrix Elementsa

Tables Icon

Table 2 Statistics of the Retrieved Values of the Complex Index of Refraction

Tables Icon

Table 3 Mean Values of the Real and the Imaginary Parts of the Complex Index of Refraction

Tables Icon

Table 4 Mode Parameters for Aerosol Volume Spectra

Equations (15)

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

M1=0 s1θ, m, xs1*θ, m, xnrdr,
M2=0 s2θ, m, xs2*θ, m, xnrdr,
D21=120 is2θ, m, xs1*θ, m, x-s1θ, m, xs2*θ, m, xnrdr,
Ga=k1λ2I04π2R21+cos2 2ρM2 for β=0°,
Ga=k2λ2I04π2R21-cos2 2ρM1 for β=90°,
Ga=k3λ2I04π2R212M2+M1+1/2 cos2 2ρM2-M1-2D21ElEr for β=45°,
Gm=k124π2n-1NI0λ4R2Nt26-7Δ1+cos2 2ρ×Δ+1-Δcos2 θ for β=0°,
Gm=k224π2n-1NI0λ4R2Nt26-7Δ1-cos2 2ρ for β=90°,
Gm=k324π2n-1NI0λ4R2Nt26-7Δ1/21+1-Δcos2 θ+Δ+1/2 cos2 2ρ1-Δ×cos2 θ+Δ-1 for β=45°,
set I: D21150°, M2100°, set II: M24°, M210°, M230°, M250°, M14°, M15°, M16°, M17°, M110°, M130°, M150°, M180°, M1125°, M1150°.
δ=i=12121-β1icm, θ, λ, nrβ1im21/2,
β2im=rminrmax k2im, θ, r, λnrdr+2i=j=1Nrjrj+1 k2im, θ, r, λnrdr+2i, i=1, 2,, 14,
j=1Nrjrj+1 k2im, θ, r, λnrdr.
nr=1.400.05, 1.60, ni=0.005, 0.01, 0.02, 0.03, 0.05.
vr=i=12 ki exp-ln r-ln r0i2/2 ln2 σi,

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