Abstract

An integral equation method is used to study spectral and polarization effects for the scattering and absorption of electromagnetic radiation incident on arbitrarily oriented flat disk aerosols of major dimension comparable to the wavelength of the radiation. Numerical results for flat plate ice crystals are presented.

© 1980 Optical Society of America

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References

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  1. P. C. Waterman, Alta Freq. 38, 348 (1969).
  2. M. A. Morgan, K. K. Mei, IEEE Trans. Antennas Propag. AP-27, 202 (1979).
    [CrossRef]
  3. D-S. Wang, P. Barber, Appl. Opt. 18, 1190 (1979).
    [CrossRef] [PubMed]
  4. A. R. Holt, N. K. Uzunoglu, B. G. Evans, IEEE Trans. Antennas Propag. AP-26, 706 (1978).
    [CrossRef]
  5. B. W. Fowler, C. C. Sung, J. Opt. Soc. Am. 69, 756 (1979).
    [CrossRef]
  6. S. Asano, Appl. Opt. 18, 712 (1979).
    [CrossRef] [PubMed]
  7. C. M. Chu, H. Weil, J. Comput. Phys. 22, 111 (1976).
    [CrossRef]
  8. H. Weil, C. M. Chu, “Scattering and Absorption of Electromagnetic Radiation by Clouds of Disc Shaped Aerosols,” Report 016234-1-F, Radiation Laboratory, Department of Electrical and Computer Engineering, U. Michigan, Ann Arbor 48109 (Dec.1978).This report is the Final Report on NOAA grant 04-78-B01-1, U.S. Dept. of Commerce, Boulder, Colo. 80302.
  9. J. W. Schaaf, D. Williams, J. Opt. Soc. Am. 63, 726 (1973).
    [CrossRef]
  10. W. M. Irvine, J. B. Pollock, Icarus 8, 324 (1968).
    [CrossRef]
  11. H. Weil, C. M. Chu, Appl. Opt. 15, 1832 (1976).
    [CrossRef] [PubMed]

1979 (4)

1978 (1)

A. R. Holt, N. K. Uzunoglu, B. G. Evans, IEEE Trans. Antennas Propag. AP-26, 706 (1978).
[CrossRef]

1976 (2)

H. Weil, C. M. Chu, Appl. Opt. 15, 1832 (1976).
[CrossRef] [PubMed]

C. M. Chu, H. Weil, J. Comput. Phys. 22, 111 (1976).
[CrossRef]

1973 (1)

1969 (1)

P. C. Waterman, Alta Freq. 38, 348 (1969).

1968 (1)

W. M. Irvine, J. B. Pollock, Icarus 8, 324 (1968).
[CrossRef]

Asano, S.

Barber, P.

Chu, C. M.

H. Weil, C. M. Chu, Appl. Opt. 15, 1832 (1976).
[CrossRef] [PubMed]

C. M. Chu, H. Weil, J. Comput. Phys. 22, 111 (1976).
[CrossRef]

H. Weil, C. M. Chu, “Scattering and Absorption of Electromagnetic Radiation by Clouds of Disc Shaped Aerosols,” Report 016234-1-F, Radiation Laboratory, Department of Electrical and Computer Engineering, U. Michigan, Ann Arbor 48109 (Dec.1978).This report is the Final Report on NOAA grant 04-78-B01-1, U.S. Dept. of Commerce, Boulder, Colo. 80302.

Evans, B. G.

A. R. Holt, N. K. Uzunoglu, B. G. Evans, IEEE Trans. Antennas Propag. AP-26, 706 (1978).
[CrossRef]

Fowler, B. W.

Holt, A. R.

A. R. Holt, N. K. Uzunoglu, B. G. Evans, IEEE Trans. Antennas Propag. AP-26, 706 (1978).
[CrossRef]

Irvine, W. M.

W. M. Irvine, J. B. Pollock, Icarus 8, 324 (1968).
[CrossRef]

Mei, K. K.

M. A. Morgan, K. K. Mei, IEEE Trans. Antennas Propag. AP-27, 202 (1979).
[CrossRef]

Morgan, M. A.

M. A. Morgan, K. K. Mei, IEEE Trans. Antennas Propag. AP-27, 202 (1979).
[CrossRef]

Pollock, J. B.

W. M. Irvine, J. B. Pollock, Icarus 8, 324 (1968).
[CrossRef]

Schaaf, J. W.

Sung, C. C.

Uzunoglu, N. K.

A. R. Holt, N. K. Uzunoglu, B. G. Evans, IEEE Trans. Antennas Propag. AP-26, 706 (1978).
[CrossRef]

Wang, D-S.

Waterman, P. C.

P. C. Waterman, Alta Freq. 38, 348 (1969).

Weil, H.

C. M. Chu, H. Weil, J. Comput. Phys. 22, 111 (1976).
[CrossRef]

H. Weil, C. M. Chu, Appl. Opt. 15, 1832 (1976).
[CrossRef] [PubMed]

H. Weil, C. M. Chu, “Scattering and Absorption of Electromagnetic Radiation by Clouds of Disc Shaped Aerosols,” Report 016234-1-F, Radiation Laboratory, Department of Electrical and Computer Engineering, U. Michigan, Ann Arbor 48109 (Dec.1978).This report is the Final Report on NOAA grant 04-78-B01-1, U.S. Dept. of Commerce, Boulder, Colo. 80302.

Williams, D.

Alta Freq. (1)

P. C. Waterman, Alta Freq. 38, 348 (1969).

Appl. Opt. (3)

Icarus (1)

W. M. Irvine, J. B. Pollock, Icarus 8, 324 (1968).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

A. R. Holt, N. K. Uzunoglu, B. G. Evans, IEEE Trans. Antennas Propag. AP-26, 706 (1978).
[CrossRef]

M. A. Morgan, K. K. Mei, IEEE Trans. Antennas Propag. AP-27, 202 (1979).
[CrossRef]

J. Comput. Phys. (1)

C. M. Chu, H. Weil, J. Comput. Phys. 22, 111 (1976).
[CrossRef]

J. Opt. Soc. Am. (2)

Other (1)

H. Weil, C. M. Chu, “Scattering and Absorption of Electromagnetic Radiation by Clouds of Disc Shaped Aerosols,” Report 016234-1-F, Radiation Laboratory, Department of Electrical and Computer Engineering, U. Michigan, Ann Arbor 48109 (Dec.1978).This report is the Final Report on NOAA grant 04-78-B01-1, U.S. Dept. of Commerce, Boulder, Colo. 80302.

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Figures (5)

Fig. 1
Fig. 1

z matrix.

Fig. 2
Fig. 2

Disk, incident waves, and coordinate system.

Fig. 3
Fig. 3

Cross sections and refractive indices for ice disks vs wavelength.

Fig. 4
Fig. 4

Effect of material absorptivity on bistatic scattering.

Fig. 5
Fig. 5

Effect of incident wave polarization on bistatic scattering: (a) perpendicular, and (b) parallel to the plane of incidence.

Tables (1)

Tables Icon

Table I Cross Sections for n = 0.960−i = 0.193, a = 2.95, δ = 0.2 Calculated for N = 6, M = 12

Equations (17)

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J = 2 π f 0 ( n 2 1 ) E .
E 0 = ( j 2 π f 0 ) 1 [ L J J / ( n 2 1 ) ] ,
L J = D d υ J ( R ) G ( R , R ) S d s J ( R ) n ̂ ( R ) G ( R , R ) ,
J = α j W j ( R )
f , g = d υ f ( R ) g ( R ) ,
E j = i α i z i j ;
W E ( n , m ) = × [ j R ( r ) Φ m ( ϕ ) z n ] ,
W M ( n , m ) = × W E ( n , m )
J ( R ) = k = 1 6 N M α k W k ( R )
σ B ( θ 0 , ϕ 0 ; θ s , ϕ s ) = ( 4 π k ) 2 m = 1 M [ | k = 1 6 N M α k I k θ ( θ s , ϕ s , m ) | 2 + | k = 1 6 N M α k I k ϕ ( θ s , ϕ s , m ) | 2 ] .
sin ϕ s p = 1 p 0 F k p ( m ) J m ( γ k p sin θ s ) ,
σ T S = σ B ( θ 0 , ϕ 0 ; θ s , ϕ s ) sin θ s d θ s d ϕ s
σ A = 2 n r n i | n 2 1 | 2 R 0 2 i = 1 j = 1 α i α j * W i j ,
σ EXT = σ T S + σ A
σ EXT = ( 4 π / k 0 ) I m E 0 * E f f z .
= 10 log 10 ( σ k 2 )
Σ T S , Σ A , and Σ B ( 0 , ϕ 0 ; π , ϕ 0 ) .

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