Abstract

Narrow beam light transfer in a layer of small particles is treated theoretically in terms of degradation of image quality and depolarization. Computer simulations using Monte Carlo methods are described, and some results of the simulations are shown. Simulations were done for cases in which a ground-based linearly polarized light beam is transmitted to a spacecraft through cloud layers, and the light is detected on the spacecraft. Image degradation and light depolarization resulting from transmission through clouds are shown qualitatively and quantitatively. The results indicate that depolarization is negligibly small, but degradation of image quality is not negligible, especially when the light beam divergence is large. At infrared wavelengths the effect of image blurring is much smaller than at visible wavelengths.

© 1981 Optical Society of America

Full Article  |  PDF Article

Corrections

Tadashi Aruga and Takashi Igarashi, "Narrow beam light transfer in small particles: image blurring and depolarization: erratum," Appl. Opt. 20, 3831-3831 (1981)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-20-22-3831

References

  • View by:
  • |
  • |
  • |

  1. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  2. G. N. Plass, G. W. Kattawar, Appl. Opt. 7, 415 (1968).
  3. G. W. Kattawar, G. N. Plass, Appl. Opt. 7, 1519 (1968).
  4. G. W. Kattawar, G. N. Plass, Appl. Opt. 11, 2851 (1972).
  5. D. G. Collins, W. G. Blattner, M. B. Wells, H. G. Horak, Appl. Opt. 11, 2684 (1972).
  6. T. Aruga, D. F. Heath, Appl. Opt.20, 000 (1981), to be published.
  7. G. N. Plass, G. W. Kattawar, Appl. Opt. 10, 2304 (1971).
  8. K. Lion, R. M. Schotland, J. Atmos. Sci. 28, 772 (1971).
  9. E. A. Bucher, Appl. Opt. 12, 2391 (1973).
  10. T. Aruga, T. Igarashi, in Proceedings, Eighth International Laser Radar Conference (Drexel U., Philadelphia, 1977), IV-37, pp. 80–82.
  11. J. L. Bufton, L. O. Candill, T. E. Mcgunigal, K. R. Piech, J. Opt. Soc. Am. 69, 1180 (1979).
  12. T. Aruga, T. Igarashi, IEEE Trans. Aerosp. Electron. Syst. AES-13, 473 (1977).
  13. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  14. D. Diermendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969).
  15. W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).
  16. M. Diem, Met. Rundshan. 9, 10, 261 (1948).
  17. O. Miyatake, T. Nakayama, The Monte Carlo Method (Nikkan Kogyo Shinbunsha, Tokyo, 1960).
  18. S. R. Pal, A. I. Carswell, Appl. Opt. 17, 2321 (1978).

1979 (1)

1978 (1)

1977 (1)

T. Aruga, T. Igarashi, IEEE Trans. Aerosp. Electron. Syst. AES-13, 473 (1977).

1973 (1)

1972 (2)

1971 (2)

G. N. Plass, G. W. Kattawar, Appl. Opt. 10, 2304 (1971).

K. Lion, R. M. Schotland, J. Atmos. Sci. 28, 772 (1971).

1968 (3)

1948 (1)

M. Diem, Met. Rundshan. 9, 10, 261 (1948).

Aruga, T.

T. Aruga, T. Igarashi, IEEE Trans. Aerosp. Electron. Syst. AES-13, 473 (1977).

T. Aruga, D. F. Heath, Appl. Opt.20, 000 (1981), to be published.

T. Aruga, T. Igarashi, in Proceedings, Eighth International Laser Radar Conference (Drexel U., Philadelphia, 1977), IV-37, pp. 80–82.

Blattner, W. G.

Bucher, E. A.

Bufton, J. L.

Candill, L. O.

Carswell, A. I.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

Collins, D. G.

Diem, M.

M. Diem, Met. Rundshan. 9, 10, 261 (1948).

Diermendjian, D.

D. Diermendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969).

Heath, D. F.

T. Aruga, D. F. Heath, Appl. Opt.20, 000 (1981), to be published.

Horak, H. G.

Igarashi, T.

T. Aruga, T. Igarashi, IEEE Trans. Aerosp. Electron. Syst. AES-13, 473 (1977).

T. Aruga, T. Igarashi, in Proceedings, Eighth International Laser Radar Conference (Drexel U., Philadelphia, 1977), IV-37, pp. 80–82.

Irvine, W. M.

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).

Kattawar, G. W.

Lion, K.

K. Lion, R. M. Schotland, J. Atmos. Sci. 28, 772 (1971).

Mcgunigal, T. E.

Miyatake, O.

O. Miyatake, T. Nakayama, The Monte Carlo Method (Nikkan Kogyo Shinbunsha, Tokyo, 1960).

Nakayama, T.

O. Miyatake, T. Nakayama, The Monte Carlo Method (Nikkan Kogyo Shinbunsha, Tokyo, 1960).

Pal, S. R.

Piech, K. R.

Plass, G. N.

Pollack, J. B.

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).

Schotland, R. M.

K. Lion, R. M. Schotland, J. Atmos. Sci. 28, 772 (1971).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Wells, M. B.

Appl. Opt. (7)

Icarus (1)

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).

IEEE Trans. Aerosp. Electron. Syst. (1)

T. Aruga, T. Igarashi, IEEE Trans. Aerosp. Electron. Syst. AES-13, 473 (1977).

J. Atmos. Sci. (1)

K. Lion, R. M. Schotland, J. Atmos. Sci. 28, 772 (1971).

J. Opt. Soc. Am. (1)

Met. Rundshan. (1)

M. Diem, Met. Rundshan. 9, 10, 261 (1948).

Other (6)

O. Miyatake, T. Nakayama, The Monte Carlo Method (Nikkan Kogyo Shinbunsha, Tokyo, 1960).

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

D. Diermendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969).

T. Aruga, T. Igarashi, in Proceedings, Eighth International Laser Radar Conference (Drexel U., Philadelphia, 1977), IV-37, pp. 80–82.

T. Aruga, D. F. Heath, Appl. Opt.20, 000 (1981), to be published.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Size distributions of clouds used in this work.

Fig. 2
Fig. 2

Phase functions of clouds for typical wavelengths in the visible region (0.5 μm) and the infrared region (10.6 μm).

Fig. 3
Fig. 3

Cloud layer and photon history.

Fig. 4
Fig. 4

Polar angles. The suffixes b and a mean before and after collision, respectively. The X,Y,Z axes are parallel to the x,y,z axes in Fig. 3.

Fig. 5
Fig. 5

Simple geometry of photon detection using an image plate. The x′,y′ axes are parallel to the x,y axes.

Fig. 6
Fig. 6

Some examples of simulation for image blurring. The cases (a) – (h) correspond to right-hand side notes (a)–(h) in Table II. The satellite altitude a = 1000 km and the light beam transmitting zenith angle α = 45° are assumed.

Tables (3)

Tables Icon

Table I Optical Coefficients of Clouds

Tables Icon

Table II Numerical Results of Depolarization and Intensity

Tables Icon

Table III Qualitative Results

Equations (32)

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

P ( Θ ) = ( P 2 ( Θ ) 0 0 0 0 P 1 ( Θ ) 0 0 0 0 P 3 ( Θ ) P 4 ( Θ ) 0 0 P 4 ( Θ ) P 3 ( Θ ) ) .
m = 1.336 0.800 × 10 9 i ( for 0.5 μ m ) 1.179 0.0739 i ( for 10.6 μ m ) .
I = ( I t I r U V ) .
I = I t + I r , U = I cos 2 β sin 2 χ V = I sin 2 β } ,
I 0 = ( I 0 cos 2 ( φ 0 ϕ ) I 0 sin 2 ( φ 0 ϕ ) I 0 sin 2 ( φ 0 ϕ ) 0 ) .
2 π c 0 x / 2 exp [ θ 0 / ( 0.5 γ ) ] 2 sin θ 0 d θ 0 = 1 , c = const .
φ 0 = 2 π N r , 0 N r 1 .
l 0 = ( 1 / β e ) In { 1 N r [ 1 exp [ L 0 β e ) ] } ,
x 1 = ( h / cos α + l 0 ) sin θ 0 cos φ 0 y 1 = ( h / cos α + l 0 ) sin θ 0 cos φ 0 z 1 = ( h / cos α + l 0 ) cos φ 0 } .
1 4 π 0 π 0 2 π P ¯ ( Θ ) sin Θ d Θ d Φ b = 1 1 2 0 π P ¯ ( Θ ) sin Θ d Θ = 1
Φ b = 2 π N r , 0 N r 1 .
cos θ a = cos θ b cos Θ + sin θ b sin Θ cos Φ b cos Θ = cos θ a cos θ b + sin θ a sin θ b cos ( φ b φ a ) } .
I a = ω C P ( θ a , φ a ; θ b , φ b ) I b , C = 1 / P ¯ ( Θ ) ,
P ( θ a , φ a ; θ b , φ b ) = L ( π Φ b ) P ( Θ ) L ( Φ b ) ,
L ( π Φ ) = L ( Φ ) = ( cos 2 Φ sin 2 Φ ½ sin 2 Φ 0 sin 2 Φ cos 2 Φ ½ sin 2 Φ 0 sin 2 Φ sin 2 Φ cos 2 Φ 0 0 0 0 1 ) .
sin Φ a = sin θ b sin Φ b / sin θ a ,
l j = ( 1 / β e ) In { 1 N r [ 1 exp ( L j β e ) ] } , j = 1 , 2 , , n 1 ,
L j = ( h + d cos α x j tan α z j ) / ( cos θ j + sin θ j cos φ j tan α ) , j = 1 , 2 , , n 1 .
x j = x j 1 + l j 1 sin θ j 1 cos φ j 1 y j = y j 1 + l j 1 sin θ j 1 sin φ j 1 z j = z j 1 + l j 1 cos θ j 1 } , j = 2 , 3 , , n .
W j = 1 exp ( L j β e ) , j = 0 , 1 , 2 , , n 1 .
I n = Δ Ω 4 π ω exp ( β e l n ) P ( θ n , φ n ; θ n 1 , φ n 1 ) I n 1 ,
cos Θ n = ( z s z n ) / [ ( x s x n ) 2 + ( y s y n ) 2 + ( z s z n ) 2 ] 1 / 2 cos φ n = x n / ( x n 2 + y n 2 ) 1 / 2 x s = y s = 0 } .
cos Θ = cos θ n cos θ n 1 + sin Θ n sin θ n 1 cos ( φ n 1 φ n ) sin Φ n 1 = sin θ n sin ( φ n 1 φ n ) / sin Θ sin Φ n = sin θ n 1 sin ( φ n 1 φ n ) / sin θ } .
I n = Δ Ω 4 π exp ( β e l n ) P ( θ n , φ n ; θ n 1 , φ n 1 ) [ j = 1 n 1 P ( θ j , φ j ; θ j 1 , φ j 1 ) ] × [ j = 1 n 1 C j ] ω n [ j = 0 n 1 W j ] I 0 ,
j 1 n 1 P ( θ j , φ j ; θ j 1 φ j 1 ) = P ( θ n 1 , φ n 1 ; θ n 2 , φ n 2 ) P ( θ 2 , φ 2 ; θ 1 , φ 1 ) P ( θ 1 , φ 1 ; θ 0 , φ 0 ) ,
I = I ( cos 2 β cos 2 δ + sin 2 β sin 2 δ ) I = I ( cos 2 β sin 2 δ + sin 2 β cos 2 δ ) } ,
β = 0.5 sin 1 ( V / I ) ,
δ = | χ ( φ n ϕ ) | χ = 0.5 sin 1 [ U / ( I cos 2 β ) ] } .
I ¯ = 1 M n i = 1 M I n , i I ¯ = 1 M n i = 1 M I n , i I ¯ = I ¯ + I ¯ } .
D = I ¯ / I ¯ .
I ¯ ( Δ θ , Δ φ ) = 1 M n i = 1 m I n , i ( Δ θ , Δ φ ) .
D = I ¯ ( scattered ) I ¯ ( direct ) + I ¯ ( scattered ) .

Metrics