Abstract

The depolarization of light from a laser, back scattered from inhomogeneous dielectrics, was investigated both experimentally and theoretically. A theoretical model that includes back scattering from both the surface and subsurface was developed by use of the Kirchhoff approach. The subsurface polarized and depolarized back-scattered components are independent of surface roughness. The model predicts results in agreement with experimental measurements performed with a dual-polarized laser back-scattering system. The measurements indicate that a significant contribution to the total back-scattered power results from subsurface contributions; in some cases, this contribution completely masks the effects due to the surface.

© 1975 Optical Society of America

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References

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  1. J. Renau, R. K. Cheo, H. G. Cooper, and J. Opt, Soc. Am. 57, 459 (1967).
    [Crossref]
  2. A. K. Fung, Planet. Space Sci. 14, 563 (1966).
    [Crossref]
  3. P. Beckmann, The Depolarization of Electromagnetic Waves (Golem, Boulder, Colo., 1968).
  4. G. Valenzuela, IEEE Trans. AP-15, 552 (1967).
    [Crossref]
  5. J. W. Rouse, Radio Sci. 7, 889 (1972).
    [Crossref]
  6. J. C. Leader and W. Dalton, J. Appl. Phys. 43, 3080 (1972).
    [Crossref]
  7. G. J. Wilhelmi, W. T. Mayo, and J. W. Rouse, Laser and Unconven. Optics J. 43, 3 (1973).
  8. P. Beckman and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).
  9. S. Silver, Microwave Antenna Theory and Design, MIT Rad. Lab. Series 12 (McGraw–Hill, New York, 1947).
  10. J. C. Leader, J. Appl. Phys. 42, 4808 (1971).
    [Crossref]

1973 (1)

G. J. Wilhelmi, W. T. Mayo, and J. W. Rouse, Laser and Unconven. Optics J. 43, 3 (1973).

1972 (2)

J. W. Rouse, Radio Sci. 7, 889 (1972).
[Crossref]

J. C. Leader and W. Dalton, J. Appl. Phys. 43, 3080 (1972).
[Crossref]

1971 (1)

J. C. Leader, J. Appl. Phys. 42, 4808 (1971).
[Crossref]

1967 (2)

G. Valenzuela, IEEE Trans. AP-15, 552 (1967).
[Crossref]

J. Renau, R. K. Cheo, H. G. Cooper, and J. Opt, Soc. Am. 57, 459 (1967).
[Crossref]

1966 (1)

A. K. Fung, Planet. Space Sci. 14, 563 (1966).
[Crossref]

Beckman, P.

P. Beckman and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).

Beckmann, P.

P. Beckmann, The Depolarization of Electromagnetic Waves (Golem, Boulder, Colo., 1968).

Cheo, R. K.

J. Renau, R. K. Cheo, H. G. Cooper, and J. Opt, Soc. Am. 57, 459 (1967).
[Crossref]

Cooper, H. G.

J. Renau, R. K. Cheo, H. G. Cooper, and J. Opt, Soc. Am. 57, 459 (1967).
[Crossref]

Dalton, W.

J. C. Leader and W. Dalton, J. Appl. Phys. 43, 3080 (1972).
[Crossref]

Fung, A. K.

A. K. Fung, Planet. Space Sci. 14, 563 (1966).
[Crossref]

Leader, J. C.

J. C. Leader and W. Dalton, J. Appl. Phys. 43, 3080 (1972).
[Crossref]

J. C. Leader, J. Appl. Phys. 42, 4808 (1971).
[Crossref]

Mayo, W. T.

G. J. Wilhelmi, W. T. Mayo, and J. W. Rouse, Laser and Unconven. Optics J. 43, 3 (1973).

Opt, J.

J. Renau, R. K. Cheo, H. G. Cooper, and J. Opt, Soc. Am. 57, 459 (1967).
[Crossref]

Renau, J.

J. Renau, R. K. Cheo, H. G. Cooper, and J. Opt, Soc. Am. 57, 459 (1967).
[Crossref]

Rouse, J. W.

G. J. Wilhelmi, W. T. Mayo, and J. W. Rouse, Laser and Unconven. Optics J. 43, 3 (1973).

J. W. Rouse, Radio Sci. 7, 889 (1972).
[Crossref]

Silver, S.

S. Silver, Microwave Antenna Theory and Design, MIT Rad. Lab. Series 12 (McGraw–Hill, New York, 1947).

Spizzichino, A.

P. Beckman and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).

Valenzuela, G.

G. Valenzuela, IEEE Trans. AP-15, 552 (1967).
[Crossref]

Wilhelmi, G. J.

G. J. Wilhelmi, W. T. Mayo, and J. W. Rouse, Laser and Unconven. Optics J. 43, 3 (1973).

IEEE Trans. (1)

G. Valenzuela, IEEE Trans. AP-15, 552 (1967).
[Crossref]

J. Appl. Phys. (2)

J. C. Leader and W. Dalton, J. Appl. Phys. 43, 3080 (1972).
[Crossref]

J. C. Leader, J. Appl. Phys. 42, 4808 (1971).
[Crossref]

Laser and Unconven. Optics J. (1)

G. J. Wilhelmi, W. T. Mayo, and J. W. Rouse, Laser and Unconven. Optics J. 43, 3 (1973).

Planet. Space Sci. (1)

A. K. Fung, Planet. Space Sci. 14, 563 (1966).
[Crossref]

Radio Sci. (1)

J. W. Rouse, Radio Sci. 7, 889 (1972).
[Crossref]

Soc. Am. (1)

J. Renau, R. K. Cheo, H. G. Cooper, and J. Opt, Soc. Am. 57, 459 (1967).
[Crossref]

Other (3)

P. Beckmann, The Depolarization of Electromagnetic Waves (Golem, Boulder, Colo., 1968).

P. Beckman and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).

S. Silver, Microwave Antenna Theory and Design, MIT Rad. Lab. Series 12 (McGraw–Hill, New York, 1947).

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Figures (10)

FIG. 1
FIG. 1

Scattering geometry.

FIG. 2
FIG. 2

Schematic diagram of Lidar polarimeter.

FIG. 3
FIG. 3

Experimental measurement configuration.

FIG. 4
FIG. 4

Range of depolarized data for pigment 1 (black samples) all surface roughnesses.

FIG. 5
FIG. 5

Like-polarized back-scatter data from 80 grit samples. (E case was realized for the polarization of incident field). White sample (○); green sample (□); black sample (△).

FIG. 6
FIG. 6

Depolarized back-scatter data from 80 grit samples. (E case was realized for the polarization of the incident field.) White sample (○); green sample (□); black sample (△).

FIG. 7
FIG. 7

Polarized back-scatter data for the white and black samples. (E case was realized for the polarization of incident field.) White sample 220 grit (○); white sample smooth (□); black sample 220 grit (⎔); black sample smooth (△).

FIG. 8
FIG. 8

Depolarized back-scatter data for the white and black sample (E case realized for the polarization of the incident field.) White sample 220 grit (○); white sample smooth (□); black sample 220 grit (⎔); black sample smooth (△).

FIG. 9
FIG. 9

Comparison between the calculated values and experimental data for polarized back scatter from the 80 grit white samples (E was the case realized for the polarization of the incident field). Experimental data (○); theoretical curve - - - -.

FIG. 10
FIG. 10

Comparison between the calculated values and experimental data for depolarized back scatter from the 80 grit white samples (E was the case realized for the polarization of the incident field). Experimental data (○); theoretical curve - - - -.

Equations (22)

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E s ( P ) = K n 2 × S ˙ [ n × E - η n 2 × ( n × H ) ] × exp ( j k r · n 2 ) d s ,
E S H ( P ) = 2 K E 0 S ( a + a y Z y ) exp ( - j 2 k 1 · r ) d x d y ,
E SSH ( P ) = i 4 K 1 K 2 E 0 γ 11 ( a 1 + a y 1 cot θ r ) × ( a 11 + a y 11 cot θ ) A i 11 A sub
E SSV ( P ) = ( j cos θ + k sin θ ) 4 K 1 K 2 E 0 γ 12 × ( a 1 + a y 1 cot θ r ) ( b 12 + b y 12 cot θ ) A i 11 A sub ,
σ HH = 2 A i 11 cos θ [ a - n y n z a y ] 2 Q n z 2 [ n z 4 - Q n y 2 ] 3 / 2 + 4 π A i 11 ( γ 11 ) 2 cos θ [ ( a 1 + a y 1 cot θ r ) ( a 11 + a y 11 cot θ ) ] 2 ,
σ HV = 4 π A i 11 ( γ 12 ) 2 cos θ [ ( a 1 + a y 1 cot θ r ) ( b 12 + b y 12 cot θ ) ] 2 .
E s ( P ) = K n 2 × [ n × E - η n 2 × ( n × H ) ] × exp ( j k r · n 2 ) d s ,
K = j k exp ( - j k R ) ( 4 π R ) - 1 ,
E i = b E 0 exp ( - j k 1 · r ) = b E , H i = n × b E / η .
E SH ( P ) = 2 K 1 E 0 S _ ( a + a y Z y ) exp ( - 2 j k 1 · r ) d x d y ,
t 1 = n 1 × n , d 1 = n 1 × t 1 , d 2 = n 3 × t 1 .
E t = [ T 11 ( b · t 1 ) t 1 + T 21 ( b · d 1 ) d 2 ] E 0 , H t = n 3 × E t / η ,
E S ( P ) = 2 K 2 E 0 S [ - T 11 ( b · t 1 ) cos θ 3 t 1 - T 21 ( b · d 1 ) cos θ 3 d 2 ] d s ,
E SH ( P ) = i 2 K 2 E 0 ( a 1 + a y 1 cot θ r ) A i 11 ,
γ ˜ = [ γ 11 γ 12 γ 21 γ 22 ] ,
E SH ( P ) 1 = ( i ˆ · t 1 ) t 1 E γ 11 , H SH ( P ) 1 = ( i ˆ · t 1 ) ( - n 3 × t 1 ) ( E / η ) γ 11 , E SH ( P ) 2 = ( i ˆ · d 2 ) d 2 γ 12 E , H SH ( P ) 2 = ( i ˆ · d 2 ) ( - n 3 × d 2 ) γ 12 ( E / η ) ,
E = K 2 E 0 ( a 1 + a y 1 cot θ r ) A i 11 exp ( - j k r · n 3 ) .
E SSH ( P ) = i 4 K 1 K 2 E 0 γ 11 ( a 1 + a y 1 cot θ r ) × ( a 11 + a y 11 cot θ ) A i 11 A sub ,
γ ˜ 2 = γ ˜ 2 A i 11 A sub 2 λ 4 ( R ) 2 ,
σ HH = 4 π A i 11 γ 11 2 cos θ [ ( a 1 + a y 1 cot θ r ) ( a 11 + a y 11 cot θ ) ] 2 .
σ HH = 2 A i 11 cos θ [ a - n y n z a y ] 2 Q n z 2 [ n z 4 - Q n y 2 ] 3 / 2 × 4 π A i 11 γ 11 2 cos θ [ ( a 1 + a y 1 cot θ r ) ( a 11 + a y 11 cot θ ) ] 2 ,
σ HV 4 π A i 11 γ 12 2 cos θ [ ( a 1 + a y 1 cot θ r ) ( b 12 + b y 12 cot θ ) ] 2 ,