Abstract

In this paper the calibration of nonideal diffuse targets is discussed where the targets are irradiated bypolarized light. Both measurements of conical–hemispherical or directional–hemispherical and bihemispherical reflectance are discussed. The targets do not depolarize the incident light and in some cases the wall of the integrating sphere may not be depolarizing and must be represented by a Mueller reflectance matrix. This means that the usual comparison technique of targets based on the scalar theory does not apply.

© 1990 Optical Society of America

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References

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  1. F. E. Nicodemus, J. C. Richmond, J. W. Ginsberg, J. J. Hsia, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” in Self-Study Manual on Optical Radiation Measurements, Part 1, Natl. Bur. Stand. U.S. Monogr.160 (1977), Chap. 6.
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  14. R. R. Wiley, “Results of Round Robin Measurements of Spectral Emittance in the Mid-Infrared,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, 140–147 (1987).
  15. L. M. Hansen, K. A. Snail, “Infrared Diffuse Reflectometer for Spectral, Angular, and Temperature Resolved Measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, 148–159 (1987).
  16. J. T. Neu, R. S. Dummer, O. E. Myers, “Hemispherical Directional Ellipsoidial Infrared Spectrophotometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, 165–175 (1987).
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1989 (1)

1987 (3)

R. R. Wiley, “Results of Round Robin Measurements of Spectral Emittance in the Mid-Infrared,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, 140–147 (1987).

L. M. Hansen, K. A. Snail, “Infrared Diffuse Reflectometer for Spectral, Angular, and Temperature Resolved Measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, 148–159 (1987).

J. T. Neu, R. S. Dummer, O. E. Myers, “Hemispherical Directional Ellipsoidial Infrared Spectrophotometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, 165–175 (1987).

1985 (1)

W. S. Bickel, W. M. Bailey, “Stokes Vectors and Mueller Matrices and Polarized Light,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

1981 (1)

1980 (1)

1977 (2)

J. B. Shumaker, “Distribution of Optical Radiation with Respect to Polarization,” in Self-Study Manual on Optical Measurements, Natl. Bur. Stand. U.S. Tech. Note 910-3 (1977), Chap. 6.

F. E. Nicodemus, J. C. Richmond, J. W. Ginsberg, J. J. Hsia, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” in Self-Study Manual on Optical Radiation Measurements, Part 1, Natl. Bur. Stand. U.S. Monogr.160 (1977), Chap. 6.

1976 (1)

W. H. Venable, J. J. Hsia, V. R. Wiedner, “Development of an NBS Reference Spectrophotometer for Diffuse Transmittance and Reflectance,” Natl. Bur. Stand. U.S. Tech. Note 594-11 (1976).

1975 (1)

1967 (1)

1965 (1)

L. Mandel, E. Wolf, “Coherence Properties of Optical Fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[CrossRef]

1961 (1)

1955 (1)

Anderson, T. E.

Bailey, W. M.

W. S. Bickel, W. M. Bailey, “Stokes Vectors and Mueller Matrices and Polarized Light,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Bickel, W. S.

W. S. Bickel, W. M. Bailey, “Stokes Vectors and Mueller Matrices and Polarized Light,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Bottiger, J. R.

Dummer, R. S.

J. T. Neu, R. S. Dummer, O. E. Myers, “Hemispherical Directional Ellipsoidial Infrared Spectrophotometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, 165–175 (1987).

Edwards, D. K.

Egan, W. G.

Fry, E. S.

Gier, J. T.

Ginsberg, J. W.

F. E. Nicodemus, J. C. Richmond, J. W. Ginsberg, J. J. Hsia, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” in Self-Study Manual on Optical Radiation Measurements, Part 1, Natl. Bur. Stand. U.S. Monogr.160 (1977), Chap. 6.

Goebel, D. G.

Haner, D. A.

Hansen, L. M.

L. M. Hansen, K. A. Snail, “Infrared Diffuse Reflectometer for Spectral, Angular, and Temperature Resolved Measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, 148–159 (1987).

Hilgeman, T.

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. W. Ginsberg, J. J. Hsia, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” in Self-Study Manual on Optical Radiation Measurements, Part 1, Natl. Bur. Stand. U.S. Monogr.160 (1977), Chap. 6.

W. H. Venable, J. J. Hsia, V. R. Wiedner, “Development of an NBS Reference Spectrophotometer for Diffuse Transmittance and Reflectance,” Natl. Bur. Stand. U.S. Tech. Note 594-11 (1976).

Jacquez, J. A.

Kuppenheim, H. F.

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. W. Ginsberg, J. J. Hsia, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” in Self-Study Manual on Optical Radiation Measurements, Part 1, Natl. Bur. Stand. U.S. Monogr.160 (1977), Chap. 6.

Lowell, D. J.

D. J. Lowell, “Integrating Sphere Performance,” (Labsphere Corp., N. Sutton, NH, 1981).

Mandel, L.

L. Mandel, E. Wolf, “Coherence Properties of Optical Fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[CrossRef]

Menzies, R. T.

Myers, O. E.

J. T. Neu, R. S. Dummer, O. E. Myers, “Hemispherical Directional Ellipsoidial Infrared Spectrophotometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, 165–175 (1987).

Nelson, K. E.

Neu, J. T.

J. T. Neu, R. S. Dummer, O. E. Myers, “Hemispherical Directional Ellipsoidial Infrared Spectrophotometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, 165–175 (1987).

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. W. Ginsberg, J. J. Hsia, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” in Self-Study Manual on Optical Radiation Measurements, Part 1, Natl. Bur. Stand. U.S. Monogr.160 (1977), Chap. 6.

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. W. Ginsberg, J. J. Hsia, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” in Self-Study Manual on Optical Radiation Measurements, Part 1, Natl. Bur. Stand. U.S. Monogr.160 (1977), Chap. 6.

Roddick, R. D.

Shumaker, J. B.

J. B. Shumaker, “Distribution of Optical Radiation with Respect to Polarization,” in Self-Study Manual on Optical Measurements, Natl. Bur. Stand. U.S. Tech. Note 910-3 (1977), Chap. 6.

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard U. P.Cambridge, 1962).

Snail, K. A.

L. M. Hansen, K. A. Snail, “Infrared Diffuse Reflectometer for Spectral, Angular, and Temperature Resolved Measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, 148–159 (1987).

Thompson, R. C.

Venable, W. H.

W. H. Venable, J. J. Hsia, V. R. Wiedner, “Development of an NBS Reference Spectrophotometer for Diffuse Transmittance and Reflectance,” Natl. Bur. Stand. U.S. Tech. Note 594-11 (1976).

Wiedner, V. R.

W. H. Venable, J. J. Hsia, V. R. Wiedner, “Development of an NBS Reference Spectrophotometer for Diffuse Transmittance and Reflectance,” Natl. Bur. Stand. U.S. Tech. Note 594-11 (1976).

Wiley, R. R.

R. R. Wiley, “Results of Round Robin Measurements of Spectral Emittance in the Mid-Infrared,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, 140–147 (1987).

Wolf, E.

L. Mandel, E. Wolf, “Coherence Properties of Optical Fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[CrossRef]

Zerlaut, G. A.

Am. J. Phys. (1)

W. S. Bickel, W. M. Bailey, “Stokes Vectors and Mueller Matrices and Polarized Light,” Am. J. Phys. 53, 468–478 (1985).
[CrossRef]

Appl. Opt. (5)

J. Opt. Soc. Am. (2)

Natl. Bur. Stand. U.S. Tech. Note 594-11 (1)

W. H. Venable, J. J. Hsia, V. R. Wiedner, “Development of an NBS Reference Spectrophotometer for Diffuse Transmittance and Reflectance,” Natl. Bur. Stand. U.S. Tech. Note 594-11 (1976).

Proc. Soc. Photo-Opt. Instrum. Eng. (3)

R. R. Wiley, “Results of Round Robin Measurements of Spectral Emittance in the Mid-Infrared,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, 140–147 (1987).

L. M. Hansen, K. A. Snail, “Infrared Diffuse Reflectometer for Spectral, Angular, and Temperature Resolved Measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, 148–159 (1987).

J. T. Neu, R. S. Dummer, O. E. Myers, “Hemispherical Directional Ellipsoidial Infrared Spectrophotometer,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, 165–175 (1987).

Rev. Mod. Phys. (1)

L. Mandel, E. Wolf, “Coherence Properties of Optical Fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[CrossRef]

Self-Study Manual on Optical Measurements (1)

J. B. Shumaker, “Distribution of Optical Radiation with Respect to Polarization,” in Self-Study Manual on Optical Measurements, Natl. Bur. Stand. U.S. Tech. Note 910-3 (1977), Chap. 6.

Self-Study Manual on Optical Radiation Measurements (1)

F. E. Nicodemus, J. C. Richmond, J. W. Ginsberg, J. J. Hsia, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” in Self-Study Manual on Optical Radiation Measurements, Part 1, Natl. Bur. Stand. U.S. Monogr.160 (1977), Chap. 6.

Other (2)

W. A. Shurcliff, Polarized Light (Harvard U. P.Cambridge, 1962).

D. J. Lowell, “Integrating Sphere Performance,” (Labsphere Corp., N. Sutton, NH, 1981).

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Tables (1)

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Table I Scalar Bihemispherical Reflectance of the Wall and the Sample

Equations (47)

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d Φ ¯ r ( θ r , ϕ r ) = ρ ^ ( θ i , ϕ i ; θ r , ϕ r ) d Φ ¯ i ( θ i , ϕ i ) .
Φ ¯ r ( 2 π ) = ρ ^ ( ω i ; 2 π ) Φ ¯ i ( θ i ; ϕ i ) .
d Φ ¯ i ( θ i , ϕ i ) = L ¯ i ( θ i , ϕ i ) cos θ i d ω i d A i .
Φ ¯ r ( 2 π ) = ρ ^ ( ω i ; 2 π ) Φ ¯ i ( θ i , ϕ i ) = ρ ^ ( ω i ; 2 π ) [ ω i L ¯ i ( θ i , ϕ i ) cos θ i d ω i ] A i = { 2 π [ ω i ρ ^ ( θ i , ϕ i ; θ r , ϕ r ) L ¯ i ( θ i , ϕ i ) cos θ i d ω i cos θ r d ω r ] A i } .
ρ ^ ( ω i ; 2 π ) L ¯ i = 1 / ω i { 2 π [ ω i ρ ^ ( θ i , ϕ i ; θ r , ϕ r ) cos θ i d ω i ] cos θ r d ω r } L ¯ i = 1 / ω i { 2 π [ ω i ρ ^ ( θ i , ϕ i ; θ r , ϕ r ) d Ω i ] d Ω r } L ¯ i ,
ρ ^ ( 2 π ; 2 π ) L ¯ i = 1 / π { 2 π [ 2 π ρ ^ ( θ i , ϕ i ; θ r , ϕ r ) d Ω i ] d Ω r } L ¯ i .
( 1 - i = 1 n f i ) .
Φ ¯ 1 = ρ ^ ω ( ω i ; 2 π ) Φ ¯ i ( θ i , ϕ i ) .
Φ ¯ 2 = [ ρ ^ w ( 2 π ; 2 π ) ( 1 - i = 1 n f i ) + i = 1 n f i ρ ^ i ( 2 π ; 2 π ) ] Φ ¯ 1 ,
ρ ¯ ^ w ( 2 π ; 2 π ) = ρ ^ w ( 2 π ; 2 π ) ( 1 - i = 1 n f i ) + i = 1 n f i ρ ^ i ( 2 π ; 2 π ) ,
Φ ¯ 2 = ρ ¯ ^ w ( 2 π ; 2 π ) Φ ¯ 1 .
Φ ¯ 3 = ρ ¯ ^ w ( 2 π ; 2 π ) 2 Φ ¯ 2 .
Φ ¯ m = [ I ^ + ρ ¯ ^ w ( 2 π ; 2 π ) + ρ ¯ ^ w ( 2 π ; 2 π ) 2 + ρ ¯ ^ w ( 2 π ; 2 π ) 3 + ρ ¯ ^ w ( 2 π , 2 π ) m ] Φ ¯ 1 .
Φ ¯ e = f e [ I ^ - ρ ^ w ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) - f s ρ ^ t ( 2 π ; 2 π ) ] - 1 × ρ ^ w ( ω i ; 2 π ) Φ ¯ i ( θ i , ϕ i ) .
M ^ = [ I ^ - ρ ^ w ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) - f s ρ ^ t ( 2 π ; 2 π ) ] - 1 ,
Φ ¯ e t = f e M ^ ρ ^ w ( ω i ; 2 π ) Φ ¯ i ( θ i , ϕ i ) .
Φ ¯ e t = Φ i 1 ( θ i , ϕ i ) ρ w 11 ( ω i ; 2 π ) { M 11 M 21 M 31 M 41 } ,
M ^ w = [ I ^ - ρ ^ w ( 2 π ; 2 π ) ( 1 - f i - f e ) ] - 1 , M ^ o = [ I ^ - ρ ^ w ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) ] - 1 , M ^ t = [ I ^ - ρ ^ w ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) - f s ρ ^ t ( 2 π ; 2 π ) ] - 1 .
V ¯ e w = M ^ w C f e ρ ^ w ( ω i ; 2 π ) Φ ¯ i x ( θ i , ϕ i ) , V ¯ e o = M ^ o C f e ρ ^ w ( ω i ; 2 π ) Φ ¯ i x ( θ i , ϕ i ) , V ¯ e t = M ^ t C f e ρ ^ w ( ω i ; 2 π ) Φ ¯ i x ( θ i , ϕ i ) ,
½ ( A ^ h V ¯ e t x + A ^ v V ¯ e t x ) = V 1 e t x , ½ ( A ^ h V ¯ e t x - A ^ v V ¯ e t x ) = V 2 e t x , ½ ( A ^ + V ¯ e t x - A ^ - V ¯ e t x ) = V 3 e t x , ½ ( A ^ r V ¯ e t x - A ^ l V ¯ e t x ) = V 4 e t x ,
V ¯ e t x = ( V 1 e t x V 2 e t x V 3 e t x V 4 e t x ) = C 2 ( ( A ^ h Φ ¯ e t x + A ^ v Φ ¯ e t x ) 1 ( A ^ h Φ ¯ e t x - A ^ v Φ ¯ e t x ) 1 ( A ^ + Φ ¯ e t x - A ^ - Φ ¯ e t x ) 1 ( A ^ r Φ ¯ e t x - A ^ l Φ ¯ e t x ) 1 ) ,
M ^ w - 1 V ¯ e w x = M ^ o - 1 V ¯ e o x , M ^ w - 1 V ¯ e w x = M ^ t - 1 V ¯ e t x .
ρ ^ w ( 2 π ; 2 π ) [ ( 1 - f i - f e ) ( V ¯ e w x - V ¯ e o x ) + f s V ¯ e o x ] = [ V ¯ e w x - V ¯ e o x ] .
ρ ^ t ( 2 π ; 2 π ) V ¯ e t x = { [ ( 1 - f i - f e ) ρ ^ w ( 2 π , 2 π ) - I ^ ] ( V ¯ e w x - V ¯ e t x ) + f s ρ ^ w ( 2 π ; 2 π ) V ¯ e t x } .
Φ ¯ 1 = ρ ^ t ( ω i ; 2 π ) Φ ¯ i ( θ i , ϕ i ) .
Φ ¯ 2 = [ ρ ^ w ( 2 π ; 2 π ) ( 1 - i = 1 n f i ) + i = 3 n - 1 f i ρ ^ i ( 2 π ; 2 π ) ] Φ ¯ 1 .
Φ ¯ 3 = [ ρ ^ w ( 2 π ; 2 π ) ( 1 - i = 1 n f i ) + i = 3 n f i ρ ^ i ( 2 π ; 2 π ) ] Φ ¯ 2 .
ρ ¯ ^ w ( 2 π ; 2 π ) = ρ ^ w ( 2 π ; 2 π ) ( 1 - i = 1 n f 1 ) + i = 3 n - 1 f i ρ ^ i ( 2 π ; 2 π ) , ρ ¯ ^ w ( 2 π ; 2 π ) = ρ ^ w ( 2 π ; 2 π ) ( 1 - i = 1 n f i ) + i = 3 n f i ρ ^ i ( 2 π ; 2 π ) .
Φ ¯ e = f e [ I ^ + ρ ¯ ^ w ( 2 π ; 2 π ) + ρ ¯ ^ w ( 2 π ; 2 π ) 2 + + ρ ¯ ^ w ( 2 π ; 2 π ) m ] × ρ ¯ ^ w ( 2 π ; 2 π ) ρ ^ t ( ω i ; 2 π ) Φ ¯ i ( θ i , ϕ i ) .
Φ ¯ e = f e [ I ^ - ρ ¯ ^ w ( 2 π ; 2 π ) ] - 1 ρ ¯ ^ w ( 2 π ; 2 π ) ρ ^ t ( ω i ; 2 π ) Φ ¯ i ( θ i , ϕ i ) .
Φ ¯ e = f e [ I ^ - ρ ^ w ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) - f s ρ t ( 2 π ; 2 π ) ] - 1 × [ ρ ^ w ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) ] ρ ^ t ( ω i ; 2 π ) Φ ¯ i ( θ i , ϕ i ) .
Φ e 1 = { [ f e ρ w 11 ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) ] [ 1 - ρ ^ w 11 ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) - f s ρ t 11 ( 2 π ; 2 π ) ] × [ ρ t 11 ( ω i ; 2 π ) Φ i 1 ( θ i , ϕ i ) ] [ 1 - ρ ^ w 11 ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) - f s ρ t 11 ( 2 π ; 2 π ) ] } .
Φ e w 1 = { [ f e ρ w 11 ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) ] [ 1 - ρ w 11 ( 2 π ; 2 π ) ( 1 - f i - f e ) ] × [ ρ w 11 ( ω i ; 2 π ) Φ i 1 ( θ i , ϕ i ) ] [ 1 - ρ w 11 ( 2 π ; 2 π ) ( 1 - f i - f e ) ] } ,
Φ e t 1 = { [ f e ρ w 11 ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) ] [ 1 - ρ ^ w 11 ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) - f s ρ t 11 ( 2 π ; 2 π ) ] × [ ρ t 11 ( ω i ; 2 π ) Φ i 1 ( θ i , ϕ i ) ] [ 1 - ρ ^ w 11 ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) - f s ρ t 11 ( 2 π ; 2 π ) ] } .
Φ e w 1 = [ f e ρ w 11 ( 2 π ; 2 π ) ρ w 11 ( ω i ; 2 π ) Φ i 1 ( θ i , ϕ i ) ] [ 1 - ρ w 11 ( 2 π ; 2 π ) ] ,
Φ e t 1 = [ f e ρ w 11 ( 2 π ; 2 π ) ρ t 11 ( ω i ; 2 π ) Φ i 1 ( θ i , ϕ i ) ] [ 1 - ρ w 11 ( 2 π ; 2 π ) ] .
ρ t 11 ( ω i ; 2 π ) = ρ w 11 ( ω i ; 2 π ) V e t 1 / V e w 1 .
Φ ¯ e w = { f e [ I ^ - ρ ^ w ( 2 π ; 2 π ) ] - 1 ρ ^ w ( 2 π ; 2 π ) ρ w ( ω i ; 2 π ) Φ ¯ i ( θ i , ϕ i ) } , Φ ¯ e t = { f e [ I ^ - ρ ^ w ( 2 π ; 2 π ) ] - 1 ρ ^ w ( 2 π ; 2 π ) ρ ^ t ( ω i ; 2 π ) Φ ¯ i ( θ i , ϕ i ) } .
Φ e w 1 = { f e [ 1 - ρ ^ w 11 ( 2 π ; 2 π ) ] - 1 ρ ^ w 11 ( 2 π ; 2 π ) ρ w 11 ( ω i ; 2 π ) Φ i 1 } , Φ e t 1 = f e { [ 1 - ρ ^ w 11 ( 2 π ; 2 π ) ] - 1 ρ w 11 ( 2 π , 2 π ) [ ρ t 11 ( ω i ; 2 π ) Φ i 1 + ρ ^ t 12 ( ω i ; 2 π ) Φ i 2 + ρ t 13 ( ω i ; 2 π ; 2 π ) Φ i 3 + ρ t 14 ( ω i ; 2 π ) Φ i 4 ] } .
M ^ = [ I ^ - ρ ^ w ( 2 π ; 2 π ) ] - 1 ρ ^ w ( 2 π ; 2 π ) ,
Φ ¯ e t = f e M ^ ρ ^ t ( ω i ; 2 π ) Φ ¯ i ( θ i , ϕ i ) .
V w 1 = C Φ w e 1 = f e C ρ w 11 ( ω i ; 2 π ) Φ i 1 ( θ i , ϕ i ) [ 1 - ρ w 11 ( 2 π ; 2 π ) ( 1 - f i - f e ) ] ,
V t 1 = C Φ t e 1 = f e C ρ w 11 ( ω i ; 2 π ) Φ i 1 ( θ i , ϕ i ) [ 1 - ρ w 11 ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) - f s ρ t 11 ( 2 π ; 2 π ) ] ,
V o 1 = C Φ o e 1 = f e C ρ w 11 ( ω i ; 2 π ) Φ i 1 ( θ i , ϕ i ) [ 1 - ρ w 11 ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) ] .
ρ w 11 ( 2 π ; 2 π ) = 1 / [ ( 1 - f i - f e ) - f s V w 1 / ( V o 1 - V w 1 ) ] .
ρ t 11 ( 2 π ; 2 π ) = { ( V w 1 - V t 1 ) [ 1 - ρ w 11 ( 2 π ; 2 π ) ( 1 - f i - f e ) ] f s V t 1 - ρ w 11 ( 2 π , 2 π ) f s V t 1 } .
ρ t 11 ( 2 π ; 2 π ) = { ( V t 1 - V o 1 ) [ 1 - ρ w 11 ( 2 π ; 2 π ) ( 1 - f i - f e - f s ) ] } f s V t 1 .

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