Abstract

Although several attempts have been made in the past to use the partially polarized nature of optical fields in constructing images, the technique is not widely known or used. This paper reviews the principles of single-parameter polarization imaging and introduces the concept of multiparameter Stokes vector imaging. The Stokes vector image construction is discussed in the context of a recently introduced model of the human visual system perception space. It is shown that this perception space model allows one to take advantage of more of the information contained in the optical field to create an intelligible color display. The perception space model is also used to define a quantitative visual discrimination threshold applicable to multiparameter image construction and display.

© 1981 Optical Society of America

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References

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  1. G. F. J. Garlick, G. A. Steigman, U.K. patent1-7-854 and U.S. patent3-992-571, Department of Physics, U. Hull, England.
  2. R. Walraven, Proc. Soc. Photo-Opt. Instrum. Eng. 112, 165 (1977).
  3. R. S. Fraser, J. Opt. Soc. Am. 54, 289 (1964).
    [CrossRef]
  4. K. L. Coulson, Appl. Opt. 5, 905 (1966).
    [CrossRef] [PubMed]
  5. P. Koepke, K. T. Kriebel, Appl. Opt. 17, 260 (1978).
    [CrossRef] [PubMed]
  6. G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Ocean. 3, 353(1973).
    [CrossRef]
  7. M. D. Buchanan, R. Pendergrass, Electro-Opt. Syst. Des. (29Mar.1980).
  8. O. D. Faugeras, IEEE Trans. Acoust. Speech, Signal Process. ASSP-27, 380 (1979).
    [CrossRef]
  9. An excellent discussion of these various representations appear in R. M. A. Assam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chaps. 1 and 2.
  10. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  11. D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971).
  12. The author would like to thank an unknown reviewer for pointing out this property of the polarization factor.
  13. J. P. Millard, J. C. Arvesen, Development and Test of Video Systems for Airborne Surveillance of Oil Spills, NASA Technical Memorandum, NASA TM X-62, 429 (Mar.1975).
  14. O. D. Faugeras, “Digital Color Image Processing and Psychophysics Within the Framework of a Human Visual Model,” Ph.D. Dissertation, U. Utah, Salt Lake City (June1976).
  15. K. R. Castleman, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1979), Chaps. 5 and 6.
  16. R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977), pp. 118–136.
  17. For a discussion of the implications of correlated data sets in multiparameter pseudo-color displays see A. B. Kahle, D. P. Madura, J. M. Soha, Appl. Opt. 19, 2279 (1980).
    [CrossRef] [PubMed]
  18. H. R. Gordon, Appl. Opt. 17, 1631 (1978) and references contained therein.
    [CrossRef] [PubMed]
  19. K. L. Coulson, Planet. Space Sci. 1, 265 (1959).
    [CrossRef]
  20. R. S. Fraser, J. Opt. Soc. Am. 54, 157 (1964).
    [CrossRef]
  21. G. W. Kattawar, G. N. Plass, S. J. Hitzfelder, Appl. Opt. 15, 632 (1976).
    [CrossRef] [PubMed]
  22. A. V. Oppenheim, R. W. Schaffer, T. G. Stockham, IEEE Trans. Audio Electroacoust. AU-16, 437 (1968).
    [CrossRef]
  23. T. G. Stockham, Proc. IEEE 60, 828 (1972).
    [CrossRef]
  24. R. W. Fries, J. W. Modestino, IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 625 (1979).
    [CrossRef]
  25. W. G. Egan, H. B. Hallock, in Proceedings, Fourth Symposium on Remote Sensing of Environment (Infrared Physics Laboratory, U. Mich., Ann Arbor, April1966), p. 671; Proc. IEEE 57, 621 (1969).
  26. P. N. Slater, Remote Sensing: Optics and Optical Systems (Addison-Wesley, Reading, Mass., 1980), pp. 468–471.

1980 (2)

1979 (2)

O. D. Faugeras, IEEE Trans. Acoust. Speech, Signal Process. ASSP-27, 380 (1979).
[CrossRef]

R. W. Fries, J. W. Modestino, IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 625 (1979).
[CrossRef]

1978 (2)

1977 (1)

R. Walraven, Proc. Soc. Photo-Opt. Instrum. Eng. 112, 165 (1977).

1976 (1)

1973 (1)

G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Ocean. 3, 353(1973).
[CrossRef]

1972 (1)

T. G. Stockham, Proc. IEEE 60, 828 (1972).
[CrossRef]

1968 (1)

A. V. Oppenheim, R. W. Schaffer, T. G. Stockham, IEEE Trans. Audio Electroacoust. AU-16, 437 (1968).
[CrossRef]

1966 (1)

1964 (2)

1959 (1)

K. L. Coulson, Planet. Space Sci. 1, 265 (1959).
[CrossRef]

Arvesen, J. C.

J. P. Millard, J. C. Arvesen, Development and Test of Video Systems for Airborne Surveillance of Oil Spills, NASA Technical Memorandum, NASA TM X-62, 429 (Mar.1975).

Assam, R. M. A.

An excellent discussion of these various representations appear in R. M. A. Assam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chaps. 1 and 2.

Bashara, N. M.

An excellent discussion of these various representations appear in R. M. A. Assam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chaps. 1 and 2.

Buchanan, M. D.

M. D. Buchanan, R. Pendergrass, Electro-Opt. Syst. Des. (29Mar.1980).

Castleman, K. R.

K. R. Castleman, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1979), Chaps. 5 and 6.

Chandrasekhar, S.

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

Clarke, D.

D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971).

Coulson, K. L.

K. L. Coulson, Appl. Opt. 5, 905 (1966).
[CrossRef] [PubMed]

K. L. Coulson, Planet. Space Sci. 1, 265 (1959).
[CrossRef]

Egan, W. G.

W. G. Egan, H. B. Hallock, in Proceedings, Fourth Symposium on Remote Sensing of Environment (Infrared Physics Laboratory, U. Mich., Ann Arbor, April1966), p. 671; Proc. IEEE 57, 621 (1969).

Faugeras, O. D.

O. D. Faugeras, IEEE Trans. Acoust. Speech, Signal Process. ASSP-27, 380 (1979).
[CrossRef]

O. D. Faugeras, “Digital Color Image Processing and Psychophysics Within the Framework of a Human Visual Model,” Ph.D. Dissertation, U. Utah, Salt Lake City (June1976).

Fraser, R. S.

Fries, R. W.

R. W. Fries, J. W. Modestino, IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 625 (1979).
[CrossRef]

Garlick, G. F. J.

G. F. J. Garlick, G. A. Steigman, U.K. patent1-7-854 and U.S. patent3-992-571, Department of Physics, U. Hull, England.

Gonzalez, R. C.

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977), pp. 118–136.

Gordon, H. R.

Grainger, J. F.

D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971).

Guinn, J. A.

G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Ocean. 3, 353(1973).
[CrossRef]

Hallock, H. B.

W. G. Egan, H. B. Hallock, in Proceedings, Fourth Symposium on Remote Sensing of Environment (Infrared Physics Laboratory, U. Mich., Ann Arbor, April1966), p. 671; Proc. IEEE 57, 621 (1969).

Hitzfelder, S. J.

Kahle, A. B.

Kattawar, G. W.

G. W. Kattawar, G. N. Plass, S. J. Hitzfelder, Appl. Opt. 15, 632 (1976).
[CrossRef] [PubMed]

G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Ocean. 3, 353(1973).
[CrossRef]

Koepke, P.

Kriebel, K. T.

Madura, D. P.

Millard, J. P.

J. P. Millard, J. C. Arvesen, Development and Test of Video Systems for Airborne Surveillance of Oil Spills, NASA Technical Memorandum, NASA TM X-62, 429 (Mar.1975).

Modestino, J. W.

R. W. Fries, J. W. Modestino, IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 625 (1979).
[CrossRef]

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schaffer, T. G. Stockham, IEEE Trans. Audio Electroacoust. AU-16, 437 (1968).
[CrossRef]

Pendergrass, R.

M. D. Buchanan, R. Pendergrass, Electro-Opt. Syst. Des. (29Mar.1980).

Plass, G. N.

G. W. Kattawar, G. N. Plass, S. J. Hitzfelder, Appl. Opt. 15, 632 (1976).
[CrossRef] [PubMed]

G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Ocean. 3, 353(1973).
[CrossRef]

Schaffer, R. W.

A. V. Oppenheim, R. W. Schaffer, T. G. Stockham, IEEE Trans. Audio Electroacoust. AU-16, 437 (1968).
[CrossRef]

Slater, P. N.

P. N. Slater, Remote Sensing: Optics and Optical Systems (Addison-Wesley, Reading, Mass., 1980), pp. 468–471.

Soha, J. M.

Steigman, G. A.

G. F. J. Garlick, G. A. Steigman, U.K. patent1-7-854 and U.S. patent3-992-571, Department of Physics, U. Hull, England.

Stockham, T. G.

T. G. Stockham, Proc. IEEE 60, 828 (1972).
[CrossRef]

A. V. Oppenheim, R. W. Schaffer, T. G. Stockham, IEEE Trans. Audio Electroacoust. AU-16, 437 (1968).
[CrossRef]

Walraven, R.

R. Walraven, Proc. Soc. Photo-Opt. Instrum. Eng. 112, 165 (1977).

Wintz, P.

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977), pp. 118–136.

Appl. Opt. (5)

Electro-Opt. Syst. Des. (1)

M. D. Buchanan, R. Pendergrass, Electro-Opt. Syst. Des. (29Mar.1980).

IEEE Trans. Acoust. Speech Signal Process. (1)

R. W. Fries, J. W. Modestino, IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 625 (1979).
[CrossRef]

IEEE Trans. Acoust. Speech, Signal Process. (1)

O. D. Faugeras, IEEE Trans. Acoust. Speech, Signal Process. ASSP-27, 380 (1979).
[CrossRef]

IEEE Trans. Audio Electroacoust. (1)

A. V. Oppenheim, R. W. Schaffer, T. G. Stockham, IEEE Trans. Audio Electroacoust. AU-16, 437 (1968).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. Ocean. (1)

G. W. Kattawar, G. N. Plass, J. A. Guinn, J. Phys. Ocean. 3, 353(1973).
[CrossRef]

Planet. Space Sci. (1)

K. L. Coulson, Planet. Space Sci. 1, 265 (1959).
[CrossRef]

Proc. IEEE (1)

T. G. Stockham, Proc. IEEE 60, 828 (1972).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

R. Walraven, Proc. Soc. Photo-Opt. Instrum. Eng. 112, 165 (1977).

Other (11)

G. F. J. Garlick, G. A. Steigman, U.K. patent1-7-854 and U.S. patent3-992-571, Department of Physics, U. Hull, England.

An excellent discussion of these various representations appear in R. M. A. Assam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chaps. 1 and 2.

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

D. Clarke, J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, New York, 1971).

The author would like to thank an unknown reviewer for pointing out this property of the polarization factor.

J. P. Millard, J. C. Arvesen, Development and Test of Video Systems for Airborne Surveillance of Oil Spills, NASA Technical Memorandum, NASA TM X-62, 429 (Mar.1975).

O. D. Faugeras, “Digital Color Image Processing and Psychophysics Within the Framework of a Human Visual Model,” Ph.D. Dissertation, U. Utah, Salt Lake City (June1976).

K. R. Castleman, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1979), Chaps. 5 and 6.

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977), pp. 118–136.

W. G. Egan, H. B. Hallock, in Proceedings, Fourth Symposium on Remote Sensing of Environment (Infrared Physics Laboratory, U. Mich., Ann Arbor, April1966), p. 671; Proc. IEEE 57, 621 (1969).

P. N. Slater, Remote Sensing: Optics and Optical Systems (Addison-Wesley, Reading, Mass., 1980), pp. 468–471.

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Figures (6)

Fig. 1
Fig. 1

Block diagram of polarization ratio imaging scheme with monochrome display.

Fig. 2
Fig. 2

Block diagram of single-parameter polarization imaging scheme based on measurement of the Stokes parameter.

Fig. 3
Fig. 3

Illustration of the perception space model of Faugeras,8 showing the visual discrimination properties of this space.

Fig. 4
Fig. 4

Illustration of a special mapping of the Stokes parameters into perception space coordinates.

Fig. 5
Fig. 5

Block diagram of Stokes vector image acquisition scheme.

Fig. 6
Fig. 6

Block diagram of Stokes vector image processing and display method.

Equations (33)

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S ˜ = M ˜ S ˜ ,
S 0 = E x 2 + E y 2 , S 2 = 2 E x E y cos γ , S 1 = E x 2 E y 2 , S 3 = 2 E x E y sin γ ,
I ( α ) = E x 2 cos 2 α + E y 2 sin 2 α + E x E y cos γ sin 2 α ,
I ( α ) = 1 2 S 0 + 1 2 S 1 cos 2 α + 1 2 S 2 sin 2 α .
degree of polarization : P = ( S 1 2 + S 2 2 + S 3 2 ) 1 / 2 S 0 ;
polarization factor : P = S 1 / S 0 ,
azimuthal angle : tan 2 θ = S 2 / S 1 .
I d ( x , y ) = a + b P ( x , y ) ,
S 0 ( x , y ) = I X ( x , y ) + I Y ( x , y ) S 1 ( x , y ) = I X ( x , y ) I Y ( x , y ) S 2 ( x , y ) = 2 I < ( x , y ) I X ( x , y ) I y ( x , y ) } .
P ( x , y ) = [ S 1 2 ( x , y ) + S 2 2 ( x , y ) ] 1 / 2 S 0 ( x , y ) ,
P ( x , y ) = S 1 ( x , y ) S 0 ( x , y ) ,
θ ( x , y ) = 1 2 tan 1 [ S 2 ( x , y ) S 1 ( x , y ) ] .
C = ( I t I b ) / I b ,
C = ( μ t μ b ) / μ b .
L ( x , y ) = I ( x , y , λ ) l ( λ ) d λ M ( x , y ) = I ( x , y , λ ) m ( λ ) d λ S ( x , y ) = I ( x , y , λ ) s ( λ ) d λ } ,
A = a ( α L * + β M * + λ S * ) C 1 = u 1 ( L * M * ) C 2 = u 2 ( L * S * ) } ,
L * = log L , M * = log M , S * = log S ,
[ R n G n B n ] = [ 1.910 0.533 0.288 0.985 2.000 0.028 0.058 0.118 0.896 ] [ L M S ] ,
L = exp ( A a + β u 1 C 1 γ u 2 C 2 ) , M = exp [ A a ( α + γ ) u 1 C 1 + γ u 2 C 2 ] , S = exp [ A a + β u 1 C 1 ( α + β ) u 2 C 2 ] .
S 0 A , S 1 C 1 , S 2 C 2 .
( hue ) χ = 2 θ = tan 1 ( S 2 / S 1 ) ( saturation ) ρ = ( S 1 2 + S 2 2 ) 1 / 2 } .
( hue ) χ = 2 θ = tan 1 ( S 2 / S 1 ) ( saturation ) ρ = P = ( S 1 2 + S 2 2 ) 1 / 2 S 0 } .
χ = a 1 P , ρ = a 2 θ , A = S 0 ,
C 1 = ρ cos χ = a 2 θ cos ( a 1 P ) C 2 = ρ sin χ = a 2 θ sin ( a 1 P ) } .
A = b 1 P , χ = b 2 θ , ρ = b 3 ,
C 1 = b 3 cos ( b 2 θ ) C 2 = b 3 sin ( b 2 θ ) } .
C = | P t P b | | P b | .
σ 2 = ( S 1 t S 1 b ) 2 + ( S 2 t S 2 b ) 2 ,
σ 2 = ( S 0 t S 0 b ) 2 + ( S 1 t S 1 b ) 2 + ( S 2 t S 2 b ) 2 .
A = S 0 , ρ = ( S 1 2 + S 2 2 ) 1 / 2 , χ = tan 1 ( S 2 / S 1 ) .
p ( ρ , χ ) = ρ 2 π σ 1 σ 2 exp [ ρ 2 cos 2 χ 2 σ 1 2 ( ρ sin χ s ¯ 2 ) 2 2 σ 2 2 ] .
I x ( x , y ) = I x ( s ) ( x , y ) + I x ( a ) ( x , y ) .
I ˆ x ( x , y ) = L ˜ [ I x ( x , y ) ] I x ( s ) ( x , y ) I y ( x , y ) = L ˜ [ I y ( x , y ) ] I y ( s ) ( x , y ) I ˆ < ( x , y ) = L ˜ [ I < ( x , y ) ] I < ( s ) ( x , y ) } ,

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