Abstract

Polarization-difference imaging (PDI) was recently presented by us as a method of imaging through scattering media [Opt. Lett. 20, 608 (1995)]. Here, PDI is compared with conventional, polarization-blind imaging systems under a variety of conditions not previously studied. Through visual and numerical comparison of polarization-difference and polarization-sum images of metallic targets suspended in scattering media, target features initially visible in both types of images are shown to disappear in polarization-sum images as the scatterer concentration is increased, whereas these features remain visible in polarization-difference images. Target features producing an observed degree of linear polarization of less than 1% are visible in polarization-difference images. The ability of PDI to suppress partially polarized background variations selectively is demonstrated, and discrimination of target features on the basis of polarization information is discussed. Our results show that, when compared with conventional imaging, PDI yields a factor of 2–3 increase in the distance at which certain target features can be detected.

© 1996 Optical Society of America

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  1. S. Q. Duntley, “Underwater visibility and photography,” in Optical Aspects of Oceanography, N. G. Jerlov, ed. (Academic, London, 1974), pp. 138–149.
  2. L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast Kerr gate,” Science 253, 769–771 (1991).
  3. A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
  4. S. Q. Duntley, “Light in the sea,” J. Opt. Soc. Am. 53, 214–233 (1963).
  5. D. A. Cameron, E. N. Pugh, “Double cones as a basis for a new type of polarization vision in vertebrates,” Nature (London) 353, 161–164 (1991).
  6. M. P. Rowe, E. N. Pugh, J. S. Tyo, N. Engheta, “Polarization-difference imaging: a biologically inspired technique for observation through scattering media,” Opt. Lett. 20, 608–610 (1995).
  7. M. P. Rowe, N. Engheta, S. S. Easter, E. N. Pugh, “Graded-index model of a fish double cone exhibits differential polarization sensitivity,” J. Opt. Soc. Am. A 11, 55–70 (1994).
  8. J. S. Tyo, “Automatic rotational polarizer for the polarization differencing camera,” undergraduate senior design project (Moore School of Electrical Engineering, University of Pennsylvania, Philadelphia, Pa., 1994).
  9. J. N. Lythgoe, “The adaptation of visual pigments to the photic environment,” in Handbook of Sensory Physiology, H. J. A. Dartnall, ed. (Springer-Verlag, New York, 1971), Vol. VII/1, pp. 566–603.
  10. We do not explicitly discuss the effects of forward-scattered light and multiple scattering. For simplicity we assume that light that is truly forward scattered acts as image-forming light. Furthermore, light that is scattered out of the imaging path and then back into it acts as veiling light.
  11. H. G. Gordon, “Modeling and simulating radiative transfer in the ocean,” in Ocean Optics, R. W. Spinrad, K. L. Carder, J. J. Perry, ed. (Oxford U. Press, New York, 1994), pp. 1–46.
  12. As a reference, for Atlantic Ocean water in the vicinity of Gibraltar at a depth of 25 m for light of wavelength 465 nm, the attenuation length is 20 m.4 The wavelength of light used in our study is 610 nm. A wavelength of 610 nm was chosen only because the TNLC was designed to operate at 610 nm. There is no relative advantage to using light of wavelength 610 nm, and the results presented here should be generalizable to any wavelength of electromagnetic radiation. We performed studies using white light in the present setup with nominally similar results (data not shown).
  13. When there is no milk in the tank, the water and the particles suspended in the water act as scatterers. This is why the beam-attenuation coefficient is not equal to zero when there is no milk.
  14. Using the notation of Stokes parameters, 〈ODLP〉 can be written as S1/S0, where S0 and S1 are the first and the second Stokes parameters. It is inherent in Eqs. (1) and (2) that PSI = S0 and 'I = S1. For discussion of Stokes parameters, see, for example, C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover, New York, 1988), pp. 118–134.
  15. G. P. Können, Polarized Light in Nature (Cambridge U. Press, London, 1985), pp. 74–99.
  16. R. Shapley, C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” Prog. Retinal Res. 3, 263–346 (1984).
  17. A. S. Sedra, K. C. Smith, Microelectronic Circuits (Saunders College, Ft. Worth, Tex., 1991), pp. 48–114.
  18. Rather than using the term noise, we use the term corrupting variations. This refers to all variations other than the signals produced by the scratched patches. In the PD case this is mostly noise that is due to the system and the medium. In the PS case we are referring to noise as well as the unwanted intensity variations described earlier.
  19. In our study the target is thought of as the scratched target patches, and the background includes the unscratched portions of the disk as well as the area outside the disk.
  20. The ARP was developed as an undergraduate senior design project by J. S. Tyo.8 We plan to test its performance under a variety of conditions, and we hope to present the details of its operation in a subsequent paper.
  21. T. H. Waterman, “Polarization sensitivity,” in Handbook of Sensory Physiology, H. Autrum, ed. (Springer-Verlag, New York, 1981), Vol. VII/6b, pp. 283–311.
  22. N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, London, 1991), pp. 7–28.
  23. In the present arrangement of the PDI system, the TNLC limits the speed with which the system performs. To ensure that the TNLC has had time to relax to its unexcited state after collection of a pair of linearly polarized images, one needs to wait approximately 3 min after turning off the excitation before capturing a subsequent pair of images. Typically, collection of the 30 images took just less than 2 h.
  24. The filter is designed by hand to be used with the Imaging Technologies, Inc., software. It is 7 × 7 pixels, is peaked in the middle, has a summed value of unity, and falls off to a value of (0.125 max) in 3 pixels.
  25. Y. Kuga, A. Ishimaru, “Modulation transfer function and image transmission through randomly distributed spherical particles,” Appl. Opt. 25, 2330–2335 (1985).
  26. Y. Kuga, A. Ishimaru, “Modulation transfer function of layered inhomogeneous random media using the small-angle approximation,” Appl. Opt. 25, 4382–4385 (1986).
  27. C. Brüning, R. Schmidt, W. Alpers, “Estimation of the ocean wave–radar modulation transfer function from synthetic aperture radar imagery,” J. Geophys. Res. C 99, 9803–9815 (1994).
  28. A. Schmidt, V. Wismann, R. Romeiser, W. Alpers, “Simultaneous measurements of the ocean wave–radar modulation transfer function at L, C, and X bands from the research platform Nordsee,” J. Geophys. Res. C 100, 8815–8827 (1995).
  29. K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Vector wave imagery with a lens masked by polarizers,” J. Mod. Opt. 40, 379–390 (1993).
  30. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), pp. 301–306, 448–454.
  31. R. Walraven, “Polarization imagery,” in Optical Polarimetry: Instrumentation and Applications, R. M. Azzam, D. L. Coffeen, eds., Proc. SPIE 112, 164–167 (1977).
  32. G. F. J. Garlick, C. A. Steigmann, W. E. Lamb, “Differential optical polarisation detectors,” U.S. patent3,992,571 (16November1976).
  33. J. E. Solomon, “Polarization imaging,” Appl. Opt. 20, 1537–1544 (1981).
  34. J. Halaijan, H. Hallock, “Principles and techniques of polarimetric mapping,” in Proceedings of 8th Symposium on Remote Sensing and Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1972), Vol. 1, pp. 523–540.
  35. L. B. Wolff, T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Patt. Anal. Mach. Intell. 13, 635–657 (1991).
  36. W. G. Egan, W. R. Johnson, V. S. Whitehead, “Terrestrial polarization imagery obtained from the Space Shuttle: characterization and interpretation,” Appl. Opt. 30, 435–442 (1991).
  37. G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London Ser. B 220, 89–113 (1983).

1995

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).

A. Schmidt, V. Wismann, R. Romeiser, W. Alpers, “Simultaneous measurements of the ocean wave–radar modulation transfer function at L, C, and X bands from the research platform Nordsee,” J. Geophys. Res. C 100, 8815–8827 (1995).

M. P. Rowe, E. N. Pugh, J. S. Tyo, N. Engheta, “Polarization-difference imaging: a biologically inspired technique for observation through scattering media,” Opt. Lett. 20, 608–610 (1995).

1994

M. P. Rowe, N. Engheta, S. S. Easter, E. N. Pugh, “Graded-index model of a fish double cone exhibits differential polarization sensitivity,” J. Opt. Soc. Am. A 11, 55–70 (1994).

C. Brüning, R. Schmidt, W. Alpers, “Estimation of the ocean wave–radar modulation transfer function from synthetic aperture radar imagery,” J. Geophys. Res. C 99, 9803–9815 (1994).

1993

K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Vector wave imagery with a lens masked by polarizers,” J. Mod. Opt. 40, 379–390 (1993).

1991

L. B. Wolff, T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Patt. Anal. Mach. Intell. 13, 635–657 (1991).

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast Kerr gate,” Science 253, 769–771 (1991).

D. A. Cameron, E. N. Pugh, “Double cones as a basis for a new type of polarization vision in vertebrates,” Nature (London) 353, 161–164 (1991).

W. G. Egan, W. R. Johnson, V. S. Whitehead, “Terrestrial polarization imagery obtained from the Space Shuttle: characterization and interpretation,” Appl. Opt. 30, 435–442 (1991).

1986

1985

Y. Kuga, A. Ishimaru, “Modulation transfer function and image transmission through randomly distributed spherical particles,” Appl. Opt. 25, 2330–2335 (1985).

1984

R. Shapley, C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” Prog. Retinal Res. 3, 263–346 (1984).

1983

G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London Ser. B 220, 89–113 (1983).

1981

1963

Alfano, R. R.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast Kerr gate,” Science 253, 769–771 (1991).

Alpers, W.

A. Schmidt, V. Wismann, R. Romeiser, W. Alpers, “Simultaneous measurements of the ocean wave–radar modulation transfer function at L, C, and X bands from the research platform Nordsee,” J. Geophys. Res. C 100, 8815–8827 (1995).

C. Brüning, R. Schmidt, W. Alpers, “Estimation of the ocean wave–radar modulation transfer function from synthetic aperture radar imagery,” J. Geophys. Res. C 99, 9803–9815 (1994).

Bhattacharya, K.

K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Vector wave imagery with a lens masked by polarizers,” J. Mod. Opt. 40, 379–390 (1993).

Boult, T. E.

L. B. Wolff, T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Patt. Anal. Mach. Intell. 13, 635–657 (1991).

Brüning, C.

C. Brüning, R. Schmidt, W. Alpers, “Estimation of the ocean wave–radar modulation transfer function from synthetic aperture radar imagery,” J. Geophys. Res. C 99, 9803–9815 (1994).

Buchsbaum, G.

G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London Ser. B 220, 89–113 (1983).

Cameron, D. A.

D. A. Cameron, E. N. Pugh, “Double cones as a basis for a new type of polarization vision in vertebrates,” Nature (London) 353, 161–164 (1991).

Chakraborty, A. K.

K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Vector wave imagery with a lens masked by polarizers,” J. Mod. Opt. 40, 379–390 (1993).

Chance, B.

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).

Creelman, C. D.

N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, London, 1991), pp. 7–28.

Duntley, S. Q.

S. Q. Duntley, “Light in the sea,” J. Opt. Soc. Am. 53, 214–233 (1963).

S. Q. Duntley, “Underwater visibility and photography,” in Optical Aspects of Oceanography, N. G. Jerlov, ed. (Academic, London, 1974), pp. 138–149.

Easter, S. S.

Egan, W. G.

Engheta, N.

Enroth-Cugell, C.

R. Shapley, C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” Prog. Retinal Res. 3, 263–346 (1984).

Garlick, G. F. J.

G. F. J. Garlick, C. A. Steigmann, W. E. Lamb, “Differential optical polarisation detectors,” U.S. patent3,992,571 (16November1976).

Ghosh, A.

K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Vector wave imagery with a lens masked by polarizers,” J. Mod. Opt. 40, 379–390 (1993).

Gordon, H. G.

H. G. Gordon, “Modeling and simulating radiative transfer in the ocean,” in Ocean Optics, R. W. Spinrad, K. L. Carder, J. J. Perry, ed. (Oxford U. Press, New York, 1994), pp. 1–46.

Gottschalk, A.

G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London Ser. B 220, 89–113 (1983).

Halaijan, J.

J. Halaijan, H. Hallock, “Principles and techniques of polarimetric mapping,” in Proceedings of 8th Symposium on Remote Sensing and Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1972), Vol. 1, pp. 523–540.

Hallock, H.

J. Halaijan, H. Hallock, “Principles and techniques of polarimetric mapping,” in Proceedings of 8th Symposium on Remote Sensing and Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1972), Vol. 1, pp. 523–540.

Ho, P. P.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast Kerr gate,” Science 253, 769–771 (1991).

Ishimaru, A.

Y. Kuga, A. Ishimaru, “Modulation transfer function of layered inhomogeneous random media using the small-angle approximation,” Appl. Opt. 25, 4382–4385 (1986).

Y. Kuga, A. Ishimaru, “Modulation transfer function and image transmission through randomly distributed spherical particles,” Appl. Opt. 25, 2330–2335 (1985).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), pp. 301–306, 448–454.

Johnson, W. R.

Können, G. P.

G. P. Können, Polarized Light in Nature (Cambridge U. Press, London, 1985), pp. 74–99.

Kuga, Y.

Y. Kuga, A. Ishimaru, “Modulation transfer function of layered inhomogeneous random media using the small-angle approximation,” Appl. Opt. 25, 4382–4385 (1986).

Y. Kuga, A. Ishimaru, “Modulation transfer function and image transmission through randomly distributed spherical particles,” Appl. Opt. 25, 2330–2335 (1985).

Lamb, W. E.

G. F. J. Garlick, C. A. Steigmann, W. E. Lamb, “Differential optical polarisation detectors,” U.S. patent3,992,571 (16November1976).

Liu, C.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast Kerr gate,” Science 253, 769–771 (1991).

Lythgoe, J. N.

J. N. Lythgoe, “The adaptation of visual pigments to the photic environment,” in Handbook of Sensory Physiology, H. J. A. Dartnall, ed. (Springer-Verlag, New York, 1971), Vol. VII/1, pp. 566–603.

Macmillan, N. A.

N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, London, 1991), pp. 7–28.

Papas, C. H.

Using the notation of Stokes parameters, 〈ODLP〉 can be written as S1/S0, where S0 and S1 are the first and the second Stokes parameters. It is inherent in Eqs. (1) and (2) that PSI = S0 and 'I = S1. For discussion of Stokes parameters, see, for example, C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover, New York, 1988), pp. 118–134.

Pugh, E. N.

Romeiser, R.

A. Schmidt, V. Wismann, R. Romeiser, W. Alpers, “Simultaneous measurements of the ocean wave–radar modulation transfer function at L, C, and X bands from the research platform Nordsee,” J. Geophys. Res. C 100, 8815–8827 (1995).

Rowe, M. P.

Schmidt, A.

A. Schmidt, V. Wismann, R. Romeiser, W. Alpers, “Simultaneous measurements of the ocean wave–radar modulation transfer function at L, C, and X bands from the research platform Nordsee,” J. Geophys. Res. C 100, 8815–8827 (1995).

Schmidt, R.

C. Brüning, R. Schmidt, W. Alpers, “Estimation of the ocean wave–radar modulation transfer function from synthetic aperture radar imagery,” J. Geophys. Res. C 99, 9803–9815 (1994).

Sedra, A. S.

A. S. Sedra, K. C. Smith, Microelectronic Circuits (Saunders College, Ft. Worth, Tex., 1991), pp. 48–114.

Shapley, R.

R. Shapley, C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” Prog. Retinal Res. 3, 263–346 (1984).

Smith, K. C.

A. S. Sedra, K. C. Smith, Microelectronic Circuits (Saunders College, Ft. Worth, Tex., 1991), pp. 48–114.

Solomon, J. E.

Steigmann, C. A.

G. F. J. Garlick, C. A. Steigmann, W. E. Lamb, “Differential optical polarisation detectors,” U.S. patent3,992,571 (16November1976).

Tyo, J. S.

M. P. Rowe, E. N. Pugh, J. S. Tyo, N. Engheta, “Polarization-difference imaging: a biologically inspired technique for observation through scattering media,” Opt. Lett. 20, 608–610 (1995).

J. S. Tyo, “Automatic rotational polarizer for the polarization differencing camera,” undergraduate senior design project (Moore School of Electrical Engineering, University of Pennsylvania, Philadelphia, Pa., 1994).

Walraven, R.

R. Walraven, “Polarization imagery,” in Optical Polarimetry: Instrumentation and Applications, R. M. Azzam, D. L. Coffeen, eds., Proc. SPIE 112, 164–167 (1977).

Wang, L.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast Kerr gate,” Science 253, 769–771 (1991).

Waterman, T. H.

T. H. Waterman, “Polarization sensitivity,” in Handbook of Sensory Physiology, H. Autrum, ed. (Springer-Verlag, New York, 1981), Vol. VII/6b, pp. 283–311.

Whitehead, V. S.

Wismann, V.

A. Schmidt, V. Wismann, R. Romeiser, W. Alpers, “Simultaneous measurements of the ocean wave–radar modulation transfer function at L, C, and X bands from the research platform Nordsee,” J. Geophys. Res. C 100, 8815–8827 (1995).

Wolff, L. B.

L. B. Wolff, T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Patt. Anal. Mach. Intell. 13, 635–657 (1991).

Yodh, A.

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).

Zhang, G.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast Kerr gate,” Science 253, 769–771 (1991).

Appl. Opt.

IEEE Trans. Patt. Anal. Mach. Intell.

L. B. Wolff, T. E. Boult, “Constraining object features using a polarization reflectance model,” IEEE Trans. Patt. Anal. Mach. Intell. 13, 635–657 (1991).

J. Geophys. Res. C

C. Brüning, R. Schmidt, W. Alpers, “Estimation of the ocean wave–radar modulation transfer function from synthetic aperture radar imagery,” J. Geophys. Res. C 99, 9803–9815 (1994).

A. Schmidt, V. Wismann, R. Romeiser, W. Alpers, “Simultaneous measurements of the ocean wave–radar modulation transfer function at L, C, and X bands from the research platform Nordsee,” J. Geophys. Res. C 100, 8815–8827 (1995).

J. Mod. Opt.

K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Vector wave imagery with a lens masked by polarizers,” J. Mod. Opt. 40, 379–390 (1993).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nature (London)

D. A. Cameron, E. N. Pugh, “Double cones as a basis for a new type of polarization vision in vertebrates,” Nature (London) 353, 161–164 (1991).

Opt. Lett.

Phys. Today

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).

Proc. R. Soc. London Ser. B

G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London Ser. B 220, 89–113 (1983).

Prog. Retinal Res.

R. Shapley, C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” Prog. Retinal Res. 3, 263–346 (1984).

Science

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast Kerr gate,” Science 253, 769–771 (1991).

Other

S. Q. Duntley, “Underwater visibility and photography,” in Optical Aspects of Oceanography, N. G. Jerlov, ed. (Academic, London, 1974), pp. 138–149.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), pp. 301–306, 448–454.

R. Walraven, “Polarization imagery,” in Optical Polarimetry: Instrumentation and Applications, R. M. Azzam, D. L. Coffeen, eds., Proc. SPIE 112, 164–167 (1977).

G. F. J. Garlick, C. A. Steigmann, W. E. Lamb, “Differential optical polarisation detectors,” U.S. patent3,992,571 (16November1976).

J. Halaijan, H. Hallock, “Principles and techniques of polarimetric mapping,” in Proceedings of 8th Symposium on Remote Sensing and Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1972), Vol. 1, pp. 523–540.

A. S. Sedra, K. C. Smith, Microelectronic Circuits (Saunders College, Ft. Worth, Tex., 1991), pp. 48–114.

Rather than using the term noise, we use the term corrupting variations. This refers to all variations other than the signals produced by the scratched patches. In the PD case this is mostly noise that is due to the system and the medium. In the PS case we are referring to noise as well as the unwanted intensity variations described earlier.

In our study the target is thought of as the scratched target patches, and the background includes the unscratched portions of the disk as well as the area outside the disk.

The ARP was developed as an undergraduate senior design project by J. S. Tyo.8 We plan to test its performance under a variety of conditions, and we hope to present the details of its operation in a subsequent paper.

T. H. Waterman, “Polarization sensitivity,” in Handbook of Sensory Physiology, H. Autrum, ed. (Springer-Verlag, New York, 1981), Vol. VII/6b, pp. 283–311.

N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, London, 1991), pp. 7–28.

In the present arrangement of the PDI system, the TNLC limits the speed with which the system performs. To ensure that the TNLC has had time to relax to its unexcited state after collection of a pair of linearly polarized images, one needs to wait approximately 3 min after turning off the excitation before capturing a subsequent pair of images. Typically, collection of the 30 images took just less than 2 h.

The filter is designed by hand to be used with the Imaging Technologies, Inc., software. It is 7 × 7 pixels, is peaked in the middle, has a summed value of unity, and falls off to a value of (0.125 max) in 3 pixels.

J. S. Tyo, “Automatic rotational polarizer for the polarization differencing camera,” undergraduate senior design project (Moore School of Electrical Engineering, University of Pennsylvania, Philadelphia, Pa., 1994).

J. N. Lythgoe, “The adaptation of visual pigments to the photic environment,” in Handbook of Sensory Physiology, H. J. A. Dartnall, ed. (Springer-Verlag, New York, 1971), Vol. VII/1, pp. 566–603.

We do not explicitly discuss the effects of forward-scattered light and multiple scattering. For simplicity we assume that light that is truly forward scattered acts as image-forming light. Furthermore, light that is scattered out of the imaging path and then back into it acts as veiling light.

H. G. Gordon, “Modeling and simulating radiative transfer in the ocean,” in Ocean Optics, R. W. Spinrad, K. L. Carder, J. J. Perry, ed. (Oxford U. Press, New York, 1994), pp. 1–46.

As a reference, for Atlantic Ocean water in the vicinity of Gibraltar at a depth of 25 m for light of wavelength 465 nm, the attenuation length is 20 m.4 The wavelength of light used in our study is 610 nm. A wavelength of 610 nm was chosen only because the TNLC was designed to operate at 610 nm. There is no relative advantage to using light of wavelength 610 nm, and the results presented here should be generalizable to any wavelength of electromagnetic radiation. We performed studies using white light in the present setup with nominally similar results (data not shown).

When there is no milk in the tank, the water and the particles suspended in the water act as scatterers. This is why the beam-attenuation coefficient is not equal to zero when there is no milk.

Using the notation of Stokes parameters, 〈ODLP〉 can be written as S1/S0, where S0 and S1 are the first and the second Stokes parameters. It is inherent in Eqs. (1) and (2) that PSI = S0 and 'I = S1. For discussion of Stokes parameters, see, for example, C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover, New York, 1988), pp. 118–134.

G. P. Können, Polarized Light in Nature (Cambridge U. Press, London, 1985), pp. 74–99.

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Figures (11)

Fig. 1
Fig. 1

Experimental setup (not drawn to scale): A. Setup used for all backillumination experiments. Light is emitted by two slide projectors shown at the right side of the figure. The light is diffused by a translucent white Plexiglass sheet before entering a glass tank of linear dimension 30 cm × 30 cm × 15 cm (13.5 L in volume). The tank is filled with a milk/water mixture that acts as a scattering medium. Inside the tank is a target (the targets are described in the caption of Fig. 2). The target is suspended from above by a clear Plexiglass sheet. There is a rod fitted to the back face of the target, i.e., the face away from the camera. This rod is then attached to the clear Plexiglass sheet for support. The clear Plexiglass is transparent at optical wavelengths and has a linear extent larger than the area of view of the camera. Since it is oriented perpendicular to the line of sight, it does not introduce a partial polarization and it is completely undetectable in all of the images. The images are captured by a CCD camera. In front of the camera are a twisted-nematic liquid-crystal cell (TNLC), a linear polarization analyzer (A), and a narrow-band filter (F). For a description of the polarizing properties of the optical path, see the description in Rowe et al.6 B. The modified setup used for the side-illumination experiments described in Subsection 6.B. One projector is removed, and the other is moved so as to provide light in a direction perpendicular to the line of sight of the camera. This geometry gives rise to a partial polarization in the vertical direction as seen by the camera and is effectively similar to horizontal viewing underwater at noon when the sun is directly overhead. All other features of the imaging system remain unchanged from Fig. 1A.

Fig. 2
Fig. 2

Targets: A. Aluminum disk with scratched patches. The disk is 3.8 cm in diameter, and the patches are 1 cm × 1 cm. Except for the two patches, the disk face is sandblasted, rendering it nearly Lambertian. The patches are raised a few thousandths of an inch above the face of the disk and are abraded lightly in orthogonal directions with emory paper. The target is shown with the same orientation used in the images presented in Fig. 5; i.e., the left patch is scratched vertically as we look at it, the right patch is scratched horizontally. Light reaches the front of the disk through multiple scattering events. Light from the projectors is scattered by milk particles toward the face of the disk, then is scattered at the face of the disk toward the camera. The scratched patches have facets that act like mirrors at different orientation angles. These facets selectively reflect light incident upon the target from specific directions toward the camera. The polarization is caused at least in part by the initial scattering event involving the milk particle. B. The Aluminum disk without scratched patches. This target was used as the nonsignal (blank) target for the signal-detection-theory experiments described in Section 8. It is identical to the target of Fig. 2A except for the lack of scratched patches. The entire face is sandblasted, so light reflecting from its surface is nearly unpolarized everywhere under the illumination conditions of Fig. 1A.

Fig. 3
Fig. 3

Major paths of light in the scattering medium: (1) Image-forming light is scattered at the target plane and travels directly to the camera head without being scattered off the path. (2) Veiling light is ultimately scattered by the particles in the medium between the target plane and the image plane, then reaches the camera head. (3) Image-forming light lost because of scattering. This light can be scattered back into the line of sight, but when this happens, it becomes veiling light. (4) Image-forming and veiling light can both be partially absorbed throughout the medium. This figure is an adaptation of a figure presented by Lythgoe (Ref. 9, p. 586, Fig. 13).

Fig. 4
Fig. 4

Measurement of approximate values of c and K: A. Schematic of the setup used to measure the beam-attenuation coefficient. A He–Ne laser (632.8 nm) emits a pencil beam, which is attenuated by the scattering medium. The photodiode is used to measure intensity, and Eq. (5) is used to solve for c. Attenuation length is c −1. B. Schematic of setup used for measuring the diffuse-attenuation coefficient in the direction of propagation. The sources are placed on one side of the tank, and the CCD camera is placed on the other side. The CCD camera is calibrated with the photodiode. Intensity measurements are made with various amounts of milk added to the 13.5-L tank full of water, and Eq. (6) is used to estimate K. C. Beam-attenuation coefficient. As the amount of milk added to the tank increases, the reliability of the measurement decreases because we approach the lower limit of the photodiode sensitivity. The points plotted are the values of c calculated from the experimental data; the line is fitted through the points corresponding to milk additions of less than 8 mL. The fitted line has the form c = 3.6 × (milk in milliliters) + 1.8 (m−1). To determine the effective length (in attenuation lengths) of the scattering medium, multiply the beam-attenuation coefficient c by the path length within the medium between the target and the front face of the tank, i.e., 0.075 m (effective length = c × 7.5 × 10−2). In this study, for values of added milk greater than 8 mL, we used the extrapolated values of c along the fitted line to determine the effective length. D. Diffuse-attenuation coefficient. The fitted line has the form K = [3.8 × (milk in milliliters) + 0.6] × 10−3 (m−1). Notice that c is approximately 3 orders of magnitude greater than K. This indicates that a large amount of veiling light is being scattered into the camera, thus degrading the images.

Fig. 5
Fig. 5

PS and PD images after transformation for optimal display [Eqs. (3)] at different effective lengths. The images in the left-hand column are the PS images, the images in the right-hand column are PD images. Panels A and B were obtained at a distance of 0.13 attenuation length (no milk added to the tank). Panels C and D were obtained at 2.8 attenuation lengths (10 mL of milk). Panels E and F were obtained at 4.8 attenuation lengths (17.5 mL of milk). The PD images in the right column were transformed with the maximum and the minimum values on the screen in original PD images, while the PS images were transformed with the maximum and the minimum intensities on the disk face alone. We obtain the untransformed images as follows: the vertically and the horizontally polarized images are obtained by adding 128 consecutive images into the 16-bit accumulator and dividing the resulting sum by 8. This results in a linear amplification factor of 16. This procedure is used because the narrow-band filter eliminates the majority of the light, and since the gain mechanism on the camera is highly nonlinear, we could not compensate for the loss of intensity by increasing the gain. Therefore we set the gain to its minimum setting at which linearity is verified. The linearly polarized images are then filtered with a spatial low-pass filter with an effective linear width of ~5 pixels. This filter is used to eliminate an artifact of the image-processing system. We then obtain PS images by adding the two raw images together and dividing by 2 and obtain PD images by subtracting the horizontally (⊥) polarized image from the vertically (||) polarized image and adding an offset of 128 to the difference. The offset was used to compensate for the negative values introduced by the subtraction operation because such values cannot be displayed on our system. The bands across the centers of the images represent the area within which the intensity plots displayed in Fig. 6 are taken.

Fig. 6
Fig. 6

Intensity plots across the center of the images presented in Fig. 5. We obtained the plots by averaging ten vertically adjacent pixels within the band shown in Fig. 5 for each horizontal position in the display. The plots corresponding to the PS images (A, C, and E) show clearly the intensity gradients that are corrupting the images, i.e., the drop from the background to the disk face and the gradient across the disk. The plots of the PD images show that these variations were removed. The large noiselike variations in the PD line plots are largely due to quantization. Despite this, the areas corresponding to the scratched patches can clearly be made out in the PD intensity plots.

Fig. 7
Fig. 7

Side-illuminated images transformed for optimal display. The target is rotated by 45° about the line of sight so that the signals created by the patches are not subtracted out in the PD images after the analyzer is rotated. A. PS image. Notice that the upper-left patch is visible in this PS image, but the lower-right patch is practically invisible. B. Intensity plots across the bands shown in panel A. There is a pronounced decay of intensity across the screen that masks the presence of the signal caused by the patches. C. PD image created with the analyzer oriented vertically. D. Intensity plots across the bands shown in panel C. Since the light is predominantly vertically polarized, the decaying intensity gradient is not common to both raw images. Therefore it is not subtracted out in the final image. E. PD image created with the analyzer oriented at 45°. F. Intensity plots across the bands shown in panel E. The decaying intensity gradient is suppressed, and both target patches are easily visible.

Fig. 8
Fig. 8

Example of a SDT experiment designed to test our decision process. In such an experiment an observer would be presented with two stimuli in succession and would be asked to determine which was the signal stimulus and which was the nonsignal stimulus. This paradigm is referred to as two-alternative forced choice because the observer must choose one of the two stimuli. Panels A and B are the PS images, and panels C and D are the PD images. These images were created at a distance of 4.8 attenuation lengths. It is clear that panel C is the signal stimulus for the PD images, but it is not at all clear whether panel A or panel B is the stimulus for the PS images. (It is in fact panel A). Even though the quality of the image in panel C does not seem as good as the images in Figs. 5B and 5D, it is still obvious that the target shown in panel C of this figure has scratched patches, whereas the target shown in panel D does not.

Fig. 9
Fig. 9

Determination of d a for one spatial unit of an image. The average intensity within the 5 × 5 pixel unit on each of the 30 PS and PD images is calculated for both the signal and the nonsignal cases. These data are collected and plotted as a histogram that is normalized to yield an integrated value of unity. The mean and the standard deviation are calculated for each of the histograms, and, from these values, d a is determined for the PS and PD images. The PS images have d a , and the PD images have d a . The minus sign in the value of d a for the PD case is there because the right patch is darker (more negative) in the signal trials than in the blank trials. The curves plotted through the histograms are normal distributions with the appropriate means and standard deviations. These data were obtained from the 5 × 5 pixel region surrounding the point (314, 243) [the image is 512 × 480 pixels, and the point (1, 1) is in the upper-left corner of the image] in the PS and PD images obtained at 2.8 attenuation lengths, which are shown in panels C and D of Fig. 5. The position pointed out at the top of this figure is the approximate location of the spatial unit considered.

Fig. 10
Fig. 10

Maps of d a in the shaded region shown at the top of the figure. The rectangular region shown shaded at the top of the figure is 245 × 135 pixels. It is completely on the face of the disk and includes the center of the disk, both scratched patches, and a significant area of the disk face outside the scratched patches. It is subdivided into 5 × 5 pixel spatial units; the process depicted in Fig. 9 is carried out for each spatial unit, and the resulting values of d a are plotted as a function of position. The maps correspond to the images in Fig. 5. Panels A and B are the sensitivity-index maps of the PS and PD images obtained at 0.13 attenuation length. Panels C and D show the maps of d a for the PS and PD images obtained at 2.8 attenuation lengths. Panels E and F are the maps of the PS and PD images obtained at 4.8 attenuation lengths. Maps were formulated with Matlab (see text). Panels A and B are presented with the same d a scale, as are panels C and D. Panels E and F are presented on different scales, but note that the range of the sensitivity index presented in each of these panels has the same magnitude (3.5). We are currently unable to explain the slope in panel E, and we believe that it may be an artifact. However, it is interesting to note that the map in panel F, obtained from the same data as the map in panel E, shows no sign of any artifact.

Fig. 11
Fig. 11

Spatial sensitivity index of the variable d a , D ( d a ) , computed at each effective distance for both types of images. Panel A presents the data from the left target patch; panel B presents the data from the right target patch. At all times, PDI performs as well or better than the conventional (PS) system. In addition, the PS images degrade faster as a function of scatterer concentration. The exponential curves fitted to the data indicate that if any particular value of D ( d a ) is chosen as the threshold of detectability, then the PD system will reach this level at distances at least double that of conventional (PS) systems. The exponentials have the form D ( d a ) = A exp ( - x / χ ) , where x is the effective length of the scattering medium and χ is the decay constant. For the left target patch, A PDA PS = 5.5, and χPD = 6.3 while χPS = 3.2. For the right target patch, A PDA PS = 5.1, and χPD = 7.1 while χPS = 2.3. The points shown as diamonds correspond to measurements at 1.40 attenuation lengths. Examination of the PS sensitivity-index map for this single effective distance indicates that errors may have occurred during the collection of images. Furthermore, these points lie well below the curve fitted to the data (excluding the points corresponding to 1.40 attenuation lengths) in the PS case, especially for the right patch. For this reason, the points shown as diamonds corresponding to the single case of 1.40 attenuation lengths were left out in the exponential fitting; however, they are presented here for completeness. Note that the points from the PD images obtained at 1.40 attenuation lengths (open diamonds) lie much closer to the fitted curve.

Tables (1)

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Table 1 Summary of the Numerical Results for the Backillumination Condition Organized by Attenuation Lengtha

Equations (10)

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I ps ( x , y ) = I ( x , y ) + I ( x , y ) ,
I pd ( x , y ) = I ( x , y ) + I ( x , y ) .
I ps ( x , y ) trans = γ ps [ ps I ( x , y ) - ps I ( x , y ) min ] , I pd ( x , y ) trans = γ pd [ pd I ( x , y ) - pd I ( x , y ) min ] .
γ ps = C / [ ps I ( x , y ) max - ps I ( x , y ) min ] , γ pd = C / [ pd I ( x , y ) max - pd I ( x , y ) min ] ,
c = - 1 I d I d z ,
K ( r ) = - 1 E ( r ) d E ( r ) d z ,
ODLP region = PD I ( x , y ) region PS I ( x , y ) region ,
C l ( x , y ) = 2 PS I ( x , y ) target - PS I ( x , y ) blank PS I ( x , y ) target + PS I ( x , y ) blank ,
d a = 2 μ s - μ n σ s 2 + σ n 2 ,
D ( d a ) = 2 | d a p - d a f σ p 2 + σ f 2 | ,

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