Abstract

The imaging quality of optical systems in a turbid environment is influenced not only by the content of the turbid layer between the object and the optical receiver but also by the inhomogeneity of that medium. This is important, particularly when imaging is performed through clouds, nonhomogeneous layers of dust, or over vertical or slant paths through the atmosphere. Forward small-angle scattering influences image quality and blur more severely when the scattering layer is closer to the receiver. In this study it is the influence of the relative position of the scattering layer on the image quality and modulation transfer function (MTF) that is investigated. The scattering layer in controlled laboratory experiments consists of calibrated polystyrene particles of known size and quantity in a small cuvette. A point source was imaged by a computerized imaging system through a layer containing polystyrene particles, and the point-spread function (PSF) was recorded. The aerosol MTF was calculated using the measured PSF. The MTF was measured as a function of changing relative distance of the scattering layer from the receiver, whereas the object-plane-to-receiver distance was constant. The experimental results were compared to theoretical shower curtain effect models based on the solution from radiative transfer theory under the small-angle approximation. Although the general trend of the experimental results certainly agrees with the theoretical models, it could be that the small-angle approximation method might be of limited validity at such low spatial frequencies. Aggregation also causes some disagreement with predictions from theory.

© 1998 Optical Society of America

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References

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    [CrossRef]
  4. D. Sadot, N. S. Kopeika, “Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol MTF,” J. Opt. Soc. Am. A 10, 177–179 (1993); reply to comment, J. Opt. Soc. Am. A 12(5), 1017–1023 (1995).
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    [CrossRef]
  11. Y. Kuga, A. Ishimaru, “Modulation transfer function and image transmission through randomly distributed spherical particles,” J. Opt. Soc. Am. A 2, 2230–2236 (1985).
    [CrossRef]
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    [CrossRef] [PubMed]
  13. 1996 Product Catalog (Sigma Chemical Company, P.O. Box. 14508, St. Louis, Missouri 63178).
  14. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4.
  15. A. C. Dogariu, G. D. Boreman, “Transfer functions of weakly scattering fractal layers,” in Image Propagation through the Atmosphere, J. C. Dainty, L. R. Bissonnette, eds., Proc. SPIE2828, 353–361 (1996).
    [CrossRef]

1995 (1)

1993 (1)

D. Sadot, N. S. Kopeika, “Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol MTF,” J. Opt. Soc. Am. A 10, 177–179 (1993); reply to comment, J. Opt. Soc. Am. A 12(5), 1017–1023 (1995).

1989 (1)

V. V. Belov, “The theory of linear vision systems; modeling the linear-system characteristics,” Atmos. Opt. 2(8), 787–799 (1989).

1988 (1)

V. V. Belov, “Spatial image resolution imposed by a scattering medium,” Atmos. Opt. 1(9), 17–24 (1988).

1986 (1)

1985 (1)

Y. Kuga, A. Ishimaru, “Modulation transfer function and image transmission through randomly distributed spherical particles,” J. Opt. Soc. Am. A 2, 2230–2236 (1985).
[CrossRef]

1984 (1)

A. S. Drofa, “Visibility of small-dimensional objects in a turbid atmosphere,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 20(10), 939–946 (1984).

1983 (1)

V. E. Zuev, V. V. Belov, B. D. Borisov, V. N. Genin, M. V. Kabanov, G. M. Krekov, Dokl. Akad. Nauk SSSR 268, 321–324 (1983).

1978 (1)

1969 (1)

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin, V. A. Saveliev, “Structure of a narrow light beam in sea water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 5, 672–684 (1969).

Belov, V. V.

V. V. Belov, “The theory of linear vision systems; modeling the linear-system characteristics,” Atmos. Opt. 2(8), 787–799 (1989).

V. V. Belov, “Spatial image resolution imposed by a scattering medium,” Atmos. Opt. 1(9), 17–24 (1988).

V. E. Zuev, V. V. Belov, B. D. Borisov, V. N. Genin, M. V. Kabanov, G. M. Krekov, Dokl. Akad. Nauk SSSR 268, 321–324 (1983).

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4.

Boreman, G. D.

A. C. Dogariu, G. D. Boreman, “Transfer functions of weakly scattering fractal layers,” in Image Propagation through the Atmosphere, J. C. Dainty, L. R. Bissonnette, eds., Proc. SPIE2828, 353–361 (1996).
[CrossRef]

Borisov, B. D.

V. E. Zuev, V. V. Belov, B. D. Borisov, V. N. Genin, M. V. Kabanov, G. M. Krekov, Dokl. Akad. Nauk SSSR 268, 321–324 (1983).

Bravo-Zhivotovsky, D. M.

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin, V. A. Saveliev, “Structure of a narrow light beam in sea water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 5, 672–684 (1969).

Dogariu, A. C.

A. C. Dogariu, G. D. Boreman, “Transfer functions of weakly scattering fractal layers,” in Image Propagation through the Atmosphere, J. C. Dainty, L. R. Bissonnette, eds., Proc. SPIE2828, 353–361 (1996).
[CrossRef]

Dolin, L. S.

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin, V. A. Saveliev, “Structure of a narrow light beam in sea water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 5, 672–684 (1969).

Drofa, A. S.

A. S. Drofa, “Visibility of small-dimensional objects in a turbid atmosphere,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 20(10), 939–946 (1984).

Dror, I.

Genin, V. N.

V. E. Zuev, V. V. Belov, B. D. Borisov, V. N. Genin, M. V. Kabanov, G. M. Krekov, Dokl. Akad. Nauk SSSR 268, 321–324 (1983).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4.

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).
[CrossRef] [PubMed]

Y. Kuga, A. Ishimaru, “Modulation transfer function and image transmission through randomly distributed spherical particles,” J. Opt. Soc. Am. A 2, 2230–2236 (1985).
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

Ivanov, A. P.

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991), Chap. 6.
[CrossRef]

Kabanov, M. V.

V. E. Zuev, V. V. Belov, B. D. Borisov, V. N. Genin, M. V. Kabanov, G. M. Krekov, Dokl. Akad. Nauk SSSR 268, 321–324 (1983).

Katsev, I. L.

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991), Chap. 6.
[CrossRef]

Kopeika, N. S.

I. Dror, N. S. Kopeika, “Experimental comparison of turbulence modulation transfer function and aerosol modulation transfer function through the open atmosphere,” J. Opt. Soc. Am. A 12, 970–980 (1995).
[CrossRef]

D. Sadot, N. S. Kopeika, “Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol MTF,” J. Opt. Soc. Am. A 10, 177–179 (1993); reply to comment, J. Opt. Soc. Am. A 12(5), 1017–1023 (1995).

Krekov, G. M.

V. E. Zuev, V. V. Belov, B. D. Borisov, V. N. Genin, M. V. Kabanov, G. M. Krekov, Dokl. Akad. Nauk SSSR 268, 321–324 (1983).

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).
[CrossRef] [PubMed]

Y. Kuga, A. Ishimaru, “Modulation transfer function and image transmission through randomly distributed spherical particles,” J. Opt. Soc. Am. A 2, 2230–2236 (1985).
[CrossRef]

Luchinin, A. G.

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin, V. A. Saveliev, “Structure of a narrow light beam in sea water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 5, 672–684 (1969).

Lutomirsky, R. F.

Sadot, D.

D. Sadot, N. S. Kopeika, “Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol MTF,” J. Opt. Soc. Am. A 10, 177–179 (1993); reply to comment, J. Opt. Soc. Am. A 12(5), 1017–1023 (1995).

Saveliev, V. A.

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin, V. A. Saveliev, “Structure of a narrow light beam in sea water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 5, 672–684 (1969).

Zege, E. P.

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991), Chap. 6.
[CrossRef]

Zuev, V. E.

V. E. Zuev, V. V. Belov, B. D. Borisov, V. N. Genin, M. V. Kabanov, G. M. Krekov, Dokl. Akad. Nauk SSSR 268, 321–324 (1983).

Appl. Opt. (2)

Atmos. Opt. (2)

V. V. Belov, “Spatial image resolution imposed by a scattering medium,” Atmos. Opt. 1(9), 17–24 (1988).

V. V. Belov, “The theory of linear vision systems; modeling the linear-system characteristics,” Atmos. Opt. 2(8), 787–799 (1989).

Dokl. Akad. Nauk SSSR (1)

V. E. Zuev, V. V. Belov, B. D. Borisov, V. N. Genin, M. V. Kabanov, G. M. Krekov, Dokl. Akad. Nauk SSSR 268, 321–324 (1983).

Izv. Acad. Sci. USSR Atmos. Oceanic Phys. (1)

D. M. Bravo-Zhivotovsky, L. S. Dolin, A. G. Luchinin, V. A. Saveliev, “Structure of a narrow light beam in sea water,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 5, 672–684 (1969).

Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana (1)

A. S. Drofa, “Visibility of small-dimensional objects in a turbid atmosphere,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 20(10), 939–946 (1984).

J. Opt. Soc. Am. A (3)

Y. Kuga, A. Ishimaru, “Modulation transfer function and image transmission through randomly distributed spherical particles,” J. Opt. Soc. Am. A 2, 2230–2236 (1985).
[CrossRef]

I. Dror, N. S. Kopeika, “Experimental comparison of turbulence modulation transfer function and aerosol modulation transfer function through the open atmosphere,” J. Opt. Soc. Am. A 12, 970–980 (1995).
[CrossRef]

D. Sadot, N. S. Kopeika, “Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol MTF,” J. Opt. Soc. Am. A 10, 177–179 (1993); reply to comment, J. Opt. Soc. Am. A 12(5), 1017–1023 (1995).

Other (5)

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

1996 Product Catalog (Sigma Chemical Company, P.O. Box. 14508, St. Louis, Missouri 63178).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 4.

A. C. Dogariu, G. D. Boreman, “Transfer functions of weakly scattering fractal layers,” in Image Propagation through the Atmosphere, J. C. Dainty, L. R. Bissonnette, eds., Proc. SPIE2828, 353–361 (1996).
[CrossRef]

E. P. Zege, A. P. Ivanov, I. L. Katsev, Image Transfer through a Scattering Medium (Springer-Verlag, Berlin, 1991), Chap. 6.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Shower curtain effect geometry: z 0 is the point object distance from the camera, z is the distance of the cuvette from camera, and H is the distance of the cuvette from the point object.

Fig. 2
Fig. 2

Image degradation as a function of the position of the scattering layer.

Fig. 3
Fig. 3

Experimental setup of the shower curtain effect.

Fig. 4
Fig. 4

Measured PSF’s for various distances of the cuvette scattering layer from the receiver. Particles in the cuvette have 11.9-μm radius and 0.1 transmittance at 550-nm wavelength.

Fig. 5
Fig. 5

(a) Experimental MTF with scattering layer distance from the object plane as a parameter. (b) Theoretical MTF based on the small-angle approximation.

Fig. 6
Fig. 6

Scattering diagram of polystyrene particles suspended in water: refractive index is n, wavelength is λ, and particle radius is r.

Fig. 7
Fig. 7

Fourier transform of the scattering diagram.

Equations (2)

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MTF Ω = exp - 0 z 0   σ z 1 - x Ω   z 0 - z z 0 ,   z d z ,
MTF Ω = exp - τ 1 - x Ω   H z 0 ,

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