Abstract

Image transmission through a random medium is important in many areas. Transmitted images are often affected by the presence of particulate matter and turbulence between the object and the detector. This paper presents the results for controlled experiments for the modulation transfer function (MTF) through a random distribution of polystyrene microspheres suspended in water. Experimental results show that the MTF has two distinct regions separated by a cutoff frequency. When the spatial frequency is higher than the cutoff frequency, the MTF becomes almost constant. On the other hand, when the spatial frequency is less than the cutoff frequency, the MTF increases exponentially with decreasing spatial frequency, and the slope depends on the optical distance of the medium. The cutoff frequency increases as the particle size increases. The results are obtained for particle sizes of 0.109, 0.46, 1.101, 2.02, 5.7, and 11.9 μm, densities much less than 1%, and optical distances between 0 and 15. The experimental results are compared with the results of the small-angle approximation for the equation of transfer.

© 1985 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. H. W. Chang, A. Ishimaru, “Optical beam propagation in random media based on radiative transfer theory,” presented at the meeting of the International Union of Radio Science and the Institute of Electrical and Electronics Engineers Antennas and Propagation Society, Vancouver, Canada, June 17–21, 1985.

1984 (1)

1982 (2)

1981 (1)

1978 (2)

1968 (1)

M. V. Kabanov, “The optical transfer function for scattering media,” Izv. Atmos. Ocean. Phys. 4, 835–843 (1968).

1964 (1)

Chang, H. W.

H. W. Chang, A. Ishimaru, “Optical beam propagation in random media based on radiative transfer theory,” presented at the meeting of the International Union of Radio Science and the Institute of Electrical and Electronics Engineers Antennas and Propagation Society, Vancouver, Canada, June 17–21, 1985.

Embury, J. F.

Gencay, Y.

Gerstl, S. A. W.

Hufnagel, R. E.

Ishimaru, A.

A. Ishimaru, Y. Kuga, “Attenuation constant of a coherent field in a dense distribution of particles,” J. Opt. Soc. Am. 72, 1317–1320 (1982).
[CrossRef]

H. W. Chang, A. Ishimaru, “Optical beam propagation in random media based on radiative transfer theory,” presented at the meeting of the International Union of Radio Science and the Institute of Electrical and Electronics Engineers Antennas and Propagation Society, Vancouver, Canada, June 17–21, 1985.

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

Isimaru, A.

Kabanov, M. V.

M. V. Kabanov, “The optical transfer function for scattering media,” Izv. Atmos. Ocean. Phys. 4, 835–843 (1968).

Kopeika, N. S.

Kuga, Y.

Lutomirski, R. L.

Mertens, L. E.

L. E. Mertens, In-Water Photography (Wiley-Interscience, New York, 1970).

Solomon, S.

Stanley, N. R.

Zardecki, A.

Appl. Opt. (3)

Izv. Atmos. Ocean. Phys. (1)

M. V. Kabanov, “The optical transfer function for scattering media,” Izv. Atmos. Ocean. Phys. 4, 835–843 (1968).

J. Opt. Soc. Am. (4)

Other (3)

L. E. Mertens, In-Water Photography (Wiley-Interscience, New York, 1970).

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

H. W. Chang, A. Ishimaru, “Optical beam propagation in random media based on radiative transfer theory,” presented at the meeting of the International Union of Radio Science and the Institute of Electrical and Electronics Engineers Antennas and Propagation Society, Vancouver, Canada, June 17–21, 1985.

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup. SC is the spectrophotometer cell, and the path length is 20 mm. ID is the iris diaphragm (aperture diameter, 5 mm). The equivalent air length L = 185, and d = 70 mm. The focal length of the lens is 50 mm.

Fig. 2
Fig. 2

Output signal from the Reticon detector and the magnitude of the Fourier-transformed signal. In a, the solid line is the signal with particles, and the dotted line is without particles. The particle size is 2.02 μm, the density is 0.00316%, and the object-spatial wavelength is 5 mm.

Fig. 3
Fig. 3

MTF for 0.109-μm particles. μ ¯ is 0.0895, and σt is 7.72E-5 μm2. A is the experimental data for the volume density 0.0372% (τ = 0.853), B = 0.0745% (τ = 1.71), C = 0.149% (τ = 3.41), D = 0.198% (τ = 4.55), and E = 0.298% (τ = 6.82).

Fig. 4
Fig. 4

MTF for 0.46-μm particles. μ ¯ is 0.792, and σt is 0.103 μm2. A is the experimental data for the volume density 0.00465% (τ = 1.88), B = 0.0093% (τ = 3.76), and C = 0.0124% (τ = 5.01).

Fig. 5
Fig. 5

MTF for 1.101-μm particles. μ ¯ is 0.9246, and σt is 2.732 σm2. A is the experimental data for the volume density 0.00232% (τ = 1.81), B = 0.0031% (τ = 2.42); C = 0.00464% (τ = 3.63), D = 0.00619% (τ = 4.84), E = 0.929% (τ = 7.26), and F = 0.0124% (τ = 9.68).

Fig. 6
Fig. 6

MTF for 2.02-μm particles. μ ¯ is 0.924, and σt is 10.32 μm2. A is the experimental data for the volume density 0.00316% (τ = 1.512), B = 0.00475% (τ = 2.27), C = 0.00633% (τ = 3.03), D = 0.00949% (τ = 4.54), E = 0.0127% (τ = 6.05), and F = 0.019% (τ = 9.07).

Fig. 7
Fig. 7

MTF for 5.7-μm particles. μ ¯ is 0.8871, and σt is 62.8 μm2. A is the experimental data for the volume density 0.00928% (τ = 0.99), B = 0.0186% (τ = 1.97), C = 0.0371% (τ = 3.95), D = 0.0494% (τ = 5.26), E = 0.0743% (τ = 7.89), and F = 0.099% (τ = 10.53).

Fig. 8
Fig. 8

MTF for 11.9-μm particles. μ ¯ is 0.911, and σt is 250.5 μm2. A is the experimental data for the volume density 0.371% (τ = 1.97), B = 0.0743% (τ = 3.94), C = 0.099% (τ = 5.26), D = 0.149% (τ = 7.89), E = 0.198% (τ = 10.52), and F = 0.297% (τ = 15.78).

Fig. 9
Fig. 9

Simplified model of MTF. f1 is the 0-dB spatial frequency. f2 is the cutoff spatial frequency. Z is the value of the flat part in decibels.

Fig. 10
Fig. 10

Z as the function of optical distance (τ). □, 0.109 μm; ○, 0.46 μm; △, 1.101 μm; +, 2.02 μm.

Fig. 11
Fig. 11

MTF at two spatial frequencies. Solid and dashed lines are for 0.4 and 1.05 cycles/mm, respectively.

Fig. 12
Fig. 12

f1 nd f2 s the function of the normalized size (D/λ). D is the particulate diameter and λ is the wavelength (0.475 μm in water). Δ, f1; +, f2.

Fig. 13
Fig. 13

Small-angle approximation MTF. Solid lines are for α = 4.7 corresponding to μ ¯ = 0.8, and dashed lines are for α = 7.6 corresponding to μ ¯ = 0.9. A, B, and C are for τ = 1, 3, and 5, respectively.

Equations (6)

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1 / L + 1 / d = 1 / f 0 ,
M S ( f ) = M T ( f ) / M I ( f ) ,
f 2 = C 1 ( D / λ ) C 2 ,
M S A ( f ) = exp [ τ + α τ s 2 π f d erf ( π f d α ) ] ,
M S A ( f ) = exp ( τ ) if f > f C ,
f C = const . ( 1 / d ) ( D / λ ) .

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