Abstract

The response of a simulated single-ended transmissometer, based on the Mie theory of the scattering of light, has been computed for monochromatic light similar to that of a ruby laser (λ = 0.7 μ) and for white light (0.4 μ ≤ λ ≤ 0.7 μ) for many fog and haze models. The results for white light are compared with data obtained from actual field measurements. The strong dependence of backscatter on the size distribution of the scatterers and on the spectral energy distribution of the source is illustrated, and the limitations of the single-ended transmissometer as a device for determining the visibility in haze and fog are discussed. A table of Mie extinction efficiency (or scattering coefficient) and intensity function (for the backscatter direction) is presented for integral values of size parameter up to 100.

© 1965 Optical Society of America

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References

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  1. C. A. Douglas, U. S. National Bureau of Standards, Washington, D. C., private communication.
  2. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 129.
  3. S. Q. Duntley, J. Opt. Soc. Am. 38, 237 (1948).
    [CrossRef] [PubMed]
  4. V. Hagemann, Beitr. Geophysik. 46, 261 (1936).
  5. H. G. Houghton, W. H. Radford, Papers Phys. Ocean. Meteorol. Mass. Inst. Technol. Woods Hole Ocean. Inst. 6, No. 4 (1938).
  6. S. Kinoshita, J. Meterol. Res. (Tokyo) 4, 235 (March1952).
  7. K. Kamiyama, M. Moriguchi, J. Meterol. Res.(Tokyo) 4, 43 (March1952).
  8. R. C. Srivastava, R. K. Kapoor, Indian J. Met. Geophys. (Quarterly) 11, 157 (1960).
  9. L. W. Pollak, A. L. Metnieks, Geofis. Pura Appl. 42, 89 (1959).
    [CrossRef]
  10. P. Squires, S. Twomey (to be published).
  11. J. A. Curcio, G. L. Knestrick, T. H. Cosden, Naval Res. Lab. Rept. 5143 (June1958).
  12. D. E. Spencer, J. Opt. Soc. Am. 50, 584 (1960).
    [CrossRef]

1960 (2)

R. C. Srivastava, R. K. Kapoor, Indian J. Met. Geophys. (Quarterly) 11, 157 (1960).

D. E. Spencer, J. Opt. Soc. Am. 50, 584 (1960).
[CrossRef]

1959 (1)

L. W. Pollak, A. L. Metnieks, Geofis. Pura Appl. 42, 89 (1959).
[CrossRef]

1952 (2)

S. Kinoshita, J. Meterol. Res. (Tokyo) 4, 235 (March1952).

K. Kamiyama, M. Moriguchi, J. Meterol. Res.(Tokyo) 4, 43 (March1952).

1948 (1)

1938 (1)

H. G. Houghton, W. H. Radford, Papers Phys. Ocean. Meteorol. Mass. Inst. Technol. Woods Hole Ocean. Inst. 6, No. 4 (1938).

1936 (1)

V. Hagemann, Beitr. Geophysik. 46, 261 (1936).

Cosden, T. H.

J. A. Curcio, G. L. Knestrick, T. H. Cosden, Naval Res. Lab. Rept. 5143 (June1958).

Curcio, J. A.

J. A. Curcio, G. L. Knestrick, T. H. Cosden, Naval Res. Lab. Rept. 5143 (June1958).

Douglas, C. A.

C. A. Douglas, U. S. National Bureau of Standards, Washington, D. C., private communication.

Duntley, S. Q.

Hagemann, V.

V. Hagemann, Beitr. Geophysik. 46, 261 (1936).

Houghton, H. G.

H. G. Houghton, W. H. Radford, Papers Phys. Ocean. Meteorol. Mass. Inst. Technol. Woods Hole Ocean. Inst. 6, No. 4 (1938).

Kamiyama, K.

K. Kamiyama, M. Moriguchi, J. Meterol. Res.(Tokyo) 4, 43 (March1952).

Kapoor, R. K.

R. C. Srivastava, R. K. Kapoor, Indian J. Met. Geophys. (Quarterly) 11, 157 (1960).

Kinoshita, S.

S. Kinoshita, J. Meterol. Res. (Tokyo) 4, 235 (March1952).

Knestrick, G. L.

J. A. Curcio, G. L. Knestrick, T. H. Cosden, Naval Res. Lab. Rept. 5143 (June1958).

Metnieks, A. L.

L. W. Pollak, A. L. Metnieks, Geofis. Pura Appl. 42, 89 (1959).
[CrossRef]

Moriguchi, M.

K. Kamiyama, M. Moriguchi, J. Meterol. Res.(Tokyo) 4, 43 (March1952).

Pollak, L. W.

L. W. Pollak, A. L. Metnieks, Geofis. Pura Appl. 42, 89 (1959).
[CrossRef]

Radford, W. H.

H. G. Houghton, W. H. Radford, Papers Phys. Ocean. Meteorol. Mass. Inst. Technol. Woods Hole Ocean. Inst. 6, No. 4 (1938).

Spencer, D. E.

Squires, P.

P. Squires, S. Twomey (to be published).

Srivastava, R. C.

R. C. Srivastava, R. K. Kapoor, Indian J. Met. Geophys. (Quarterly) 11, 157 (1960).

Twomey, S.

P. Squires, S. Twomey (to be published).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 129.

Beitr. Geophysik (1)

V. Hagemann, Beitr. Geophysik. 46, 261 (1936).

Geofis. Pura Appl. (1)

L. W. Pollak, A. L. Metnieks, Geofis. Pura Appl. 42, 89 (1959).
[CrossRef]

Indian J. Met. Geophys. (Quarterly) (1)

R. C. Srivastava, R. K. Kapoor, Indian J. Met. Geophys. (Quarterly) 11, 157 (1960).

J. Meterol. Res. (Tokyo) (1)

S. Kinoshita, J. Meterol. Res. (Tokyo) 4, 235 (March1952).

J. Meterol. Res.(Tokyo) (1)

K. Kamiyama, M. Moriguchi, J. Meterol. Res.(Tokyo) 4, 43 (March1952).

J. Opt. Soc. Am. (2)

Papers Phys. Ocean. Meteorol. Mass. Inst. Technol. Woods Hole Ocean. Inst. (1)

H. G. Houghton, W. H. Radford, Papers Phys. Ocean. Meteorol. Mass. Inst. Technol. Woods Hole Ocean. Inst. 6, No. 4 (1938).

Other (4)

C. A. Douglas, U. S. National Bureau of Standards, Washington, D. C., private communication.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), p. 129.

P. Squires, S. Twomey (to be published).

J. A. Curcio, G. L. Knestrick, T. H. Cosden, Naval Res. Lab. Rept. 5143 (June1958).

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of the coaxial single-ended transmissometer.

Fig. 2
Fig. 2

Size distributions for fog models.

Fig. 3
Fig. 3

The white source used in computations.

Fig. 4
Fig. 4

The ratio ζ vs radius (r) for monochromatic light (λ = 0.7 μ). Key: ⊙, monochromatic light (λ = 0.7 μ); ▲ white light (λ = 0.4 μ to 0.7 μ).

Fig. 5
Fig. 5

The ratio ζ vs extinction coefficient (γ) for monochromatic light (λ = 0.7 μ).

Fig. 6
Fig. 6

The ratio ζ vs extinction coefficient (γ) for white light (0.4 μ ≤ λ ≤ 0.7 μ).

Fig. 7
Fig. 7

The ratio ζ vs the shape factor σr/ r ¯ for monochromatic light (λ = 0.7 μ).

Fig. 8
Fig. 8

The ratio ζ vs the shape factor, σr/ r ¯ for “white” light (0.4 μ ≤ λ ≤ 0.7 μ).

Fig. 9
Fig. 9

Backscattered intensity vs extinction coefficient for monochromatic light (λ = 0.7 μ).

Fig. 10
Fig. 10

Backscattered intensity vs extinction coefficient for white light (0.4 μ ≤ λ ≤ 0.7 μ).

Fig. 11
Fig. 11

Backscattered intensity vs meteorological range for white light (0.4 μ ≤ λ ≤ 0.7 μ). Key: ○, result of simulation study; △, data from Curcio, Krestrick, and Cosden.

Fig. 12
Fig. 12

Backscattered intensity vs meteorological range for monochromatic light (λ = 0.7 μ).

Tables (1)

Tables Icon

Table I Mie Scattering Coefficients and Backscatter-Intensity Function (for Index of Refraction = 1.33)

Equations (4)

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Δ I = I · Δ l d Ω S ( θ , α ) N ( α ) d α ,
d I d x = - γ I ,
I 0 c 2 t 0 exp ( - 2 β ) ρ t - 2 d t ,
R = x 0 ζ γ exp ( - 2 γ d x ) x - 2 d x .

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