Abstract

The transfer of diffuse city light from a localized source through a dust-laden atmosphere with optical depth <0.5 has been analyzed in the source–observer plane on the basis of an approximate treatment. The effect on several types of astronomical observation at night has been studied, considering different size distributions and amounts as well as particle shapes of the aerosols. The analysis is made not as a function of the absolute aerosol amount but in terms of the signal-to-noise ratios for a given amount of aerosol. The model is applied to conditions at the Wise Astronomical Observatory in the Negev desert and limiting backgrounds for spectroscopy, photometry, and photography of stars and extended objects have been calculated for a variety of signal-to-noise ratios. Applications to observations with different equipment at various distances from an urban area of any size are possible. Due to the use of signal-to-noise ratios, the conclusions are different for the different experimental techniques used in astronomy.

© 1991 Optical Society of America

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References

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  1. S. M. Faber, “Sky-Glow at Lick Observatory,” Light. Des. Appl.18–22 (1980).
  2. D. M. Finch, “Atmospheric Light Pollution,” J. Illum. Eng. Soc. 7, 105–117 (1978).
  3. M. F. Walker, “Light Pollution in California and Arizona,” Publ. Astron. Soc. Pac. 85, 508–519 (1973).
    [CrossRef]
  4. M. F. Walker, “The Effect of Urban Lighting on the Brightness of the Night Sky,” Publ. Astron. Soc. Pac. 89, 405–409 (1977).
    [CrossRef]
  5. P. J. Treanor, “A Simple Propagation Law for Artificial Night-Sky Illumination,” Observatory 93, 117 (1973).
  6. Z. Levin, J. Lindberg, “Size Distributions, Chemical Composition and Optical Properties of Urban and Desert Aerosols in Israel,” J. Geophys. Res. 20, 6941 (1979).
    [CrossRef]
  7. A. C. Holland, G. Gagne, “The Scattering of Polarized Light by Polydisperse Systems of Irregular Particles,” Appl. Opt. 9, 1113–1121 (1970).
    [CrossRef] [PubMed]
  8. Y. Mekler, A. Eviatar, “on the Detectability of Forbidden Lines,” J. Quant. Spectrosc. Radiat. Transfer 18, 531–533 (1977).
    [CrossRef]
  9. Y. Mekler, D. Goorvitch, “Detectability Criteria of Forbidden Lines of NII and OIII,” J. Quant. Spectrosc. Radiat. Transfer 40, 85–91 (1988).
    [CrossRef]
  10. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960), p. 393.
  11. Y. J. Kaufman, “Effect of Earth’s Atmosphere on Contrast for Zenith Observations,” J. Geophys. Res. 84, 3165 (1979).
    [CrossRef]

1988

Y. Mekler, D. Goorvitch, “Detectability Criteria of Forbidden Lines of NII and OIII,” J. Quant. Spectrosc. Radiat. Transfer 40, 85–91 (1988).
[CrossRef]

1980

S. M. Faber, “Sky-Glow at Lick Observatory,” Light. Des. Appl.18–22 (1980).

1979

Y. J. Kaufman, “Effect of Earth’s Atmosphere on Contrast for Zenith Observations,” J. Geophys. Res. 84, 3165 (1979).
[CrossRef]

Z. Levin, J. Lindberg, “Size Distributions, Chemical Composition and Optical Properties of Urban and Desert Aerosols in Israel,” J. Geophys. Res. 20, 6941 (1979).
[CrossRef]

1978

D. M. Finch, “Atmospheric Light Pollution,” J. Illum. Eng. Soc. 7, 105–117 (1978).

1977

M. F. Walker, “The Effect of Urban Lighting on the Brightness of the Night Sky,” Publ. Astron. Soc. Pac. 89, 405–409 (1977).
[CrossRef]

Y. Mekler, A. Eviatar, “on the Detectability of Forbidden Lines,” J. Quant. Spectrosc. Radiat. Transfer 18, 531–533 (1977).
[CrossRef]

1973

P. J. Treanor, “A Simple Propagation Law for Artificial Night-Sky Illumination,” Observatory 93, 117 (1973).

M. F. Walker, “Light Pollution in California and Arizona,” Publ. Astron. Soc. Pac. 85, 508–519 (1973).
[CrossRef]

1970

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960), p. 393.

Eviatar, A.

Y. Mekler, A. Eviatar, “on the Detectability of Forbidden Lines,” J. Quant. Spectrosc. Radiat. Transfer 18, 531–533 (1977).
[CrossRef]

Faber, S. M.

S. M. Faber, “Sky-Glow at Lick Observatory,” Light. Des. Appl.18–22 (1980).

Finch, D. M.

D. M. Finch, “Atmospheric Light Pollution,” J. Illum. Eng. Soc. 7, 105–117 (1978).

Gagne, G.

Goorvitch, D.

Y. Mekler, D. Goorvitch, “Detectability Criteria of Forbidden Lines of NII and OIII,” J. Quant. Spectrosc. Radiat. Transfer 40, 85–91 (1988).
[CrossRef]

Holland, A. C.

Kaufman, Y. J.

Y. J. Kaufman, “Effect of Earth’s Atmosphere on Contrast for Zenith Observations,” J. Geophys. Res. 84, 3165 (1979).
[CrossRef]

Levin, Z.

Z. Levin, J. Lindberg, “Size Distributions, Chemical Composition and Optical Properties of Urban and Desert Aerosols in Israel,” J. Geophys. Res. 20, 6941 (1979).
[CrossRef]

Lindberg, J.

Z. Levin, J. Lindberg, “Size Distributions, Chemical Composition and Optical Properties of Urban and Desert Aerosols in Israel,” J. Geophys. Res. 20, 6941 (1979).
[CrossRef]

Mekler, Y.

Y. Mekler, D. Goorvitch, “Detectability Criteria of Forbidden Lines of NII and OIII,” J. Quant. Spectrosc. Radiat. Transfer 40, 85–91 (1988).
[CrossRef]

Y. Mekler, A. Eviatar, “on the Detectability of Forbidden Lines,” J. Quant. Spectrosc. Radiat. Transfer 18, 531–533 (1977).
[CrossRef]

Treanor, P. J.

P. J. Treanor, “A Simple Propagation Law for Artificial Night-Sky Illumination,” Observatory 93, 117 (1973).

Walker, M. F.

M. F. Walker, “The Effect of Urban Lighting on the Brightness of the Night Sky,” Publ. Astron. Soc. Pac. 89, 405–409 (1977).
[CrossRef]

M. F. Walker, “Light Pollution in California and Arizona,” Publ. Astron. Soc. Pac. 85, 508–519 (1973).
[CrossRef]

Appl. Opt.

J. Geophys. Res.

Y. J. Kaufman, “Effect of Earth’s Atmosphere on Contrast for Zenith Observations,” J. Geophys. Res. 84, 3165 (1979).
[CrossRef]

Z. Levin, J. Lindberg, “Size Distributions, Chemical Composition and Optical Properties of Urban and Desert Aerosols in Israel,” J. Geophys. Res. 20, 6941 (1979).
[CrossRef]

J. Illum. Eng. Soc.

D. M. Finch, “Atmospheric Light Pollution,” J. Illum. Eng. Soc. 7, 105–117 (1978).

J. Quant. Spectrosc. Radiat. Transfer

Y. Mekler, A. Eviatar, “on the Detectability of Forbidden Lines,” J. Quant. Spectrosc. Radiat. Transfer 18, 531–533 (1977).
[CrossRef]

Y. Mekler, D. Goorvitch, “Detectability Criteria of Forbidden Lines of NII and OIII,” J. Quant. Spectrosc. Radiat. Transfer 40, 85–91 (1988).
[CrossRef]

Light. Des. Appl.

S. M. Faber, “Sky-Glow at Lick Observatory,” Light. Des. Appl.18–22 (1980).

Observatory

P. J. Treanor, “A Simple Propagation Law for Artificial Night-Sky Illumination,” Observatory 93, 117 (1973).

Publ. Astron. Soc. Pac.

M. F. Walker, “Light Pollution in California and Arizona,” Publ. Astron. Soc. Pac. 85, 508–519 (1973).
[CrossRef]

M. F. Walker, “The Effect of Urban Lighting on the Brightness of the Night Sky,” Publ. Astron. Soc. Pac. 89, 405–409 (1977).
[CrossRef]

Other

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960), p. 393.

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Figures (6)

Fig. 1
Fig. 1

Aerosol phase functions: β = 1.96 and 2.84 for Mie spheres and β = 1.96 for nonspherical particles.

Fig. 2
Fig. 2

Geometry and notation of the radiative transfer model.

Fig. 3
Fig. 3

Specific intensities of the detector for Q = 1 × 2424 photons/s; λ = 0.55 μm; τ = 0.30; ASFC = 0.20; β = 2.84 and 1.96; + = nonspherical particles; SMX = spectrometry extended source; PGS = photography star; PMS = photometry star; PQX = photography extended source.

Fig. 4
Fig. 4

Specific intensities at zenith, ASFC = 0.20.

Fig. 5
Fig. 5

Intensity as a function of the distance from city x. The thick lines show the r−2.5 relation. The calculations are for spherical aerosols and for zero surface reflectance. The values of aerosol optical thickness τ and the cosine of the zenith angle are indicated.

Fig. 6
Fig. 6

Exponent ν as a function of the cosine of the observation angle for three optical thicknesses: —, spherical aerosol; – – – – – – –, nonspherical aerosol; — — —, empircal value of ν from Ref. 3.

Tables (5)

Tables Icon

Table I Properties of the Power-Law Size Distributions at Mizpeh Ramona

Tables Icon

Table II Limiting Background for Signal-to-Noise Ratios from 1/2 to 16

Tables Icon

Table III Values of Parameters of SNR for the George Wise Observatory at Mizpe Ramon

Tables Icon

Table IV Intensities In Different Directions of Observation

Tables Icon

Table V Typical Values of B for Aerosols and the Rayleigh Atmosphere

Equations (44)

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Q * = 4.5 × 10 6 400 × 4 × 10 4 × 4.11 × 10 15 = 1.85 × 10 24 photons / s ,
1 × 10 23 Q 1 × 10 24 photons / s .
d N d log r = C r - β .
γ = E ( A T η E + E b ) 1 / 2 .
E b E b , 1 = E 2 A T η γ 1 2 - E .
L = Q 2 π r 2
L * = Δ A × Δ r × k ( z ) × L ,
N = L * P ( ζ ) Δ Ω ,
Δ ω = A * r 2 .
ζ = cos θ cos θ + ( 1 - cos 2 θ ) ( 1 - cos 2 θ ) 1 / 2 cos ϕ ,
Δ L r = [ N A * ] Δ Ω * ,
Δ L r = Q 2 π r 2 k ( z ) P ( ζ ) Δ r ,
Δ r Δ A Δ A Δ r .
E = exp [ - B ( z ) ( τ 0 - τ ) cos θ ] .
E = exp [ - B ( z ) ( τ 0 - τ ) cos θ ] .
B M ( z ) = 1 - F M tan - 1 ( z / R ) π 2 ,
B R ( z ) = 1 - F R tan - 1 ( z / R ) π 2 ,
F = 1 2 0 1 P ( ζ ) sin ζ d ζ
Δ L r = Q 2 π r 2 k ( z ) P ( ζ ) Δ r exp [ - B ( z ) ( τ 0 - τ ) ( 1 cos θ + 1 cos θ ) ] .
k ( z ) ( Δ r ) = k ( z ) Δ ( z ) cos θ = - Δ τ cos θ ,
r = ( z cos θ ) .
Δ L r = - Q Δ τ 2 π cos θ P ( ζ ) cos 2 θ z 2 × exp [ - B ( τ ) ( τ 0 - τ ) ( 1 cos θ + 1 cos θ ) ] .
τ i = τ 0 , i exp ( - z / H i ) ,
z i = H i ln ( τ 0 , i τ 0 ) .
cos θ = z ( z 2 + R 2 ) 1 / 2 = z [ z 2 + ( x - z tan θ ) 2 ] 1 / 2 .
L r , i = Q 2 π cos θ 0 τ 0 d τ P i ( ζ ) cos 2 θ i z i × exp [ - B i ( z ) ( τ 0 - τ ) ( 1 cos θ + 1 cos θ ) ] .
L r = Q 2 π cos θ 0 T 0 d τ [ W M P M ( ζ ) cos 2 θ M z M 2 + W R P R ( ζ ) cos 2 θ R z R ] × exp { - B M ( τ ) ( τ 0 - τ ) W M ( 1 cos θ + 1 cos θ M ) ] - B g ( τ ) ( τ 0 - τ ) W g ( 1 cos θ + 1 cos θ g ) ] } ,
W M = τ M ( τ M + τ R ) ,
W R = 1 - W M .
A m = 1 1 - 1 A L ,
l = γ * τ 0 1 + γ * τ 0 ,             γ * = 2 β ,
β = 1 4 π 0 1 d μ 0 1 d μ 0 2 π d ϕ [ W M P M ( μ i - μ i ) + W R P R ( μ i - μ i ϕ ) ] .
S = K 1 K 2 B π D 2 4 F α s η T ,
K 1 K 2 B b π D 2 4 F α s 2 η T / ( f 1 d θ d λ Δ λ ) .
s N = γ = [ B D ( π K 1 K 2 α s 2 η 2 T 2 ) 1 / 2 ] / 2 F [ B + B b s / ( f 1 d θ d λ Δ λ ) ] 1 / 2 .
S = K 1 K 2 E π D 2 4 η T .
K 1 K 2 B b π D 2 4 s 2 h η T ˙ / ( f 1 d θ d λ Δ λ ) .
γ = E D 2 ( π K 1 K 2 η T E + B b s 2 h f 1 d θ d λ Δ λ ) 1 / 2 .
K 1 E π D 2 4 η T .
K 1 B b π D 2 4 β 2 η T .
γ = E D 2 [ π K 1 η T E + B b α 2 ] 1 / 2 .
F = 1 2 0 1 P ( ζ ) sin ζ d ζ .
tan - 1 ( z R ) π 2 .
B = 1 - F tan - 1 ( z R ) π 2 ,

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