Abstract

The apparent contrast of objects lying on the surface of the earth, when observed in the visible spectrum from above the earth’s atmosphere, is calculated for three model atmospheres. The earth is illuminated by sunlight, and light is reflected from the earth’s surface according to Lambert’s law. The apparent contrast increases with increasing wavelength. The apparent contrast is lower when aerosols are in the atmosphere, than when the atmosphere is free of aerosols. The apparent contrast can be enhanced significantly, if the albedo of the object space is low, when an analyzer, such as a piece of Polaroid, is used in the optical system of the receiver.

© 1964 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Los Angeles, 1960), pp. 275–467.
  2. “A Scientific Investigation into Photographic Reconnaissance from Space Vehicles,” Appendix B of , Cornell Aeronautical Laboratory, Inc., Buffalo, New York (1961); ASTIA No. AD 260694.
  3. S. Chandrasekhar, Radiative Transfer (Oxford University Press, New York, 1950).
  4. Z. Sekera and E. V. Ashburn, “Tables Relating to Rayleigh Scattering of Light in the Atmosphere,” , U. S. Naval Ordnance Test Station, Inyokern, California (1953).
  5. Z. Sekera and G. Blanch, “Tables Relating to Rayleigh Scattering of Light in the Atmosphere,” Contract No. AF 19(122)-239, University of California, Department of Meteorology, Los Angeles (1952).
  6. Z. Sekera, Advan. Geophys. 3, 43–104 (1956).
    [CrossRef]
  7. R. S. Fraser, J. Opt. Soc. Am. 54, 157 (1964).
    [CrossRef]
  8. Z. Sekera, Union Géodésique Géophys. Intern. Monogram 10, 66 (1961).

1964 (1)

1961 (1)

Z. Sekera, Union Géodésique Géophys. Intern. Monogram 10, 66 (1961).

1956 (1)

Z. Sekera, Advan. Geophys. 3, 43–104 (1956).
[CrossRef]

Ashburn, E. V.

Z. Sekera and E. V. Ashburn, “Tables Relating to Rayleigh Scattering of Light in the Atmosphere,” , U. S. Naval Ordnance Test Station, Inyokern, California (1953).

Blanch, G.

Z. Sekera and G. Blanch, “Tables Relating to Rayleigh Scattering of Light in the Atmosphere,” Contract No. AF 19(122)-239, University of California, Department of Meteorology, Los Angeles (1952).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Oxford University Press, New York, 1950).

Coulson, K. L.

K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Los Angeles, 1960), pp. 275–467.

Dave, J. V.

K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Los Angeles, 1960), pp. 275–467.

Fraser, R. S.

Sekera, Z.

Z. Sekera, Union Géodésique Géophys. Intern. Monogram 10, 66 (1961).

Z. Sekera, Advan. Geophys. 3, 43–104 (1956).
[CrossRef]

Z. Sekera and G. Blanch, “Tables Relating to Rayleigh Scattering of Light in the Atmosphere,” Contract No. AF 19(122)-239, University of California, Department of Meteorology, Los Angeles (1952).

K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Los Angeles, 1960), pp. 275–467.

Z. Sekera and E. V. Ashburn, “Tables Relating to Rayleigh Scattering of Light in the Atmosphere,” , U. S. Naval Ordnance Test Station, Inyokern, California (1953).

Advan. Geophys. (1)

Z. Sekera, Advan. Geophys. 3, 43–104 (1956).
[CrossRef]

J. Opt. Soc. Am. (1)

Union Géodésique Géophys. Intern. Monogram (1)

Z. Sekera, Union Géodésique Géophys. Intern. Monogram 10, 66 (1961).

Other (5)

K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Los Angeles, 1960), pp. 275–467.

“A Scientific Investigation into Photographic Reconnaissance from Space Vehicles,” Appendix B of , Cornell Aeronautical Laboratory, Inc., Buffalo, New York (1961); ASTIA No. AD 260694.

S. Chandrasekhar, Radiative Transfer (Oxford University Press, New York, 1950).

Z. Sekera and E. V. Ashburn, “Tables Relating to Rayleigh Scattering of Light in the Atmosphere,” , U. S. Naval Ordnance Test Station, Inyokern, California (1953).

Z. Sekera and G. Blanch, “Tables Relating to Rayleigh Scattering of Light in the Atmosphere,” Contract No. AF 19(122)-239, University of California, Department of Meteorology, Los Angeles (1952).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (17)

Fig. 1
Fig. 1

Coordinates in the vertical plane perpendicular to the earth and through the sun and observer. The target lies in the vertical plane in this particular case.

Fig. 2
Fig. 2

Contrast attenuation coefficients in the sun’s vertical for a Rayleigh atmosphere. The wavelength λ=0.495 μ (τ1=0.15); the albedo A=0.25; the solar zenith angle θ0=53.1°.

Fig. 3
Fig. 3

The contrast attenuation coefficients that are valid when no analyzer is used (left) and when the transmission plane of the analyzer is perpendicular to the plane of polarization of the skylight (right). The total normal optical thickness τ1=0.25, which corresponds to λ=0.436 μ. The albedo of the object space A=0.25, except that the albedo of the target is arbitrary. The solar zenith angle θ0=53.1°.

Fig. 4
Fig. 4

The maximum contrast attenuation coefficients, which are valid when the transmission plane of the analyzer is perpendicular to the plane of polarization of the skylight, for low sun (left) and for sun at the zenith (right). The albedo of the object space is A=0.25, except that the albedo of the target is arbitrary. τ1=0.25; λ=0.436 μ.

Fig. 5
Fig. 5

The maximum contrast attenuation coefficients (transmission plane of analyzer is perpendicular to the plane of polarization of the skylight) when the albedo is high (A=0.8), except that the albedo of the target is arbitrary. τ1=0.25; λ=0.436 μ; θ0=53.1°.

Fig. 6
Fig. 6

The apparent contrast when the albedo of the target is At=0.25 and the albedo of the object space surrounding the target is A=0. τ1=0.25; λ=0.436 μ; θ0=53.1°.

Fig. 7
Fig. 7

The contrast attenuation coefficients for small and large total normal optical thickness. The albedo of the object space is A=0.25, except that the albedo of the target is arbitrary. θ0=53.1°.

Fig. 8
Fig. 8

The specific intensity of light from the nadir. The light is reflected from the earth’s surface, then passes through a Rayleigh atmosphere and then an analyzer. The albedo of the object space is A=0.25.

Fig. 9
Fig. 9

Specific intensities of light reflected from object spaces of different albedos and passing through the atmosphere and an analyzer 1 2 ( I s e - τ 1 ). At and As indicate the albedos of the target and of the object space surrounding the target, respectively. Observation direction is toward the nadir.

Fig. 10
Fig. 10

The contrast attenuation coefficients for three model atmospheres. The data apply to the sun’s vertical. The albedo of the object space is A=0.25, except that the albedo of the target is arbitrary. The sun’s zenith angle θ0=53.1°; the wavelength λ=0.625 μ.

Fig. 11
Fig. 11

Contrast attenuation coefficients as a function of wavelength for a continental atmosphere and for the sun’s vertical. The albedo of the object space is A=0.25, except that the albedo of the target is arbitrary. The sun’s zenith angle θ0=53.1°.

Fig. 12
Fig. 12

The contrast attenuation coefficients for low and high sun. The coefficients are calculated for the continental atmosphere model and apply to the sun’s vertical. The albedo of the object space is A=0.25, except that the albedo of the target is arbitrary. The wavelength λ=0.625 μ.

Fig. 13
Fig. 13

The contrast attenuation coefficients in the directions where the maximum occurs and towards the nadir. The coefficients apply to the continental atmosphere model. The albedo of the object space is A=0.25, except that the albedo of the target is arbitrary. The wavelength λ=0.625 μ.

Fig. 14
Fig. 14

The contrast attenuation coefficients when the albedo of the object space is A=0.8 for three curves and A=0.25 for one curve, except that the albedo of the target is arbitrary. The coefficients apply to the continental atmosphere and the sun’s vertical. The sun’s zenith angle is θ0=53.1°. The wavelength is λ=0.625 μ.

Fig. 15
Fig. 15

The maximum apparent contrast for a continental atmosphere when the object space is black, except that the albedo of the target is At=0.25. The target is in the sun’s vertical. The wavelength is λ=0.625 μ. The sun’s zenith angle is θ0=53.1°.

Fig. 16
Fig. 16

The maximum apparent contrast for two model atmospheres when the object space is black, except that the albedo of the target is At=0.25. The target is in the sun’s vertical and is observed through an analyzer with its transmission plane parallel to the sun’s vertical. The sun’s zenith angle is θ0=53.1°.

Fig. 17
Fig. 17

The specific intensity of light that is reflected from the object space with an albedo of A=0.25 and passes through the earth’s atmosphere and an analyzer. π units of incident solar flux pass through a unit area normal to the direction of propagation. The wavelength is λ=0.625 μ.

Tables (2)

Tables Icon

Table I The contrast attenuation coefficients and optical parameters for three aerosol models. The contrast attenuation coefficients and degree of polarization of skylight apply to the direction where the contrast attenuation coefficients are a maxima. λ=0.625 μ; θ0=53.1°.

Tables Icon

Table II The ratio of the apparent contrast which is observed when the transmission plane of the analyzer is parallel to the sun’s vertical to the apparent contrast which is observed without an analyzer. The observer is above the earth’s atmosphere. The object space is at the surface of the earth. The sun’s zenith angle is θ0=53.1°. The albedo of the object space, except for the target, is given by the value of A.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

C ( τ ; μ , φ ) = I t ( τ ; μ , φ ) - I s ( τ ; μ , φ ) I s ( τ ; μ , φ ) ,
I ( τ ; θ , φ ) = I ( τ 1 ; θ , φ ) e - ( τ 1 - τ ) sec θ + τ τ 1 J ( t ; θ , φ ) e - ( t - τ ) sec θ sec θ d t ,
C ( τ = 0 ; θ , φ ) = [ I t ( τ 1 ; θ , φ ) - I s ( τ 1 ; θ , φ ) ] e - τ 1 sec θ / [ I s ( τ 1 ; θ , φ ) e - τ 1 sec θ + 0 τ 1 J ( t ; θ , φ ) e - t sec θ sec θ d t ]
= y ( τ 1 ; θ , φ ) C ( τ 1 ; θ , φ ) ,
y ( τ 1 ; θ , φ ) = I s ( τ 1 ; θ , φ ) e - τ 1 sec θ / [ I s ( τ 1 ; θ , φ ) e - τ 1 sec θ + 0 τ 1 J ( t ; θ , φ ) e - t sec θ sec θ d t ] .
I g ( τ 1 , μ 0 ) = μ 0 A 2 [ 1 - A s ¯ ( τ 1 ) ] [ γ l ( τ 1 , μ 0 ) + γ r ( τ 1 , μ 0 ) ] ,
I s ( τ 1 , μ 0 ) = I g ( τ 1 , μ 0 ) .
I t ( θ ) = I t ( θ = 0 ° ) exp [ - τ 1 ( sec θ - 1 ) ] .
0.5 I s ( τ 1 , μ 0 , A ) e - τ 1 / μ ,