Abstract

Measurements of illuminance at sea level, directional luminous reflectances of ocean water and other surfaces, atmospheric beam transmittance, and path luminance for a day with an unobscured, low sun are presented. These data are applicable for visibility calculations for downward paths of sight.

© 1966 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Q. Duntley, J. I. Gordon, J. H. Taylor, C. T. White, A. R. Boileau, J. E. Tyler, R. W. Austin, J. L. Harris, Appl. Opt. 3, 549–581, Sec. II, Sec. III, and Sec. VI (1964).
    [CrossRef]
  2. S. Q. Duntley, A. R. Boileau, R. W. Preisendorfer, J. Opt. Soc. Am. 47, 499 (1957).
    [CrossRef]
  3. S. Q. Duntley, final report of a contract, Visibility Laboratory, Massachusetts Institute of Technology, pp. 9 and 12 (1952).
  4. W. E. K. Middleton, A. G. Mungall, J. Opt. Soc. Am. 42, 572 (1952).
    [CrossRef]
  5. L. Elterman, “A Model of a Clear Standard Atmosphere for Attenuation in the Visible Region and Infrared Windows,” Optical Physics Laboratory, U.S. Air Force Cambridge Research Laboratories, Bedford, Massachusetts (1963).
  6. F. Kasten, “A New Table and Approximation Formula for the Relative Optical Air Mass,” Cold Regions Research and Engineering Laboratory, U.S. Army Material Command, Hanover, New Hampshire (1964).

1964 (1)

1957 (1)

1952 (1)

Austin, R. W.

Boileau, A. R.

Duntley, S. Q.

Elterman, L.

L. Elterman, “A Model of a Clear Standard Atmosphere for Attenuation in the Visible Region and Infrared Windows,” Optical Physics Laboratory, U.S. Air Force Cambridge Research Laboratories, Bedford, Massachusetts (1963).

Gordon, J. I.

Harris, J. L.

Kasten, F.

F. Kasten, “A New Table and Approximation Formula for the Relative Optical Air Mass,” Cold Regions Research and Engineering Laboratory, U.S. Army Material Command, Hanover, New Hampshire (1964).

Middleton, W. E. K.

Mungall, A. G.

Preisendorfer, R. W.

Taylor, J. H.

Tyler, J. E.

White, C. T.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

Other (3)

S. Q. Duntley, final report of a contract, Visibility Laboratory, Massachusetts Institute of Technology, pp. 9 and 12 (1952).

L. Elterman, “A Model of a Clear Standard Atmosphere for Attenuation in the Visible Region and Infrared Windows,” Optical Physics Laboratory, U.S. Air Force Cambridge Research Laboratories, Bedford, Massachusetts (1963).

F. Kasten, “A New Table and Approximation Formula for the Relative Optical Air Mass,” Cold Regions Research and Engineering Laboratory, U.S. Army Material Command, Hanover, New Hampshire (1964).

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 (7)

Fig. 1
Fig. 1

Upper sky luminances measured at sea level, values in foot lamberts. When expressed in apostilbs the metric luminance unit, the numerical values are increased by the factor 10.76. The indicated azimuths of 0°, 90°, 180°, and 270° are with respect to the sun. The position of the sun on the 0° meridian, zenith angle 77.3°, is indicated by the +.

Fig. 2
Fig. 2

Attenuation length L(z) measured continuously during 1000 ft/min (305 m/min) descent with aircraft held in level attitude. Equivalent attenuation length L ¯(z) was computed.

Fig. 3
Fig. 3

Atmospheric beam transmittance, graphs of Eq. (3), for various zenith angles from 0°/180° to 88°/92° as indicated.

Fig. 4
Fig. 4

Atmospheric beam transmittance for various zenith angles from 0°/180° to 78°/102° on expanded horizontal scale.

Fig. 5
Fig. 5

Lower sky luminance in ft-L. Map depicts the inherent luminance of ocean water at sea level. The position of the specular reflection of the sun is indicated by the +. Multiply value in ft-L by 10.76 to obtain value in apostilbs.

Fig. 6
Fig. 6

Lower sky luminance as measured at 5000 ft (1.52 km).

Fig. 7
Fig. 7

Lower sky luminance as measured at 20,000 ft (6.10 km).

Tables (9)

Tables Icon

Table I Directional Luminous Reflectance bR0(0,θ,φ) of Terrains

Tables Icon

Table II Unidirectional Luminous Reflectance bR0(0,180°,0°) of Ocean Background: Vertically Downward Path of Sight

Tables Icon

Table III Directional Luminous Reflectance tR0(0,θ,φ) of Surfaces

Tables Icon

Table IV Measured and Equivalent Attenuation Lengths, and Ratio of Altitude to Equivalent Attenuation Length

Tables Icon

Table V Path Luminance Br*(z,θ,0°),a Lower Sky in Azimuth of Sunb

Tables Icon

Table VI Path Luminance Br*(z,θ,±45°),a Lower Sky, 45° from Azimuth of Sunb

Tables Icon

Table VII Path Luminance Br*(z,θ,±90°),a Lower Sky, 90° from Azimuth of Sunb

Tables Icon

Table VIII Path Luminance Br*(z,θ,±135°),a Lower Sky, 135° from Azimuth of Sunb

Tables Icon

Table IX Path Luminance Br*(z,θ,80°),a Lower Sky, 180° from Azimuth of Sunb

Equations (5)

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

R 0 ( 0 , θ , φ ) B 0 ( 0 , θ , φ ) / E ( 0 , 0 ° , 0 ° ) .
C 0 ( 0 , θ , φ ) = [ R t 0 ( 0 , θ , φ ) / R b 0 ( 0 , θ , φ ) ] - 1 ,
T r ( z , θ ) = exp { - [ z / L ¯ ( z ) ] f ( z , θ ) }
B r ( z , θ , φ ) = B 0 ( z t , θ , φ ) T r ( z , θ ) + B r * ( z , θ , φ ) .
τ b r ( z , θ , φ ) = [ 1 + B r * ( z , θ , φ ) / T r ( z , θ ) B b 0 ( z t , θ , φ ) ] - 1 .

Metrics