Abstract

If a photocell is calibrated by means of a source of known spectral energy distribution, employment of the cell for the measurement of the illumination produced by another source of different energy distribution will entail correction of the initial calibration constant. The basic principles for obtaining such a correction factor, applicable for the general case, of wavelength selective receivers, are set out in this paper. As an example, the case is discussed in detail of deriving the natural illumination flux from radiometric measurements of solar shortwave radiation with the aid of current standard meteorological filters. Equations are presented from which the illumination can be computed from known values of the air mass (i.e., optical path length) and the atmospheric turbidity. These equations have been applied to a comprehensive series of measurements of illumination and shortwave radiation assembled in South Africa. It is shown that the equations are valid over very wide ranges of air mass and turbidity.

© 1962 Optical Society of America

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References

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  1. A. J. Drummond, Arch. Meteorol., Geophys. u. Bioklimatol., Ser. B, 7, 437 (1956).
    [CrossRef]
  2. A. J. Drummond, Arch. Meteorol., Geophys. u. Bioklimatol., Ser. B, 9, 149 (1958).
    [CrossRef]
  3. A. K. Ångström, A. J. Drummond, J. Opt. Soc. Am. 49, 1096 (1959).
    [CrossRef]
  4. A. K. Ångström, A. J. Drummond, J. Opt. Soc. Am. 50, 974 (1960).
    [CrossRef]
  5. A. K. Ångström, A. J. Drummond, J. Meteorol. 18, 360 (1961).
    [CrossRef]
  6. Robert J. List, Smithsonian Meteorological Tables, 6th revised ed. (Smithsonian Institution, Washington, 1951), p. 422.
  7. A. K. Ångström, Geogr. Ann. 11, 156 (1929).
    [CrossRef]
  8. A. K. Ångström, Geogr. Ann. 12, 130 (1930).
    [CrossRef]
  9. A. K. Ångström, Compendium of Meteorology (American Meteorological Society, Boston, 1951), p. 50.
  10. Linke’s Meteorologisches Taschenbuch (Geest and Portig, Leipzig, 1953), Vol. 2, Table 95, p. 508.
  11. R. Penndorf, J. Opt. Soc. Am. 47, 176 (1957).
    [CrossRef]
  12. L. B. Aldrich, W. H. Hoover, Annals of the Astrophysical Observatory (Smithsonian Institution, Washington, 1954), Vol. 7 and previous volumes.
  13. IGY Instruction Manual, V, Part VI, Radiation Instruments and Measurements (Pergamon Press, London, 1958), Table 7, p. 464.
  14. E. Elvegård, G. Sjöstedt, Gerlands Beitr. z. Geophys. 56, 41 (1940).

1961 (1)

A. K. Ångström, A. J. Drummond, J. Meteorol. 18, 360 (1961).
[CrossRef]

1960 (1)

1959 (1)

1958 (1)

A. J. Drummond, Arch. Meteorol., Geophys. u. Bioklimatol., Ser. B, 9, 149 (1958).
[CrossRef]

1957 (1)

1956 (1)

A. J. Drummond, Arch. Meteorol., Geophys. u. Bioklimatol., Ser. B, 7, 437 (1956).
[CrossRef]

1940 (1)

E. Elvegård, G. Sjöstedt, Gerlands Beitr. z. Geophys. 56, 41 (1940).

1930 (1)

A. K. Ångström, Geogr. Ann. 12, 130 (1930).
[CrossRef]

1929 (1)

A. K. Ångström, Geogr. Ann. 11, 156 (1929).
[CrossRef]

Aldrich, L. B.

L. B. Aldrich, W. H. Hoover, Annals of the Astrophysical Observatory (Smithsonian Institution, Washington, 1954), Vol. 7 and previous volumes.

Ångström, A. K.

A. K. Ångström, A. J. Drummond, J. Meteorol. 18, 360 (1961).
[CrossRef]

A. K. Ångström, A. J. Drummond, J. Opt. Soc. Am. 50, 974 (1960).
[CrossRef]

A. K. Ångström, A. J. Drummond, J. Opt. Soc. Am. 49, 1096 (1959).
[CrossRef]

A. K. Ångström, Geogr. Ann. 12, 130 (1930).
[CrossRef]

A. K. Ångström, Geogr. Ann. 11, 156 (1929).
[CrossRef]

A. K. Ångström, Compendium of Meteorology (American Meteorological Society, Boston, 1951), p. 50.

Drummond, A. J.

A. K. Ångström, A. J. Drummond, J. Meteorol. 18, 360 (1961).
[CrossRef]

A. K. Ångström, A. J. Drummond, J. Opt. Soc. Am. 50, 974 (1960).
[CrossRef]

A. K. Ångström, A. J. Drummond, J. Opt. Soc. Am. 49, 1096 (1959).
[CrossRef]

A. J. Drummond, Arch. Meteorol., Geophys. u. Bioklimatol., Ser. B, 9, 149 (1958).
[CrossRef]

A. J. Drummond, Arch. Meteorol., Geophys. u. Bioklimatol., Ser. B, 7, 437 (1956).
[CrossRef]

Elvegård, E.

E. Elvegård, G. Sjöstedt, Gerlands Beitr. z. Geophys. 56, 41 (1940).

Hoover, W. H.

L. B. Aldrich, W. H. Hoover, Annals of the Astrophysical Observatory (Smithsonian Institution, Washington, 1954), Vol. 7 and previous volumes.

List, Robert J.

Robert J. List, Smithsonian Meteorological Tables, 6th revised ed. (Smithsonian Institution, Washington, 1951), p. 422.

Penndorf, R.

Sjöstedt, G.

E. Elvegård, G. Sjöstedt, Gerlands Beitr. z. Geophys. 56, 41 (1940).

Arch. Meteorol., Geophys. u. Bioklimatol., Ser. B (2)

A. J. Drummond, Arch. Meteorol., Geophys. u. Bioklimatol., Ser. B, 7, 437 (1956).
[CrossRef]

A. J. Drummond, Arch. Meteorol., Geophys. u. Bioklimatol., Ser. B, 9, 149 (1958).
[CrossRef]

Geogr. Ann. (2)

A. K. Ångström, Geogr. Ann. 11, 156 (1929).
[CrossRef]

A. K. Ångström, Geogr. Ann. 12, 130 (1930).
[CrossRef]

Gerlands Beitr. z. Geophys. (1)

E. Elvegård, G. Sjöstedt, Gerlands Beitr. z. Geophys. 56, 41 (1940).

J. Meteorol. (1)

A. K. Ångström, A. J. Drummond, J. Meteorol. 18, 360 (1961).
[CrossRef]

J. Opt. Soc. Am. (3)

Other (5)

Robert J. List, Smithsonian Meteorological Tables, 6th revised ed. (Smithsonian Institution, Washington, 1951), p. 422.

A. K. Ångström, Compendium of Meteorology (American Meteorological Society, Boston, 1951), p. 50.

Linke’s Meteorologisches Taschenbuch (Geest and Portig, Leipzig, 1953), Vol. 2, Table 95, p. 508.

L. B. Aldrich, W. H. Hoover, Annals of the Astrophysical Observatory (Smithsonian Institution, Washington, 1954), Vol. 7 and previous volumes.

IGY Instruction Manual, V, Part VI, Radiation Instruments and Measurements (Pergamon Press, London, 1958), Table 7, p. 464.

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Figures (5)

Fig. 1
Fig. 1

Correction procedure for photometric calibrations. (Curve φ(λ) represents the standard I.C.I. spectral luminosity distribution for the human eye, curve f(λ) the relative spectral response of a filtered selenium photocell, curve F(λ) the measured relative emission of a tungsten-filament calibration lamp, and F1(λ) the spectral energy distribution of the direct solar radiation corresponding to an air mass (m) value of 2.0 and an atmospheric turbidity (β) of 0.20.)

Fig. 2
Fig. 2

Values of the luminous efficiency (ρ1) for different Schott filters, at different air masses (m) and turbidities (β).

Fig. 3
Fig. 3

Dependence of sunlight illumination of a horizontal surface at the ground, on solar height (h) and turbidity (β). (o values refer to computations, by Elvegård and Sjöstedt,14 based on measurements mainly at Helsinki and Stockholm.)

Fig. 4
Fig. 4

Dependence of sunlight illumination of a surface perpendicular to the solar beam at the ground on air mass (m) and turbidity (β). (x and Δ values refer to the Pretoria series of measurements.)

Fig. 5
Fig. 5

Comparison between measured and computed volues of illumination of a surface perpendicular to the solar beam, at Pretoria, for March and September 1955.

Tables (5)

Tables Icon

Table I The Dependence of Sunlight Illumination (Kilolux), on a Surface Perpendicular to the Rays, on Air Mass and Turbidity, for Mean Solar Distance

Tables Icon

Table II Comparison between Measured (E0) and Computed (E1 and E2) Values of Illumination at Pretoria (25° 45 S, 1370 meters) During a Period of Relatively Low Atmospheric Turbidity at the End of the Wet Season

Tables Icon

Table III Comparison between Measured (E0) and Computed (E1 and E2) Values of Illumination at Pretoria (25° 45 S, 1370 meters) During a Period of Relatively High Atmospheric Turbidity at the End of the Dry Season

Tables Icon

Table IV Comparison between Measured (E0) and Computed (E1 and E2) Values of Illumination at Pretoria (25° 45 S, 1370 meters) During Periods of (a) Very High Atmospheric Turbidity (and Low Solar Height) and (b) Very Low Atmospheric Turbidity (and High Solar Height)

Tables Icon

Table V Radiation Intensity of the Sun (mcal cm−2 min−1) in Relation to Air Mass and Turbidity for the Spectral Band Isolated by the Standard RG 8 Filter ( I t I r 8 = 0 700 F ( λ ) d λ )a

Equations (30)

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E = c 0 φ ( λ ) F ( λ ) d λ ,
E = c · A .
E = k · δ ,
0 f ( λ ) F ( λ ) d λ = B .
h · δ = B ,
E = k 0 · δ = c · A ,
E 1 = k 1 · δ 1 = c 0 φ ( λ ) F 1 ( λ ) d λ = c · A 1
h · δ 1 = B 1 ,
B 1 = 0 f ( λ ) F 1 ( λ ) d λ .
E = k 0 · B h = c · A , E 1 = k 1 · B 1 h = c · A 1 ,
k 1 = B A · A 1 B 1 · k 0 .
A = 0 φ ( λ ) F ( λ ) d λ , B = 0 f ( λ ) F ( λ ) d λ , A 1 = 0 φ ( λ ) F 1 ( λ ) d λ , B 1 = 0 f ( λ ) F 1 ( λ ) d λ .
B A = 0.993 ; A 1 B 1 = 0.989 ;
B A = 1.067 ; A 1 B 1 = 0.948 ;
ρ = 0 φ ( λ ) F ( λ ) d λ 0 F ( λ ) d λ .
ρ 1 = 0 φ ( λ ) F ( λ ) d λ 0 λ m F ( λ ) d λ .
I o 1 = 0 530 F ( λ ) d λ , I r 2 = 0 630 F ( λ ) d λ , I r 8 = 0 700 F ( λ ) d λ .
F ( λ ) Δ λ = I 0 ( λ ) Δ λ · p λ · e δ m ,
0 F ( λ ) d λ 700 F ( λ ) d λ = 0 700 F ( λ ) d λ
OG 1 : ρ 1 = 0.58 ( 1 + 0.235 m + 1.19 m β ) , RG 2 : ρ 1 = 0.39 ( 1 + 0.073 m + 0.305 m β ) , RG 8 : ρ 1 = 0.315 ( 1 + 0.032 m ) .
ρ 1 · W = 0 φ ( λ ) F ( λ ) d λ E ,
W = 0 λ m F ( λ ) d λ .
E = 475 · ρ 1 · W .
OG 1 : E = 475 · 0.58 · 0.509 = 140 , RG 2 : E = 475 · 0.39 · 0.787 = 146 , RG 8 : E = 475 · 0.315 · 0.948 = 142 .
E = k 0 0 700 F ( λ ) d λ .
k 1 = B A · A 1 B 1 · k 0 .
A = 0 φ ( λ ) F ( λ ) d λ , B = 0 700 F ( λ ) d λ , A 1 = 0 φ ( λ ) F 1 ( λ ) d λ , B 1 = 0 700 F 1 ( λ ) d λ .
A 1 B 1 = ρ 1 = 0.315 ( 1 + 0.032 m ) ,
B A = 2.88
k 1 = k 0 · 0.92 ( 1 + 0.032 m ) .

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