Abstract

A 0.7% accurate formula is derived for the easy conversion of power spectral radiance Lλ in W cm−2 sr−1μm−1 to rayleigh spectral radiance Rλ in rayleigh/μm, Rλ = 2πλLλ × 1013, where the wavelength λ is in μm. The rationale for the rayleigh unit is discussed in terms of a photon rate factor and a solid angle factor. The latter is developed in terms of an equivalence theorem about optical receivers and extended sources, and the concept is extended to the computation of photon volume emission rates from altitude profiles of zenith radiance.

© 1974 Optical Society of America

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References

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  1. Rayleigh, Proc. R. Soc. Lond. A129, 458 (1930).
  2. D. M. Hunten, F. E. Roach, J. W. Chamberlain, J. Atmos. Terr. Phys. 8, 345 (1956).
    [CrossRef]
  3. J. W. Chamberlain, Physics of the Aurora and Airglow (Academic Press, New York, 1961), p. 569.
  4. A. T. Stair, D. J. Baker, C. L. Wyatt, K. D. Baker, J. C. Ulwick, Geophys. Res. Lett. 1, July (1974).
    [CrossRef]
  5. D. R. Weast, Ed. CRC Handbook of Chemistry and Physics (CRC Publishing Co., Cleveland, 1973), pp. F-91 and F-195.

1974 (1)

A. T. Stair, D. J. Baker, C. L. Wyatt, K. D. Baker, J. C. Ulwick, Geophys. Res. Lett. 1, July (1974).
[CrossRef]

1956 (1)

D. M. Hunten, F. E. Roach, J. W. Chamberlain, J. Atmos. Terr. Phys. 8, 345 (1956).
[CrossRef]

1930 (1)

Rayleigh, Proc. R. Soc. Lond. A129, 458 (1930).

Baker, D. J.

A. T. Stair, D. J. Baker, C. L. Wyatt, K. D. Baker, J. C. Ulwick, Geophys. Res. Lett. 1, July (1974).
[CrossRef]

Baker, K. D.

A. T. Stair, D. J. Baker, C. L. Wyatt, K. D. Baker, J. C. Ulwick, Geophys. Res. Lett. 1, July (1974).
[CrossRef]

Chamberlain, J. W.

D. M. Hunten, F. E. Roach, J. W. Chamberlain, J. Atmos. Terr. Phys. 8, 345 (1956).
[CrossRef]

J. W. Chamberlain, Physics of the Aurora and Airglow (Academic Press, New York, 1961), p. 569.

Hunten, D. M.

D. M. Hunten, F. E. Roach, J. W. Chamberlain, J. Atmos. Terr. Phys. 8, 345 (1956).
[CrossRef]

Rayleigh,

Rayleigh, Proc. R. Soc. Lond. A129, 458 (1930).

Roach, F. E.

D. M. Hunten, F. E. Roach, J. W. Chamberlain, J. Atmos. Terr. Phys. 8, 345 (1956).
[CrossRef]

Stair, A. T.

A. T. Stair, D. J. Baker, C. L. Wyatt, K. D. Baker, J. C. Ulwick, Geophys. Res. Lett. 1, July (1974).
[CrossRef]

Ulwick, J. C.

A. T. Stair, D. J. Baker, C. L. Wyatt, K. D. Baker, J. C. Ulwick, Geophys. Res. Lett. 1, July (1974).
[CrossRef]

Wyatt, C. L.

A. T. Stair, D. J. Baker, C. L. Wyatt, K. D. Baker, J. C. Ulwick, Geophys. Res. Lett. 1, July (1974).
[CrossRef]

Geophys. Res. Lett. (1)

A. T. Stair, D. J. Baker, C. L. Wyatt, K. D. Baker, J. C. Ulwick, Geophys. Res. Lett. 1, July (1974).
[CrossRef]

J. Atmos. Terr. Phys. (1)

D. M. Hunten, F. E. Roach, J. W. Chamberlain, J. Atmos. Terr. Phys. 8, 345 (1956).
[CrossRef]

Proc. R. Soc. Lond. (1)

Rayleigh, Proc. R. Soc. Lond. A129, 458 (1930).

Other (2)

J. W. Chamberlain, Physics of the Aurora and Airglow (Academic Press, New York, 1961), p. 569.

D. R. Weast, Ed. CRC Handbook of Chemistry and Physics (CRC Publishing Co., Cleveland, 1973), pp. F-91 and F-195.

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Figures (3)

Fig. 1
Fig. 1

Geometry for uniform extended radiation source viewed by photometric receiver with an ideal field of view.

Fig. 2
Fig. 2

Close-up geometry of an instrument acceptance aperture moving through a radiating gas.

Fig. 3
Fig. 3

Example of the results of a computation (assuming optically thin horizontally uniform conditions) of the volume emission rate altitude distribution (right-hand figure) computed from a zenith spectral radiance profile (left-hand figure) experimentally measured from a rocket.

Equations (27)

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R λ = 1.986486 π λ L λ × 10 13 R / μ m ,
R λ = 2 π λ L λ × 10 13 R / μ m .
L λ = ( R λ / 2 π λ ) × 10 13 W cm 2 sr 1 μ m 1 .
P = L S Ω s d S ( W ) ,
Ω s = A cos α ( h / cos α ) 2 = A cos 3 α h 2
d S = 2 π r d r = 2 π ( h tan α ) ( h d α / cos 2 α ) = 2 π h 2 ( sin α / cos 3 α ) d α .
P = L 0 α A cos 3 α h 2 2 π h 2 sin α cos 3 α d α = L A 2 π 0 α sin α d α = L A 2 π ( 1 cos α ) .
Ω r = S h 2 = 0 2 π d ϕ 0 α sin α d α = 2 π ( 1 cos α ) ( sr )
Ω r = π sin 2 α
P = L A Ω r ( W ) .
Δ P Δ V = L 2 A Ω r L 1 A Ω r A Δ h = Ω r Δ h ( L 2 L 1 ) = Ω r Δ L Δ h ( W / cm 3 ) .
u = Δ P t Δ V = 4 π Ω r Ω r Δ L Δ h = 4 π Δ L Δ h ( W / cm 3 ) .
u ( h ) = 4 π ( d L ( h ) / d h ) ( W / cm 3 ) .
u ( h ) = ( d R ( h ) / d h ) ( megaphotons sec 1 cm 3 ) .
I λ = 10 6 F λ ( megaphotons sec 1 cm 3 sr 1 μ m 1 ) .
R λ = 4 π I λ = 4 π × 10 6 F λ ( R / μ m ) .
E λ = h c ( λ × 10 4 ) ( J ) ,
h = 6.626196 × 10 34 J-sec ,
c = 2.9979250 × 10 10 cm / sec .
L λ = h c λ × 10 4 F λ = h c λ × 10 4 R λ 4 π × 10 6 = ( 6.626196 × 10 34 ) ( 2.9979250 × 10 10 ) ( 10 4 ) ( 4 π × 10 6 ) R λ λ R λ 2 π λ × 10 13 ( W cm 1 sr 1 μ m 1 ) .
R λ = 2 π λ L λ × 10 13 ( R / μ m ) .
R ν = ( 2 π / ν ) L ν × 10 9 ( R / cm 1 ) ,
R = R λ Δ λ ( R )
L = L λ Δ λ ( W cm 2 sr 1 ) .
R = 2 π λ L × 10 13 ( R ) ,
L = R 2 π λ × 10 13 ( W cm 2 sr 1 ) ,
L = i = 1 n R λ i Δ λ i 2 π λ i × 10 13 = λ 0 λ n R λ 2 π λ × 10 13 d λ ( W cm 1 sr 1 ) .

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