Abstract

Spectra in the middle uv obtained on a rocket flight by a spectrometer pointed downward at the earth are compared with synthetic spectra generated by a computer. The independent variables of the synthetic spectra are the altitude of the detector, the wavelength, the zenith angles of the sun and of the detector line-of-sight, the azimuth difference between them, and three parameters characterizing the ozone distribution. In the altitude range of primary interest only two of the ozone parameters are free. Taken into account are the roundness of the earth, first-order Rayleigh scattering by the atmosphere, attenuation by air, absorption by molecular oxygen and ozone, and the line structure in the solar spectrum. The effects on the synthetic spectra of varying the parameters of the ozone distribution and the geometric parameters are also studied.

© 1967 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. F. Singer, Advan. Geophys. 3, 301 (1956).
    [Crossref]
  2. S. Twoney, Geophys. Res. 66, 2153 (1961).
    [Crossref]
  3. L. D. Kaplan, in Chemical Reactions in the Lower and Upper Atmosphere, R. D. Cadle, Ed. (Interscience Publishers, New York, 1966), Chap. 7.
  4. A. E. S. Green, ERR-AN-185, Space Science Laboratory, General Dynamics Convair (July1962); Appl. Opt. 3, 203 (1964).
  5. G. Ban, E. L. Hubbard, LAS-TR-199-37 and 48, Laboratories for Applied Science, University of Chicago, 1963.
  6. R. D. Raweliffe, G. E. Meloy, R. M. Friedman, E. H. Rogers, J. Geophys. Res. 68, 6425 (1963).
    [Crossref]
  7. A. E. S. Green, Ed., The Middle Ultraviolet, Its Science and Technology (John Wiley & Sons, Inc., New York, 1966).
  8. R. D. Rawcliffe, D. D. Elliot, J. Geophys. Res. 71, 5077 (1966).
    [Crossref]
  9. Reference 7, Chap. 5.
  10. M. Griggs, in Ref. 7, Chap. 4.
  11. S. L. Valley, Ed., “Atmospheric Composition”, Handbook of Geophysics and Space Environments (McGraw-Hill Book Co., New York, 1965), Chap. 6.
  12. J. Dowling, A. E. S. Green, in Ref. 7.
  13. R. T. Brinkmann, thesis, University of Florida, 1966.
  14. H. H. Malitson, J. D. Purcell, R. Tousey, C. E. Moore, Astrophys. J., 132, 746 (1960).
    [Crossref]
  15. N. Wilson, R. Tousey, J. D. Purcell, F. S. Johnson, C. E. Moore, Astrophys. J., 119, 590 (1954).
    [Crossref]
  16. C. R. Detwiler, D. L. Garrett, J. D. Purcell, R. Tousey, Ann. Geophys. 17, 263 (1961).
  17. R. T. Brinkmann, A. E. S. Green, C. A. Barth, “A Digitalized Solar Ultraviolet Solar Spectrum”, JPL Technical Report TR 32-951, August1966.
  18. T. L. Altshuler, “Infrared Transmission and Background Radiation by Clear Atmospheres”, General Electric M.S.V.D. Doe. No. 61SD199, December1961.
  19. L. Elterman, “Atmospheric Attenuation Model, 1964, in the Ultraviolet, Visible, and Infrared Regions for Altitudes to 50 km”, Environmental Research Papers, Number 46, July1964.
  20. U.S. Air Force Geophysics Research Directorate, Handbook of Geophysics (The Macmillan Company, New York, 1961).
  21. A. S. Jursa, M. Nakamura, Y. Tanaka, J. Geophys. Res. 70, 2699 (1965).
    [Crossref]
  22. U.S. Standard Atmosphere, 1962, NASA, USAF and U.S. Weather Bureau, Washington, D.C. (U.S. Government Printing Office, Washington, D.C., 1962).
  23. E. Vigroux, Ann. Phys. 8, 709 (1953).
  24. E. C. Y. Inn, Y. Tanaka, J. Opt. Soc. Am. 43, 870 (1953).
    [Crossref]
  25. Y. Tanaka, E. C. Y. Inn, K. Watanabe, J. Chem. Phys. 21, 1651 (1953).
    [Crossref]
  26. R. W. Ditchburn, P. A. Young, J. Atmos. Terr. Phys. 24, 127 (1962).
    [Crossref]
  27. A. Dalgarno, Geophysics Corp. of America Report, 1963.
  28. A. R. Hochstim, “Effective Collision Frequencies and Electric Conductivities of Weakly Ionized N2, O2N, O, NO, and Dry Air”, IDA/HG 64-2554, Research Paper P-124, February1965.
  29. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, M. Abramowitz, I. A. Stegun, Eds., NBS Applied Math. Series, 55, Washington, D.C. (U.S. Government Printing Office, Washington, D.C., 1965).
  30. C. A. Barth, Planet. Space Sci. 14, 623 (1966).
    [Crossref]

1966 (2)

R. D. Rawcliffe, D. D. Elliot, J. Geophys. Res. 71, 5077 (1966).
[Crossref]

C. A. Barth, Planet. Space Sci. 14, 623 (1966).
[Crossref]

1965 (1)

A. S. Jursa, M. Nakamura, Y. Tanaka, J. Geophys. Res. 70, 2699 (1965).
[Crossref]

1963 (1)

R. D. Raweliffe, G. E. Meloy, R. M. Friedman, E. H. Rogers, J. Geophys. Res. 68, 6425 (1963).
[Crossref]

1962 (1)

R. W. Ditchburn, P. A. Young, J. Atmos. Terr. Phys. 24, 127 (1962).
[Crossref]

1961 (2)

C. R. Detwiler, D. L. Garrett, J. D. Purcell, R. Tousey, Ann. Geophys. 17, 263 (1961).

S. Twoney, Geophys. Res. 66, 2153 (1961).
[Crossref]

1960 (1)

H. H. Malitson, J. D. Purcell, R. Tousey, C. E. Moore, Astrophys. J., 132, 746 (1960).
[Crossref]

1956 (1)

S. F. Singer, Advan. Geophys. 3, 301 (1956).
[Crossref]

1954 (1)

N. Wilson, R. Tousey, J. D. Purcell, F. S. Johnson, C. E. Moore, Astrophys. J., 119, 590 (1954).
[Crossref]

1953 (3)

E. Vigroux, Ann. Phys. 8, 709 (1953).

E. C. Y. Inn, Y. Tanaka, J. Opt. Soc. Am. 43, 870 (1953).
[Crossref]

Y. Tanaka, E. C. Y. Inn, K. Watanabe, J. Chem. Phys. 21, 1651 (1953).
[Crossref]

Altshuler, T. L.

T. L. Altshuler, “Infrared Transmission and Background Radiation by Clear Atmospheres”, General Electric M.S.V.D. Doe. No. 61SD199, December1961.

Ban, G.

G. Ban, E. L. Hubbard, LAS-TR-199-37 and 48, Laboratories for Applied Science, University of Chicago, 1963.

Barth, C. A.

C. A. Barth, Planet. Space Sci. 14, 623 (1966).
[Crossref]

R. T. Brinkmann, A. E. S. Green, C. A. Barth, “A Digitalized Solar Ultraviolet Solar Spectrum”, JPL Technical Report TR 32-951, August1966.

Brinkmann, R. T.

R. T. Brinkmann, A. E. S. Green, C. A. Barth, “A Digitalized Solar Ultraviolet Solar Spectrum”, JPL Technical Report TR 32-951, August1966.

R. T. Brinkmann, thesis, University of Florida, 1966.

Dalgarno, A.

A. Dalgarno, Geophysics Corp. of America Report, 1963.

Detwiler, C. R.

C. R. Detwiler, D. L. Garrett, J. D. Purcell, R. Tousey, Ann. Geophys. 17, 263 (1961).

Ditchburn, R. W.

R. W. Ditchburn, P. A. Young, J. Atmos. Terr. Phys. 24, 127 (1962).
[Crossref]

Dowling, J.

J. Dowling, A. E. S. Green, in Ref. 7.

Elliot, D. D.

R. D. Rawcliffe, D. D. Elliot, J. Geophys. Res. 71, 5077 (1966).
[Crossref]

Elterman, L.

L. Elterman, “Atmospheric Attenuation Model, 1964, in the Ultraviolet, Visible, and Infrared Regions for Altitudes to 50 km”, Environmental Research Papers, Number 46, July1964.

Friedman, R. M.

R. D. Raweliffe, G. E. Meloy, R. M. Friedman, E. H. Rogers, J. Geophys. Res. 68, 6425 (1963).
[Crossref]

Garrett, D. L.

C. R. Detwiler, D. L. Garrett, J. D. Purcell, R. Tousey, Ann. Geophys. 17, 263 (1961).

Green, A. E. S.

J. Dowling, A. E. S. Green, in Ref. 7.

A. E. S. Green, ERR-AN-185, Space Science Laboratory, General Dynamics Convair (July1962); Appl. Opt. 3, 203 (1964).

R. T. Brinkmann, A. E. S. Green, C. A. Barth, “A Digitalized Solar Ultraviolet Solar Spectrum”, JPL Technical Report TR 32-951, August1966.

Griggs, M.

M. Griggs, in Ref. 7, Chap. 4.

Hochstim, A. R.

A. R. Hochstim, “Effective Collision Frequencies and Electric Conductivities of Weakly Ionized N2, O2N, O, NO, and Dry Air”, IDA/HG 64-2554, Research Paper P-124, February1965.

Hubbard, E. L.

G. Ban, E. L. Hubbard, LAS-TR-199-37 and 48, Laboratories for Applied Science, University of Chicago, 1963.

Inn, E. C. Y.

E. C. Y. Inn, Y. Tanaka, J. Opt. Soc. Am. 43, 870 (1953).
[Crossref]

Y. Tanaka, E. C. Y. Inn, K. Watanabe, J. Chem. Phys. 21, 1651 (1953).
[Crossref]

Johnson, F. S.

N. Wilson, R. Tousey, J. D. Purcell, F. S. Johnson, C. E. Moore, Astrophys. J., 119, 590 (1954).
[Crossref]

Jursa, A. S.

A. S. Jursa, M. Nakamura, Y. Tanaka, J. Geophys. Res. 70, 2699 (1965).
[Crossref]

Kaplan, L. D.

L. D. Kaplan, in Chemical Reactions in the Lower and Upper Atmosphere, R. D. Cadle, Ed. (Interscience Publishers, New York, 1966), Chap. 7.

Malitson, H. H.

H. H. Malitson, J. D. Purcell, R. Tousey, C. E. Moore, Astrophys. J., 132, 746 (1960).
[Crossref]

Meloy, G. E.

R. D. Raweliffe, G. E. Meloy, R. M. Friedman, E. H. Rogers, J. Geophys. Res. 68, 6425 (1963).
[Crossref]

Moore, C. E.

H. H. Malitson, J. D. Purcell, R. Tousey, C. E. Moore, Astrophys. J., 132, 746 (1960).
[Crossref]

N. Wilson, R. Tousey, J. D. Purcell, F. S. Johnson, C. E. Moore, Astrophys. J., 119, 590 (1954).
[Crossref]

Nakamura, M.

A. S. Jursa, M. Nakamura, Y. Tanaka, J. Geophys. Res. 70, 2699 (1965).
[Crossref]

Purcell, J. D.

C. R. Detwiler, D. L. Garrett, J. D. Purcell, R. Tousey, Ann. Geophys. 17, 263 (1961).

H. H. Malitson, J. D. Purcell, R. Tousey, C. E. Moore, Astrophys. J., 132, 746 (1960).
[Crossref]

N. Wilson, R. Tousey, J. D. Purcell, F. S. Johnson, C. E. Moore, Astrophys. J., 119, 590 (1954).
[Crossref]

Rawcliffe, R. D.

R. D. Rawcliffe, D. D. Elliot, J. Geophys. Res. 71, 5077 (1966).
[Crossref]

Raweliffe, R. D.

R. D. Raweliffe, G. E. Meloy, R. M. Friedman, E. H. Rogers, J. Geophys. Res. 68, 6425 (1963).
[Crossref]

Rogers, E. H.

R. D. Raweliffe, G. E. Meloy, R. M. Friedman, E. H. Rogers, J. Geophys. Res. 68, 6425 (1963).
[Crossref]

Singer, S. F.

S. F. Singer, Advan. Geophys. 3, 301 (1956).
[Crossref]

Tanaka, Y.

A. S. Jursa, M. Nakamura, Y. Tanaka, J. Geophys. Res. 70, 2699 (1965).
[Crossref]

E. C. Y. Inn, Y. Tanaka, J. Opt. Soc. Am. 43, 870 (1953).
[Crossref]

Y. Tanaka, E. C. Y. Inn, K. Watanabe, J. Chem. Phys. 21, 1651 (1953).
[Crossref]

Tousey, R.

C. R. Detwiler, D. L. Garrett, J. D. Purcell, R. Tousey, Ann. Geophys. 17, 263 (1961).

H. H. Malitson, J. D. Purcell, R. Tousey, C. E. Moore, Astrophys. J., 132, 746 (1960).
[Crossref]

N. Wilson, R. Tousey, J. D. Purcell, F. S. Johnson, C. E. Moore, Astrophys. J., 119, 590 (1954).
[Crossref]

Twoney, S.

S. Twoney, Geophys. Res. 66, 2153 (1961).
[Crossref]

Vigroux, E.

E. Vigroux, Ann. Phys. 8, 709 (1953).

Watanabe, K.

Y. Tanaka, E. C. Y. Inn, K. Watanabe, J. Chem. Phys. 21, 1651 (1953).
[Crossref]

Wilson, N.

N. Wilson, R. Tousey, J. D. Purcell, F. S. Johnson, C. E. Moore, Astrophys. J., 119, 590 (1954).
[Crossref]

Young, P. A.

R. W. Ditchburn, P. A. Young, J. Atmos. Terr. Phys. 24, 127 (1962).
[Crossref]

Advan. Geophys. (1)

S. F. Singer, Advan. Geophys. 3, 301 (1956).
[Crossref]

Ann. Geophys. (1)

C. R. Detwiler, D. L. Garrett, J. D. Purcell, R. Tousey, Ann. Geophys. 17, 263 (1961).

Ann. Phys. (1)

E. Vigroux, Ann. Phys. 8, 709 (1953).

Astrophys. J. (2)

H. H. Malitson, J. D. Purcell, R. Tousey, C. E. Moore, Astrophys. J., 132, 746 (1960).
[Crossref]

N. Wilson, R. Tousey, J. D. Purcell, F. S. Johnson, C. E. Moore, Astrophys. J., 119, 590 (1954).
[Crossref]

Geophys. Res. (1)

S. Twoney, Geophys. Res. 66, 2153 (1961).
[Crossref]

J. Atmos. Terr. Phys. (1)

R. W. Ditchburn, P. A. Young, J. Atmos. Terr. Phys. 24, 127 (1962).
[Crossref]

J. Chem. Phys. (1)

Y. Tanaka, E. C. Y. Inn, K. Watanabe, J. Chem. Phys. 21, 1651 (1953).
[Crossref]

J. Geophys. Res. (3)

A. S. Jursa, M. Nakamura, Y. Tanaka, J. Geophys. Res. 70, 2699 (1965).
[Crossref]

R. D. Rawcliffe, D. D. Elliot, J. Geophys. Res. 71, 5077 (1966).
[Crossref]

R. D. Raweliffe, G. E. Meloy, R. M. Friedman, E. H. Rogers, J. Geophys. Res. 68, 6425 (1963).
[Crossref]

J. Opt. Soc. Am. (1)

Planet. Space Sci. (1)

C. A. Barth, Planet. Space Sci. 14, 623 (1966).
[Crossref]

Other (17)

U.S. Standard Atmosphere, 1962, NASA, USAF and U.S. Weather Bureau, Washington, D.C. (U.S. Government Printing Office, Washington, D.C., 1962).

A. Dalgarno, Geophysics Corp. of America Report, 1963.

A. R. Hochstim, “Effective Collision Frequencies and Electric Conductivities of Weakly Ionized N2, O2N, O, NO, and Dry Air”, IDA/HG 64-2554, Research Paper P-124, February1965.

Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, M. Abramowitz, I. A. Stegun, Eds., NBS Applied Math. Series, 55, Washington, D.C. (U.S. Government Printing Office, Washington, D.C., 1965).

A. E. S. Green, Ed., The Middle Ultraviolet, Its Science and Technology (John Wiley & Sons, Inc., New York, 1966).

R. T. Brinkmann, A. E. S. Green, C. A. Barth, “A Digitalized Solar Ultraviolet Solar Spectrum”, JPL Technical Report TR 32-951, August1966.

T. L. Altshuler, “Infrared Transmission and Background Radiation by Clear Atmospheres”, General Electric M.S.V.D. Doe. No. 61SD199, December1961.

L. Elterman, “Atmospheric Attenuation Model, 1964, in the Ultraviolet, Visible, and Infrared Regions for Altitudes to 50 km”, Environmental Research Papers, Number 46, July1964.

U.S. Air Force Geophysics Research Directorate, Handbook of Geophysics (The Macmillan Company, New York, 1961).

Reference 7, Chap. 5.

M. Griggs, in Ref. 7, Chap. 4.

S. L. Valley, Ed., “Atmospheric Composition”, Handbook of Geophysics and Space Environments (McGraw-Hill Book Co., New York, 1965), Chap. 6.

J. Dowling, A. E. S. Green, in Ref. 7.

R. T. Brinkmann, thesis, University of Florida, 1966.

L. D. Kaplan, in Chemical Reactions in the Lower and Upper Atmosphere, R. D. Cadle, Ed. (Interscience Publishers, New York, 1966), Chap. 7.

A. E. S. Green, ERR-AN-185, Space Science Laboratory, General Dynamics Convair (July1962); Appl. Opt. 3, 203 (1964).

G. Ban, E. L. Hubbard, LAS-TR-199-37 and 48, Laboratories for Applied Science, University of Chicago, 1963.

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 (8)

Fig. 1
Fig. 1

Basic geometric relationships. A photon from the sun is scattered from dV into the detector.

Fig. 2
Fig. 2

Basic geometric quantities involved in attentuation to and from the scattering volume.

Fig. 3
Fig. 3

Standard oxygen, ozone (Wp = 0.32, Yp = 23.0, H = 4.0), and air density distribution functions.

Fig. 4
Fig. 4

O2 and O3 absorption coefficients and air attenuation coefficient. The O2 curve is for zero pressure.

Fig. 5
Fig. 5

Comparison of the present calculations to Green’s 1962 results. Divergence below 2200 Å is due to oxygen absorption. - - - Green’s 1962 results. —present results.

Fig. 6
Fig. 6

Calculated spectra, described in Table II, illustrating the effects of varying the geometric factors and ozone parameters.

Fig. 7
Fig. 7

Spectra obtained from rocket flight of 17 November 1963. Horizontal axes are wavelength scales, in angstroms; vertical axes are proportional to the logarithm of the intensity. Figures marked on each spectrum give the approximate time (after launch) in seconds, altitude in kilometers, and line-of-sight zenith angle, in degrees. The data have been manually smoothed to remove the electronic noise.

Fig. 8
Fig. 8

Fits to the rocket spectra with Wp = 0.32, Yp = 12, H = 6. Data (jagged curves) have had the spectral calibration and solar line structure divided out.

Tables (3)

Tables Icon

Table I Solar Spectral Intensity at 4-Å Intervals

Tables Icon

Table II Geometric and Ozone Parameters

Tables Icon

Table III Spectra Description

Equations (37)

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

I = β Δ Ω A slit = H ( λ ) k a ( λ ) ( 3 / 16 π ) · ( 1 + cos 2 ψ ) s = 0 D ρ a ( A ) ρ a ( 0 ) T T Δ Ω d V .
I = H ( λ ) k a ( λ ) ( 3 / 16 π ) × ( 1 + cos 2 ψ ) · A slit Δ Ω s = 0 D ρ a ( A ) ρ a ( 0 ) T T d s ,
d V = Δ Ω ( D - s ) 2 d s
Δ Ω = A slit ( D - s ) 2 ,
I = H ( λ ) k a ( λ ) ( 3 / 16 π ) ( 1 + cos 2 ψ ) A slit Δ Ω s = 0 D ρ a ( A ) ρ a ( 0 ) × exp { - a = A A D [ k 3 ( λ ) ρ 3 ( a ) + k 2 ( λ , a ) ρ 2 ( a ) + k a ( λ ) ρ a ( a ) ] × sec ( a ) d a } exp { - a = A [ k 3 ( λ ) ρ 3 ( a ) + k 2 ( λ , a ) ρ 2 ( a ) + k a ( λ ) ρ a ( a ) ] sec χ ( a ) d a } d s .
I = H ( λ ) k a ( λ ) ( 3 / 16 π ) ( 1 + cos 2 ψ ) A slit Δ Ω s = 0 D ρ a ( A ) ρ a ( 0 ) × { exp - [ k 3 ( λ ) ( t 3 ( A ) - t 3 ( A D ) ) + k 2 ( λ ) ( t 2 ( A ) - t 2 ( A D ) ) × { exp - [ k 3 ( λ ) ( t 3 ( A ) - t 3 ( A D ) ) + k 2 ( λ ) ( t 2 ( A ) - t 2 ( A D ) ) + k a ( λ ) ( t a ( A ) - t a ( A D ) ) ] sec } · exp { - [ k 3 ( λ ) t 3 ( A ) + k 2 ( λ ) t 2 ( A ) + k a ( λ ) t a ( A ) ] sec χ } d s ,
ρ 3 ( a ) = W p H exp [ ( a - Y p ) / H ] { [ 1 + exp ( a - Y p ) / H ] } 2 ,
ρ 2 ( a ) = [ 14 , 170 - 22 , 020 A tan ( a - 93 ) 3 / π ] · exp { - a [ 0.138 - 0.069 exp ( - 0.5 a ) ] } ,
ρ a ( a ) = 10 5 exp { - a [ 0.127 + 0.015 ( 1 - exp [ - 0.2 ( a - 15 ) ] · ( a - 15 ) / ( a - 15 + 0.0000001 ) ] } .
ρ a ( a ) = 10 5 exp ( - 0.142 a )
σ ( P , λ ) = σ 0 ( λ ) + P · κ ( λ ) ,
ρ a ( a ) < = 100 , 000 e - 0.112 a e - 0.015 a · e ( a - 15 ) / 5
ρ a ( a ) > = 100 , 000 e - 0.142 a e 0.015 a · e ( 15 - a ) / 5
x = 1 + x + x 2 / 2 ! + x 3 / 3 ! ,
P ( a ) = y = 0 a ρ a ( y ) < d y
P ( a ) = P < ( 15 ) + y = 15 a ρ a ( y ) > d y ,
P < ( 15 ) = y = 0 15 ρ a ( y ) < d y .
k a ( λ ) = a λ b ,
cos ψ = cos θ cos Φ + sin θ sin Φ cos ( Δ A Z ) .
( R + A D ) 2 + D 2 + 2 ( R + A D ) D cos Φ = R 2
( R + A D ) 2 + ( D - s ) 2 + 2 ( R + A D ) ( D - s ) cos Φ = ( R + A ) 2 .
D = - ( R + A D ) cos Φ - [ ( R + A D ) 2 cos 2 Φ - 2 R A D - A D 2 ] ½ = - ( R + A D ) cos Φ - S Q ,
S Q = [ ( R + A D ) cos 2 Φ - 2 R A D - A D 2 ] ½ .
A = ( R 2 + s 2 + 2 s · S Q - R ) ½ .
s = - S Q + [ ( S Q ) 2 + A 2 + 2 A · R ] ½ ,
sec = ( R + L 2 ) [ ( R + L 2 ) 2 - ( R + A D ) 2 sin 2 Φ ] ½ .
cos α = cos θ cos γ + sin θ sin γ cos ( Δ A Z ) ,
cos γ = ( R + A D ) + ( D - s ) cos Φ ( R + A )
sin γ = [ ( D - s ) sin Φ ] / ( R + A ) ,
cos α = R + A D + ( D - s ) cos Φ ( R + A ) cos θ + ( D - s ) sin Φ ( R + A ) sin θ cos ( Δ A Z ) .
sin χ ( R + A ) = [ 1 - cos 2 α ] ½ ( R + L 1 ) ,
sec χ = ( R + L 1 ) ½ [ ( R + L 1 ) 2 - ( R + A ) 2 ( 1 - cos α ) ] ½ .
0 f ( x ) e - x d x i = 1 u W i f ( x i ) ,
z / C = log ( B - A ) / x - A
d z = - C d x / ( x - A ) ,
k 3 ( λ ) ρ 3 ( a ) sec η ( a ) d a ,
H ( λ ) = 1.00 × 10 - 2 exp ( λ - 2540 250 ) watts cm 2 μ .

Metrics