Abstract

The accuracy of spectroscopic absorptance measurements can be seriously affected by the presence of absorbing species in the atmosphere anywhere in the optical train. The error is due to the band-pass nature of a monochromator, and therefore is just as severe when a double-beam spectrometer is used as when a single-beam spectrometer is used.

Using a method recently developed by Sakai for the calculation of the integrated absorptance of a pair of overlapping absorption lines, we have calculated the error in the measured integrated absorptance of a sample gas which contains H2O or CO2. The method used places no restrictions on the half-width or strength of either line. Factors have been derived for correcting the measured absorptance in a number of experimentally important cases. The calculated correction factors give results which are in good agreement with experiments made using a spectrometer in which the atmospheric H2O and CO2 were removed from the optical train.

© 1964 Optical Society of America

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References

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  1. F. Paschen, Ann. Physik 50, 409 (1893).
    [Crossref]
  2. C. P. Courtoy, Can. J. Phys. 5, 608 (1957).
    [Crossref]
  3. W. M. Elsasser, Heat Transfer by Infrared Radiation in the Atmosphere (Harvard University Press, Cambridge, Massachusetts, 1942).
  4. G. P. Kuiper, Astrophys. J. 106, 252 (1947).
  5. W. M. Sinton, Planets and Satellites (University of Chicago Press, Chicago, 1961).
  6. G. N. Plass, Ann. N. Y. Acad. Sci. 95, 61 (1961).
    [Crossref]
  7. J. N. Howard, D. E. Burch, and D. Williams, J. Opt. Soc. Am. 46, 186, 237, 242, 334, 452 (1956).
    [Crossref]
  8. H. J. Babrov and R. H. Tourin, J. Quant. Spectry. Radiative Transfer 3, 17 (1963).
    [Crossref]
  9. G. J. Penzias, G. Jordan Maclay, H. J. Babrov, and NASA CR 1, “Final Report on Phase II of Contract NAS 3-1542,” NASA Lewis Research Center, Cleveland, Ohio (1962).
  10. D. E. Burch, D. Gryvanak, and D. Williams, AFCRL-255, Geophysics Research Directorate, Hanscom Field, Bedford, Massachusetts (1960).
  11. D. E. Burch and D. Gryvnak, Technical Report, Contract Nonr 3560(00) (1962).
  12. H. J. Babrov, J. Opt. Soc. Am. 51, 171 (1961).
    [Crossref]
  13. H. Sakai, Johns Hopkins University, Laboratory for Astrophysics and Meteorology, Progress Report, Contract Nonr 248(58) (1962).
  14. H. Sakai and F. Stauffer, J. Opt. Soc. Am. 53, 507 (1963).
  15. L. D. Kaplan and D. Eggers, J. Chem. Phys. 25, 876 (1956).
    [Crossref]
  16. R. Ladenburg and F. Reiche, Ann. Physik 42, 181 (1913).
    [Crossref]
  17. W. S. Benedict, R. Herman, G. E. Moore, and S. Silverman, Can. J. Phys. 34, 830 (1956).
    [Crossref]
  18. W. S. Benedict (private communication, 1963).
  19. R. H. Schwendeman and V. W. Laurie, Tables of Line Strengths for Rotational Transitions of Asymmetric Rotor Molecules (Pergamon Press, Inc., New York, 1958).
  20. W. S. Benedict and L. D. Kaplan, J. Chem. Phys. 30, 388 (1959).
  21. U. P. Oppenheim and Y. Ben-Aryeh, J. Opt. Soc. Am. 53, 344 (1963).
    [Crossref]
  22. G. N. Plass, J. Opt. Soc. Am. 48, 690 (1958).
    [Crossref]

1963 (3)

H. J. Babrov and R. H. Tourin, J. Quant. Spectry. Radiative Transfer 3, 17 (1963).
[Crossref]

H. Sakai and F. Stauffer, J. Opt. Soc. Am. 53, 507 (1963).

U. P. Oppenheim and Y. Ben-Aryeh, J. Opt. Soc. Am. 53, 344 (1963).
[Crossref]

1961 (2)

H. J. Babrov, J. Opt. Soc. Am. 51, 171 (1961).
[Crossref]

G. N. Plass, Ann. N. Y. Acad. Sci. 95, 61 (1961).
[Crossref]

1959 (1)

W. S. Benedict and L. D. Kaplan, J. Chem. Phys. 30, 388 (1959).

1958 (1)

1957 (1)

C. P. Courtoy, Can. J. Phys. 5, 608 (1957).
[Crossref]

1956 (3)

J. N. Howard, D. E. Burch, and D. Williams, J. Opt. Soc. Am. 46, 186, 237, 242, 334, 452 (1956).
[Crossref]

L. D. Kaplan and D. Eggers, J. Chem. Phys. 25, 876 (1956).
[Crossref]

W. S. Benedict, R. Herman, G. E. Moore, and S. Silverman, Can. J. Phys. 34, 830 (1956).
[Crossref]

1947 (1)

G. P. Kuiper, Astrophys. J. 106, 252 (1947).

1913 (1)

R. Ladenburg and F. Reiche, Ann. Physik 42, 181 (1913).
[Crossref]

1893 (1)

F. Paschen, Ann. Physik 50, 409 (1893).
[Crossref]

Babrov, H. J.

H. J. Babrov and R. H. Tourin, J. Quant. Spectry. Radiative Transfer 3, 17 (1963).
[Crossref]

H. J. Babrov, J. Opt. Soc. Am. 51, 171 (1961).
[Crossref]

G. J. Penzias, G. Jordan Maclay, H. J. Babrov, and NASA CR 1, “Final Report on Phase II of Contract NAS 3-1542,” NASA Lewis Research Center, Cleveland, Ohio (1962).

Ben-Aryeh, Y.

Benedict, W. S.

W. S. Benedict and L. D. Kaplan, J. Chem. Phys. 30, 388 (1959).

W. S. Benedict, R. Herman, G. E. Moore, and S. Silverman, Can. J. Phys. 34, 830 (1956).
[Crossref]

W. S. Benedict (private communication, 1963).

Burch, D. E.

J. N. Howard, D. E. Burch, and D. Williams, J. Opt. Soc. Am. 46, 186, 237, 242, 334, 452 (1956).
[Crossref]

D. E. Burch, D. Gryvanak, and D. Williams, AFCRL-255, Geophysics Research Directorate, Hanscom Field, Bedford, Massachusetts (1960).

D. E. Burch and D. Gryvnak, Technical Report, Contract Nonr 3560(00) (1962).

Courtoy, C. P.

C. P. Courtoy, Can. J. Phys. 5, 608 (1957).
[Crossref]

Eggers, D.

L. D. Kaplan and D. Eggers, J. Chem. Phys. 25, 876 (1956).
[Crossref]

Elsasser, W. M.

W. M. Elsasser, Heat Transfer by Infrared Radiation in the Atmosphere (Harvard University Press, Cambridge, Massachusetts, 1942).

Gryvanak, D.

D. E. Burch, D. Gryvanak, and D. Williams, AFCRL-255, Geophysics Research Directorate, Hanscom Field, Bedford, Massachusetts (1960).

Gryvnak, D.

D. E. Burch and D. Gryvnak, Technical Report, Contract Nonr 3560(00) (1962).

Herman, R.

W. S. Benedict, R. Herman, G. E. Moore, and S. Silverman, Can. J. Phys. 34, 830 (1956).
[Crossref]

Howard, J. N.

Jordan Maclay, G.

G. J. Penzias, G. Jordan Maclay, H. J. Babrov, and NASA CR 1, “Final Report on Phase II of Contract NAS 3-1542,” NASA Lewis Research Center, Cleveland, Ohio (1962).

Kaplan, L. D.

W. S. Benedict and L. D. Kaplan, J. Chem. Phys. 30, 388 (1959).

L. D. Kaplan and D. Eggers, J. Chem. Phys. 25, 876 (1956).
[Crossref]

Kuiper, G. P.

G. P. Kuiper, Astrophys. J. 106, 252 (1947).

Ladenburg, R.

R. Ladenburg and F. Reiche, Ann. Physik 42, 181 (1913).
[Crossref]

Laurie, V. W.

R. H. Schwendeman and V. W. Laurie, Tables of Line Strengths for Rotational Transitions of Asymmetric Rotor Molecules (Pergamon Press, Inc., New York, 1958).

Moore, G. E.

W. S. Benedict, R. Herman, G. E. Moore, and S. Silverman, Can. J. Phys. 34, 830 (1956).
[Crossref]

Oppenheim, U. P.

Paschen, F.

F. Paschen, Ann. Physik 50, 409 (1893).
[Crossref]

Penzias, G. J.

G. J. Penzias, G. Jordan Maclay, H. J. Babrov, and NASA CR 1, “Final Report on Phase II of Contract NAS 3-1542,” NASA Lewis Research Center, Cleveland, Ohio (1962).

Plass, G. N.

G. N. Plass, Ann. N. Y. Acad. Sci. 95, 61 (1961).
[Crossref]

G. N. Plass, J. Opt. Soc. Am. 48, 690 (1958).
[Crossref]

Reiche, F.

R. Ladenburg and F. Reiche, Ann. Physik 42, 181 (1913).
[Crossref]

Sakai, H.

H. Sakai and F. Stauffer, J. Opt. Soc. Am. 53, 507 (1963).

H. Sakai, Johns Hopkins University, Laboratory for Astrophysics and Meteorology, Progress Report, Contract Nonr 248(58) (1962).

Schwendeman, R. H.

R. H. Schwendeman and V. W. Laurie, Tables of Line Strengths for Rotational Transitions of Asymmetric Rotor Molecules (Pergamon Press, Inc., New York, 1958).

Silverman, S.

W. S. Benedict, R. Herman, G. E. Moore, and S. Silverman, Can. J. Phys. 34, 830 (1956).
[Crossref]

Sinton, W. M.

W. M. Sinton, Planets and Satellites (University of Chicago Press, Chicago, 1961).

Stauffer, F.

H. Sakai and F. Stauffer, J. Opt. Soc. Am. 53, 507 (1963).

Tourin, R. H.

H. J. Babrov and R. H. Tourin, J. Quant. Spectry. Radiative Transfer 3, 17 (1963).
[Crossref]

Williams, D.

J. N. Howard, D. E. Burch, and D. Williams, J. Opt. Soc. Am. 46, 186, 237, 242, 334, 452 (1956).
[Crossref]

D. E. Burch, D. Gryvanak, and D. Williams, AFCRL-255, Geophysics Research Directorate, Hanscom Field, Bedford, Massachusetts (1960).

Ann. N. Y. Acad. Sci. (1)

G. N. Plass, Ann. N. Y. Acad. Sci. 95, 61 (1961).
[Crossref]

Ann. Physik (2)

F. Paschen, Ann. Physik 50, 409 (1893).
[Crossref]

R. Ladenburg and F. Reiche, Ann. Physik 42, 181 (1913).
[Crossref]

Astrophys. J. (1)

G. P. Kuiper, Astrophys. J. 106, 252 (1947).

Can. J. Phys. (2)

C. P. Courtoy, Can. J. Phys. 5, 608 (1957).
[Crossref]

W. S. Benedict, R. Herman, G. E. Moore, and S. Silverman, Can. J. Phys. 34, 830 (1956).
[Crossref]

J. Chem. Phys. (2)

L. D. Kaplan and D. Eggers, J. Chem. Phys. 25, 876 (1956).
[Crossref]

W. S. Benedict and L. D. Kaplan, J. Chem. Phys. 30, 388 (1959).

J. Opt. Soc. Am. (5)

J. Quant. Spectry. Radiative Transfer (1)

H. J. Babrov and R. H. Tourin, J. Quant. Spectry. Radiative Transfer 3, 17 (1963).
[Crossref]

Other (8)

G. J. Penzias, G. Jordan Maclay, H. J. Babrov, and NASA CR 1, “Final Report on Phase II of Contract NAS 3-1542,” NASA Lewis Research Center, Cleveland, Ohio (1962).

D. E. Burch, D. Gryvanak, and D. Williams, AFCRL-255, Geophysics Research Directorate, Hanscom Field, Bedford, Massachusetts (1960).

D. E. Burch and D. Gryvnak, Technical Report, Contract Nonr 3560(00) (1962).

W. M. Elsasser, Heat Transfer by Infrared Radiation in the Atmosphere (Harvard University Press, Cambridge, Massachusetts, 1942).

W. M. Sinton, Planets and Satellites (University of Chicago Press, Chicago, 1961).

H. Sakai, Johns Hopkins University, Laboratory for Astrophysics and Meteorology, Progress Report, Contract Nonr 248(58) (1962).

W. S. Benedict (private communication, 1963).

R. H. Schwendeman and V. W. Laurie, Tables of Line Strengths for Rotational Transitions of Asymmetric Rotor Molecules (Pergamon Press, Inc., New York, 1958).

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Figures (6)

Fig. 1
Fig. 1

The effect of flushing the optical path of a double-beam spectrometer with nitrogen. The absorption curves for the 4.3-μ CO2 bands illustrate the error in the measured absorptance due to the air in the optical path of the spectrometer. Curve A: optical path open to atmosphere. Curve B: optical path flushed with N2. Pe=740 mm Hg. W=0.022 atm cm.

Fig. 2
Fig. 2

The effect of flushing the optical path of a single-beam spectrometer with nitrogen. The measured absorptance in the 4.3-μ spectral region of a sample of CO2 is shown with the optical train flushed (B) and with the optical train open to the atmosphere (A). The 5-in.-long sample cell contained CO2 at a pressure of 50 mm Hg and a temperature of 298°K.

Fig. 3
Fig. 3

The effect of the finite resolution of a spectrometer on the measured spectrum of closely spaced lines. Curve A: true intensity. Curve B: spectrometer trace. Δν represents spectral slitwidth.

Fig. 4
Fig. 4

Graphs of Wapparent/Wcorrected vs Watm/Wcombined for various combinations of sample and atmospheric lines. These curves are used to correct the apparent integrated absorptance of a sample line for the effects of atmospheric absorption.

Fig. 5
Fig. 5

Spectrometer traces illustrating the synthetic atmosphere experiment using two absorption cells in series. The absorption from one cell filled with HBr produced Trace A, the atmospheric trace, while the absorption from the other cell filled with HBr produced Trace S, the sample trace. The absorption from both filled cells in series produced the combined trace, Trace C. The trace labeled I0 was obtained with both cells evacuated.

Fig. 6
Fig. 6

Correction curve, based on a random band model, for a high-x atmospheric line and a high-x sample line. The crosses are experimental points. The ordinate scale at the left goes with the correction curve; the ordinate scale at the right is to be used with the experimental points. The numerical values of both ordinate scales are the same.

Tables (2)

Tables Icon

Table I Comparison of experimental results on HBr with the results of applying the correction formula.

Tables Icon

Table II Comparison of experimental results on hot H2O with the results of applying the correction formula.

Equations (29)

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Δ ν τ 1 ( ν ) d ν Δ ν τ 2 ( ν ) d ν Δ ν τ 1 ( ν ) τ 2 ( ν ) d ν ,
W combined = W 1 + W 2 - Δ ,
Δ = { 4 π γ 1 γ 2 f ( x 1 ) f ( x 2 ) / [ γ 1 x 1 f ( x 1 ) + γ 2 x 2 f ( x 2 ) ] } × ( 1 + { δ ν / [ γ 1 x 1 f ( x 1 ) + γ 2 x 2 f ( x 2 ) ] } 2 ) - 1 .
x = S L / 2 π γ ,
f ( x ) = x e - x [ J 0 ( i x ) - i J 1 ( i x ) ] ,
W = 2 π γ f ( x ) .
f ( x ) = ( 2 π x ) 1 2 ( 1 - 1 8 x + ) .
Δ = 4 π W atm W true W atm + W true .
f ( x ) = x [ 1 - ( x / 2 ) + ] ,
Δ = 2 W atm W true ( W atm / x atm ) + ( W true / x sample ) ,
Δ = 4 π W true W atm W true + ( 2 W atm / x atm ) .
- ln τ = W / d ,
n = W atm / W combined ,
k = W corrected / W combined .
k 2 - k + n 2 - n + 2 n k ( 1 - 2 / π ) = 0.
W apparent / W corrected = ( 1 - n ) / k .
π n 2 + 2 k n [ ( 1 / x sample ) - 2 ] - π n ( 1 - k ) - 2 k ( 1 - k ) / x sample = 0.
( n + k - 1 ) [ ( n / x atm ) + ( k / x sample ) ] - 2 n k = 0.
W combined = W 1 + W 2 - Δ ,
γ 1 x 1 / f ( x 1 ) ,
f ( x 1 ) ( 2 x 1 / π ) 1 2 .
γ 1 x 1 / f ( x 1 ) = [ ( π / 2 ) γ 1 2 x 1 ] 1 2 ,
γ 1 x 1 / f ( x 1 ) = 1 2 ( S 1 l 1 γ 1 ) 1 2 .
W 1 = 2 π γ 1 [ ( 2 / π ) x 1 ] 1 2 .
W 1 = 2 ( S 1 l 1 γ 1 ) 1 2 .
γ 1 x 1 / f ( x 1 ) = W 1 / 4.
γ 2 x 2 / f ( x 2 ) = W 2 / 4.
Δ = 4 π γ 1 γ 2 f ( x 1 ) f ( x 2 ) ( W 1 / 4 ) + ( W 2 / 4 ) .
Δ = ( 4 / π ) [ W 1 W 2 / ( W 1 + W 2 ) ] .