Abstract

Methods of measuring the concentration of atmospheric pollutants by laser absorption spectroscopy, such as differential absorption lidar (DIAL) and integrated long-path techniques, all rely on the validity of Beer’s exponential absorption law. It is shown here that departures from this law occur if the probing laser has a bandwidth larger than the wavelength scale of structure in the absorption spectrum of the pollutant. A comprehensive experimental and theoretical treatment of the errors resulting from these departures is presented for the particular case of SO2 monitoring at ~300 nm. It is shown that the largest error occurs where the initial calibration measurement of absorption cross section is made at low pressure, in which case errors in excess of 5% in the cross section could occur for laser bandwidths >0.01 nm. Atmospheric measurements by DIAL or long-path methods are in most cases affected less, because pressure broadening smears the spectral structure, but when measuring high concentrations errors can exceed 5%.

© 1984 Optical Society of America

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References

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  1. E. D. Hinkley, Ed., Laser Monitoring of the Atmosphere, Vol. 14 (Springer, Berlin, 1976).
    [CrossRef]
  2. J. G. Hawley, L. D. Fletcher, G. F. Wallace, Optical and Laser Remote Sensing, Vol. 39, D. K. Killinger, A. Mooradian, Ed. (Springer, Berlin, 1983), pp. 128–137.
  3. W. B. Grant, R. T. Menzies, J. Air. Pollut. Control. Assoc. 33, 187 (1983); R. L. Byer, M. Garbuny, Appl. Opt. 12, 1496 (1973).
    [CrossRef] [PubMed]
  4. C. Cahen, G. Megie, J. Quant. Spectrosc. Radiat. Transfer. 25, 151 (1981); C. L. Korb, C. Y. Weng, in Proceedings, Eleventh International Laser Radar Conference, Madison, Wisc. (American Meteorological Society, 1982).
    [CrossRef]
  5. H. Walther, Ed., Laser Spectrosopy of Atoms and Molecules, Vol. 2 (Springer, Berlin, 1976).
    [CrossRef]
  6. P. T. Woods, B. W. Jolliffe, B. R. Marx, Opt. Commun. 33, 281 (1980).
    [CrossRef]
  7. D. J. Brassington, Appl. Opt. 20, 3774 (1981).
    [CrossRef] [PubMed]
  8. R. T. H. Collis, P. B. Russell, Laser Monitoring of the Atmosphere, Vol. 14, E. D. Hinkley, Ed., (Springer, Berlin, 1976), pp. 72–151.
    [CrossRef]
  9. P. Warneck, F. F. Marmo, J. O. Sullivan, J. Chem. Phys. 40, 1132 (1964).
    [CrossRef]
  10. R. T. Thompson, J. M. Hoell, W. R. Wade, J. Appl. Phys. 46, 3040 (1975).
    [CrossRef]
  11. B. R. Marx, K. P. Birch, R. C. Felton, B. W. Jolliffe, W. R. C. Rowley, P. T. Woods, Opt. Commun. 33, 287 (1980).
    [CrossRef]
  12. E. V. Browell et al., Appl. Opt. 22, 522 (1983).
    [CrossRef] [PubMed]
  13. R. S. Adrain, D. J. Brassington, S. Sutton, R. H. Varey, Opt. Quantum. Electron. 11, 253 (1979).
    [CrossRef]
  14. R. M. Hoff, M. M. Millan, J. Air Pollut. Control. Assoc. 31, 381 (1981).
    [CrossRef]
  15. K. W. Rothe, U. Brinkman, H. Walther, Appl. Phys. 4, 181 (1974).
    [CrossRef]
  16. T. D. Wilkerson, B. Ercoli, F. S. Tomkins, U. Maryland, Tech. Note BN-784, (1974).
  17. O. Uchino, M. Maeda, T. Shibata, M. Hirono, M. Fujiwara, Appl. Opt. 19, 4175 (1980).
    [CrossRef] [PubMed]
  18. C. Cahen, J. Pelon, P. Flamant, G. Megie, C.R. Acad. Sci. Paris 292, 29 (1981).

1983

W. B. Grant, R. T. Menzies, J. Air. Pollut. Control. Assoc. 33, 187 (1983); R. L. Byer, M. Garbuny, Appl. Opt. 12, 1496 (1973).
[CrossRef] [PubMed]

E. V. Browell et al., Appl. Opt. 22, 522 (1983).
[CrossRef] [PubMed]

1981

C. Cahen, G. Megie, J. Quant. Spectrosc. Radiat. Transfer. 25, 151 (1981); C. L. Korb, C. Y. Weng, in Proceedings, Eleventh International Laser Radar Conference, Madison, Wisc. (American Meteorological Society, 1982).
[CrossRef]

D. J. Brassington, Appl. Opt. 20, 3774 (1981).
[CrossRef] [PubMed]

R. M. Hoff, M. M. Millan, J. Air Pollut. Control. Assoc. 31, 381 (1981).
[CrossRef]

C. Cahen, J. Pelon, P. Flamant, G. Megie, C.R. Acad. Sci. Paris 292, 29 (1981).

1980

O. Uchino, M. Maeda, T. Shibata, M. Hirono, M. Fujiwara, Appl. Opt. 19, 4175 (1980).
[CrossRef] [PubMed]

P. T. Woods, B. W. Jolliffe, B. R. Marx, Opt. Commun. 33, 281 (1980).
[CrossRef]

B. R. Marx, K. P. Birch, R. C. Felton, B. W. Jolliffe, W. R. C. Rowley, P. T. Woods, Opt. Commun. 33, 287 (1980).
[CrossRef]

1979

R. S. Adrain, D. J. Brassington, S. Sutton, R. H. Varey, Opt. Quantum. Electron. 11, 253 (1979).
[CrossRef]

1975

R. T. Thompson, J. M. Hoell, W. R. Wade, J. Appl. Phys. 46, 3040 (1975).
[CrossRef]

1974

K. W. Rothe, U. Brinkman, H. Walther, Appl. Phys. 4, 181 (1974).
[CrossRef]

1964

P. Warneck, F. F. Marmo, J. O. Sullivan, J. Chem. Phys. 40, 1132 (1964).
[CrossRef]

Adrain, R. S.

R. S. Adrain, D. J. Brassington, S. Sutton, R. H. Varey, Opt. Quantum. Electron. 11, 253 (1979).
[CrossRef]

Birch, K. P.

B. R. Marx, K. P. Birch, R. C. Felton, B. W. Jolliffe, W. R. C. Rowley, P. T. Woods, Opt. Commun. 33, 287 (1980).
[CrossRef]

Brassington, D. J.

D. J. Brassington, Appl. Opt. 20, 3774 (1981).
[CrossRef] [PubMed]

R. S. Adrain, D. J. Brassington, S. Sutton, R. H. Varey, Opt. Quantum. Electron. 11, 253 (1979).
[CrossRef]

Brinkman, U.

K. W. Rothe, U. Brinkman, H. Walther, Appl. Phys. 4, 181 (1974).
[CrossRef]

Browell, E. V.

Cahen, C.

C. Cahen, J. Pelon, P. Flamant, G. Megie, C.R. Acad. Sci. Paris 292, 29 (1981).

C. Cahen, G. Megie, J. Quant. Spectrosc. Radiat. Transfer. 25, 151 (1981); C. L. Korb, C. Y. Weng, in Proceedings, Eleventh International Laser Radar Conference, Madison, Wisc. (American Meteorological Society, 1982).
[CrossRef]

Collis, R. T. H.

R. T. H. Collis, P. B. Russell, Laser Monitoring of the Atmosphere, Vol. 14, E. D. Hinkley, Ed., (Springer, Berlin, 1976), pp. 72–151.
[CrossRef]

Ercoli, B.

T. D. Wilkerson, B. Ercoli, F. S. Tomkins, U. Maryland, Tech. Note BN-784, (1974).

Felton, R. C.

B. R. Marx, K. P. Birch, R. C. Felton, B. W. Jolliffe, W. R. C. Rowley, P. T. Woods, Opt. Commun. 33, 287 (1980).
[CrossRef]

Flamant, P.

C. Cahen, J. Pelon, P. Flamant, G. Megie, C.R. Acad. Sci. Paris 292, 29 (1981).

Fletcher, L. D.

J. G. Hawley, L. D. Fletcher, G. F. Wallace, Optical and Laser Remote Sensing, Vol. 39, D. K. Killinger, A. Mooradian, Ed. (Springer, Berlin, 1983), pp. 128–137.

Fujiwara, M.

Grant, W. B.

W. B. Grant, R. T. Menzies, J. Air. Pollut. Control. Assoc. 33, 187 (1983); R. L. Byer, M. Garbuny, Appl. Opt. 12, 1496 (1973).
[CrossRef] [PubMed]

Hawley, J. G.

J. G. Hawley, L. D. Fletcher, G. F. Wallace, Optical and Laser Remote Sensing, Vol. 39, D. K. Killinger, A. Mooradian, Ed. (Springer, Berlin, 1983), pp. 128–137.

Hirono, M.

Hoell, J. M.

R. T. Thompson, J. M. Hoell, W. R. Wade, J. Appl. Phys. 46, 3040 (1975).
[CrossRef]

Hoff, R. M.

R. M. Hoff, M. M. Millan, J. Air Pollut. Control. Assoc. 31, 381 (1981).
[CrossRef]

Jolliffe, B. W.

B. R. Marx, K. P. Birch, R. C. Felton, B. W. Jolliffe, W. R. C. Rowley, P. T. Woods, Opt. Commun. 33, 287 (1980).
[CrossRef]

P. T. Woods, B. W. Jolliffe, B. R. Marx, Opt. Commun. 33, 281 (1980).
[CrossRef]

Maeda, M.

Marmo, F. F.

P. Warneck, F. F. Marmo, J. O. Sullivan, J. Chem. Phys. 40, 1132 (1964).
[CrossRef]

Marx, B. R.

P. T. Woods, B. W. Jolliffe, B. R. Marx, Opt. Commun. 33, 281 (1980).
[CrossRef]

B. R. Marx, K. P. Birch, R. C. Felton, B. W. Jolliffe, W. R. C. Rowley, P. T. Woods, Opt. Commun. 33, 287 (1980).
[CrossRef]

Megie, G.

C. Cahen, G. Megie, J. Quant. Spectrosc. Radiat. Transfer. 25, 151 (1981); C. L. Korb, C. Y. Weng, in Proceedings, Eleventh International Laser Radar Conference, Madison, Wisc. (American Meteorological Society, 1982).
[CrossRef]

C. Cahen, J. Pelon, P. Flamant, G. Megie, C.R. Acad. Sci. Paris 292, 29 (1981).

Menzies, R. T.

W. B. Grant, R. T. Menzies, J. Air. Pollut. Control. Assoc. 33, 187 (1983); R. L. Byer, M. Garbuny, Appl. Opt. 12, 1496 (1973).
[CrossRef] [PubMed]

Millan, M. M.

R. M. Hoff, M. M. Millan, J. Air Pollut. Control. Assoc. 31, 381 (1981).
[CrossRef]

Pelon, J.

C. Cahen, J. Pelon, P. Flamant, G. Megie, C.R. Acad. Sci. Paris 292, 29 (1981).

Rothe, K. W.

K. W. Rothe, U. Brinkman, H. Walther, Appl. Phys. 4, 181 (1974).
[CrossRef]

Rowley, W. R. C.

B. R. Marx, K. P. Birch, R. C. Felton, B. W. Jolliffe, W. R. C. Rowley, P. T. Woods, Opt. Commun. 33, 287 (1980).
[CrossRef]

Russell, P. B.

R. T. H. Collis, P. B. Russell, Laser Monitoring of the Atmosphere, Vol. 14, E. D. Hinkley, Ed., (Springer, Berlin, 1976), pp. 72–151.
[CrossRef]

Shibata, T.

Sullivan, J. O.

P. Warneck, F. F. Marmo, J. O. Sullivan, J. Chem. Phys. 40, 1132 (1964).
[CrossRef]

Sutton, S.

R. S. Adrain, D. J. Brassington, S. Sutton, R. H. Varey, Opt. Quantum. Electron. 11, 253 (1979).
[CrossRef]

Thompson, R. T.

R. T. Thompson, J. M. Hoell, W. R. Wade, J. Appl. Phys. 46, 3040 (1975).
[CrossRef]

Tomkins, F. S.

T. D. Wilkerson, B. Ercoli, F. S. Tomkins, U. Maryland, Tech. Note BN-784, (1974).

Uchino, O.

Varey, R. H.

R. S. Adrain, D. J. Brassington, S. Sutton, R. H. Varey, Opt. Quantum. Electron. 11, 253 (1979).
[CrossRef]

Wade, W. R.

R. T. Thompson, J. M. Hoell, W. R. Wade, J. Appl. Phys. 46, 3040 (1975).
[CrossRef]

Wallace, G. F.

J. G. Hawley, L. D. Fletcher, G. F. Wallace, Optical and Laser Remote Sensing, Vol. 39, D. K. Killinger, A. Mooradian, Ed. (Springer, Berlin, 1983), pp. 128–137.

Walther, H.

K. W. Rothe, U. Brinkman, H. Walther, Appl. Phys. 4, 181 (1974).
[CrossRef]

Warneck, P.

P. Warneck, F. F. Marmo, J. O. Sullivan, J. Chem. Phys. 40, 1132 (1964).
[CrossRef]

Wilkerson, T. D.

T. D. Wilkerson, B. Ercoli, F. S. Tomkins, U. Maryland, Tech. Note BN-784, (1974).

Woods, P. T.

B. R. Marx, K. P. Birch, R. C. Felton, B. W. Jolliffe, W. R. C. Rowley, P. T. Woods, Opt. Commun. 33, 287 (1980).
[CrossRef]

P. T. Woods, B. W. Jolliffe, B. R. Marx, Opt. Commun. 33, 281 (1980).
[CrossRef]

Appl. Opt.

Appl. Phys.

K. W. Rothe, U. Brinkman, H. Walther, Appl. Phys. 4, 181 (1974).
[CrossRef]

C.R. Acad. Sci. Paris

C. Cahen, J. Pelon, P. Flamant, G. Megie, C.R. Acad. Sci. Paris 292, 29 (1981).

J. Air Pollut. Control. Assoc.

R. M. Hoff, M. M. Millan, J. Air Pollut. Control. Assoc. 31, 381 (1981).
[CrossRef]

J. Air. Pollut. Control. Assoc.

W. B. Grant, R. T. Menzies, J. Air. Pollut. Control. Assoc. 33, 187 (1983); R. L. Byer, M. Garbuny, Appl. Opt. 12, 1496 (1973).
[CrossRef] [PubMed]

J. Appl. Phys.

R. T. Thompson, J. M. Hoell, W. R. Wade, J. Appl. Phys. 46, 3040 (1975).
[CrossRef]

J. Chem. Phys.

P. Warneck, F. F. Marmo, J. O. Sullivan, J. Chem. Phys. 40, 1132 (1964).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer.

C. Cahen, G. Megie, J. Quant. Spectrosc. Radiat. Transfer. 25, 151 (1981); C. L. Korb, C. Y. Weng, in Proceedings, Eleventh International Laser Radar Conference, Madison, Wisc. (American Meteorological Society, 1982).
[CrossRef]

Opt. Commun.

P. T. Woods, B. W. Jolliffe, B. R. Marx, Opt. Commun. 33, 281 (1980).
[CrossRef]

B. R. Marx, K. P. Birch, R. C. Felton, B. W. Jolliffe, W. R. C. Rowley, P. T. Woods, Opt. Commun. 33, 287 (1980).
[CrossRef]

Opt. Quantum. Electron.

R. S. Adrain, D. J. Brassington, S. Sutton, R. H. Varey, Opt. Quantum. Electron. 11, 253 (1979).
[CrossRef]

Other

T. D. Wilkerson, B. Ercoli, F. S. Tomkins, U. Maryland, Tech. Note BN-784, (1974).

R. T. H. Collis, P. B. Russell, Laser Monitoring of the Atmosphere, Vol. 14, E. D. Hinkley, Ed., (Springer, Berlin, 1976), pp. 72–151.
[CrossRef]

H. Walther, Ed., Laser Spectrosopy of Atoms and Molecules, Vol. 2 (Springer, Berlin, 1976).
[CrossRef]

E. D. Hinkley, Ed., Laser Monitoring of the Atmosphere, Vol. 14 (Springer, Berlin, 1976).
[CrossRef]

J. G. Hawley, L. D. Fletcher, G. F. Wallace, Optical and Laser Remote Sensing, Vol. 39, D. K. Killinger, A. Mooradian, Ed. (Springer, Berlin, 1983), pp. 128–137.

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Figures (7)

Fig. 1
Fig. 1

High-resolution absorption spectra of SO2: (a) low-pressure SO2; (b) atmospherically broadened SO2.

Fig. 2
Fig. 2

Variation of low-pressure SO2 cross section with wavelength for a monitoring laser bandwidth of 5 pm: a, nL = 1.2 × 1021 m−2; b, nL = 8.3 × 1021 m−2; c, nL = 50.1 × 1021 m−2. (1) and (2)—see Sec. IV.

Fig. 3
Fig. 3

Computed variation of low-pressure SO2 absorption cross section with nL for different laser bandwidths at two monitoring laser wavelengths. Air wavelengths: 1, 300.010 nm; 2, 300.033 nm. Bandwidths: a, 2 pm; b, 5 pm; c, 40 pm.

Fig. 4
Fig. 4

Computed variation of atmospherically broadened SO2 absorption cross sections with nL for different laser bandwidths at two monitoring laser wavelengths. Air wavelengths: 1, 300.010 nm; 2, 300.033 nm. Bandwidths: a, 2 pm; b, 5 pm; c, 40 pm.

Fig. 5
Fig. 5

Comparison of measured variation of σe with nL and the variation derived from the data of Fig. 1(a). Air wavelength, 300.02 nm; bandwidth, 0.05 nm.⊙, experimental points. a, Computed curve; b, computed curve corrected by 2.9% to allow for systemic disagreement between the two data sets.

Fig. 6
Fig. 6

Measured variation of σe with nL at different wavelengths. Air wavelengths: (a) 299.33 nm; (b) 301.57 nm.

Fig. 7
Fig. 7

Variation of the parameter β with wavelength for atmospherically broadened SO2 at laser bandwidths of a, 2, b, 5, and c, 25 pm.

Tables (2)

Tables Icon

Table I Errors in Long-path Measurements

Tables Icon

Table II Errors in DIAL Measurements

Equations (20)

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

I ( x ) = I 0 exp [ - σ ( λ ) n x ] ,
I ( x ) = 0 i 0 ( λ ) exp [ - σ ( λ ) n x ] d λ ,
I 0 = 0 i 0 ( λ ) d λ .
σ ( λ ) = σ ¯ + Δ σ ( λ ) ,
σ ¯ = 1 I 0 0 i 0 ( λ ) σ ( λ ) d λ
I ( x ) = exp ( - n x σ ¯ ) { I 0 - 0 i 0 ( λ ) Δ σ ( λ ) n x d λ + 1 2 0 i 0 ( λ ) [ Δ σ ( λ ) n x ] 2 d λ + } .
I ( x ) I 0 exp ( - n x σ ¯ ) ( 1 + Δ 2 σ ¯ n 2 x 2 2 ) ,
Δ 2 σ ¯ = 1 I 0 0 i 0 ( λ ) [ Δ σ ( λ ) ] 2 d λ
σ e = - 1 n L ln [ I ( λ ) I 0 ] .
σ e σ ¯ - n L Δ 2 σ ¯ 2 ,
σ e σ ¯ ( 1 - ½ n L σ ¯ β ) ,
n e n ( 1 - n L Δ 2 σ ¯ 2 σ ¯ ) ,
n ¯ = 1 L 0 L n ( x ) d x
n ¯ e = - ln ( I on I off · I 0 off I 0 on ) / ( σ ¯ on - σ ¯ off ) L
n ¯ e n ¯ [ 1 - n ¯ L 2 ( Δ 2 σ ¯ on - Δ 2 σ ¯ off σ ¯ on - σ ¯ off ) ] .
n e ( R ) n ( R ) [ 1 - 2 n ¯ R ( Δ 2 σ ¯ on - Δ 2 σ ¯ off σ ¯ on - σ ¯ off ) ] .
n ¯ e n ¯ [ 1 - n ¯ L 2 ( σ ¯ on 2 β on - σ ¯ off 2 β off σ ¯ on - σ ¯ off ) ] ,
σ e = - ln ( I s / I r I 0 s / I 0 r ) / n ( L s - L r ) ,
I s / I r I 0 s / I 0 r exp [ - n σ ¯ ( L s - L r ) ] [ 1 + Δ 2 σ ¯ n 2 ( L s 2 - L r 2 ) / 2 ] .
σ e σ ¯ - ln [ 1 + Δ 2 σ ¯ n 2 ( L s 2 - L r 2 ) / 2 ] n ( L r - L s ) σ ¯ - n ( L s + L r ) Δ 2 σ ¯ / 2.

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