Abstract

The problem of finding individual line parameters from experimental absorption spectra is reduced to the minimization of a function of N variables. The spectra may consist of overlapping, closely spaced, and broadened lines, and need not be of high resolution. It is assumed, however, that the general response function of the instrument is given and that the line shapes are known functions of wave number and of the parameter in question for each of the N lines involved. An example of the use of the method is given by outlining a successful computer program for determining half-widths in infrared spectra, and showing results of numerical tests.

© 1966 Optical Society of America

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References

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  1. W. S. Benedict, H. H. Claasen, and J. J. Shaw, J. Res. Natl. Bur. Std. 49, 91 (1952).
    [Crossref]
  2. J. H. Taylor, W. S. Benedict, and J. Strong, J. Chem. Phys. 20, 1884 (1952).
    [Crossref]
  3. R. H. Schwendeman and V. W. Laurie, Table of Line Strengths (Pergamon Press, Inc., New York1958).
  4. W. S. Benedict and L. D. Kaplan, J. Chem. Phys. 30, 388 (1959).
  5. R. W. Anderson, Phys. Rev. 76, 647 (1949).
    [Crossref]
  6. C. H. Palmer, J. Opt. Soc. Am. 47, 1024 (1957).
    [Crossref]

1959 (1)

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

1957 (1)

1952 (2)

W. S. Benedict, H. H. Claasen, and J. J. Shaw, J. Res. Natl. Bur. Std. 49, 91 (1952).
[Crossref]

J. H. Taylor, W. S. Benedict, and J. Strong, J. Chem. Phys. 20, 1884 (1952).
[Crossref]

1949 (1)

R. W. Anderson, Phys. Rev. 76, 647 (1949).
[Crossref]

Anderson, R. W.

R. W. Anderson, Phys. Rev. 76, 647 (1949).
[Crossref]

Benedict, W. S.

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

W. S. Benedict, H. H. Claasen, and J. J. Shaw, J. Res. Natl. Bur. Std. 49, 91 (1952).
[Crossref]

J. H. Taylor, W. S. Benedict, and J. Strong, J. Chem. Phys. 20, 1884 (1952).
[Crossref]

Claasen, H. H.

W. S. Benedict, H. H. Claasen, and J. J. Shaw, J. Res. Natl. Bur. Std. 49, 91 (1952).
[Crossref]

Kaplan, L. D.

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

Laurie, V. W.

R. H. Schwendeman and V. W. Laurie, Table of Line Strengths (Pergamon Press, Inc., New York1958).

Palmer, C. H.

Schwendeman, R. H.

R. H. Schwendeman and V. W. Laurie, Table of Line Strengths (Pergamon Press, Inc., New York1958).

Shaw, J. J.

W. S. Benedict, H. H. Claasen, and J. J. Shaw, J. Res. Natl. Bur. Std. 49, 91 (1952).
[Crossref]

Strong, J.

J. H. Taylor, W. S. Benedict, and J. Strong, J. Chem. Phys. 20, 1884 (1952).
[Crossref]

Taylor, J. H.

J. H. Taylor, W. S. Benedict, and J. Strong, J. Chem. Phys. 20, 1884 (1952).
[Crossref]

J. Chem. Phys. (2)

J. H. Taylor, W. S. Benedict, and J. Strong, J. Chem. Phys. 20, 1884 (1952).
[Crossref]

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

J. Opt. Soc. Am. (1)

J. Res. Natl. Bur. Std. (1)

W. S. Benedict, H. H. Claasen, and J. J. Shaw, J. Res. Natl. Bur. Std. 49, 91 (1952).
[Crossref]

Phys. Rev. (1)

R. W. Anderson, Phys. Rev. 76, 647 (1949).
[Crossref]

Other (1)

R. H. Schwendeman and V. W. Laurie, Table of Line Strengths (Pergamon Press, Inc., New York1958).

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Figures (2)

Fig. 1
Fig. 1

Level curves in the neighborhood of the minimum point for the distance function A(γ) used in numerical tests. Heights corresponding to contours have been multiplied by 102. The path corresponds to the results of a numerical test of the minimization technique.

Fig. 2
Fig. 2

Flow chart of the iterative technique for finding line constants by numerical minimization.

Tables (3)

Tables Icon

Table I Line constants used in simulated spectrum.

Tables Icon

Table II Results of test. B=15. Values of γmi in units of cm−1×103. Run time 0.55 h.

Tables Icon

Table III Results of test. B=5. Values of γmi in units of cm−1×10−3. Run time 1.12 h.

Equations (17)

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ν 1 , , ν J , , ν K , , ν M .
γ j = γ j 0             j = 1 , , ( J - 1 ) , ( K + 1 ) , , M .
τ ( ν , γ ) = exp [ - ρ m = 1 M α m ( ν , γ m ) ] ,
γ = ( γ J , , γ K ) .
f ( ν , γ ) = - g ( ν , ν ) τ ( ν , γ ) d ν ,
A ˜ ( γ ) = { a b [ f ( ν , γ ) - F ( ν ) ] 2 d ν } 1 2
A ( γ ) = [ A ˜ ( γ ) ] 2
g ( ν ) = const .
α m ( ν , γ m ) = ( S m / π ) { γ m / [ ( ν - ν m ) 2 + ( γ m ) 2 ] } .
g ( ν , ν ) = [ B / ( π ) 1 2 ] exp [ - B 2 ( ν - ν ) 2 ] .
ρ = 0.32 precipitable cm ,
γ j = γ j 0 + ( - ) k δ m j 0 ,             m , j = J , , K ; k = 0 , 1.
L ( γ 0 , m , k ) = { γ γ j = γ j 0 + ( - ) k δ m j λ ,             λ 0 } .
A ( γ ( m ¯ , k ¯ ) ) = min { A ( γ ) γ S ( γ 0 , 0 ) } .
{ A ( γ ) γ L ( γ 0 , m ¯ , k ¯ ) }
γ j 1 = γ j 0 + ( - ) k ¯ δ m ¯ j λ ˜ , j = J , , K .
Δ 1 λ = 0.001 Δ 2 λ = 0.0005 Δ 3 λ = 0.0001.