Abstract

The distortion of spectral lines by the finite band pass of spectrometers is an effect which must be considered in measuring line shape parameters. The differences between actual line half-widths and line intensities and those which would be obtained directly from measurements by spectrometers with Gauss and Cauchy shaped slit functions have been calculated for Lorentz and Doppler lines of varying widths and intensities. A method of utilizing these results to correct actual measurements is developed.

© 1956 Optical Society of America

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References

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  1. A. C. Hardy and F. M. Young, J. Opt. Soc. Am. 39, 265 (1949).
    [Crossref]
  2. A. Adel and E. F. Barker, Revs. Modern Phys. 16, 236 (1944).
    [Crossref]
  3. W. S. Benedict and S. Silverman, Phys. Rev. 95, 752(A) (1954).
  4. Jaffe, Rank, and Wiggins, J. Opt. Soc. Am. 45, 636 (1955).
    [Crossref]
  5. W. G. Fastie and H. M. Crosswhite, J. Opt. Soc. Am. 45, 900(A) (1955).
  6. E. B. Wilson and A. J. Wells, J. Chem. Phys. 14, 578 (1946).
    [Crossref]

1955 (2)

Jaffe, Rank, and Wiggins, J. Opt. Soc. Am. 45, 636 (1955).
[Crossref]

W. G. Fastie and H. M. Crosswhite, J. Opt. Soc. Am. 45, 900(A) (1955).

1954 (1)

W. S. Benedict and S. Silverman, Phys. Rev. 95, 752(A) (1954).

1949 (1)

1946 (1)

E. B. Wilson and A. J. Wells, J. Chem. Phys. 14, 578 (1946).
[Crossref]

1944 (1)

A. Adel and E. F. Barker, Revs. Modern Phys. 16, 236 (1944).
[Crossref]

Adel, A.

A. Adel and E. F. Barker, Revs. Modern Phys. 16, 236 (1944).
[Crossref]

Barker, E. F.

A. Adel and E. F. Barker, Revs. Modern Phys. 16, 236 (1944).
[Crossref]

Benedict, W. S.

W. S. Benedict and S. Silverman, Phys. Rev. 95, 752(A) (1954).

Crosswhite, H. M.

W. G. Fastie and H. M. Crosswhite, J. Opt. Soc. Am. 45, 900(A) (1955).

Fastie, W. G.

W. G. Fastie and H. M. Crosswhite, J. Opt. Soc. Am. 45, 900(A) (1955).

Hardy, A. C.

Jaffe,

Rank,

Silverman, S.

W. S. Benedict and S. Silverman, Phys. Rev. 95, 752(A) (1954).

Wells, A. J.

E. B. Wilson and A. J. Wells, J. Chem. Phys. 14, 578 (1946).
[Crossref]

Wiggins,

Wilson, E. B.

E. B. Wilson and A. J. Wells, J. Chem. Phys. 14, 578 (1946).
[Crossref]

Young, F. M.

J. Chem. Phys. (1)

E. B. Wilson and A. J. Wells, J. Chem. Phys. 14, 578 (1946).
[Crossref]

J. Opt. Soc. Am. (3)

Phys. Rev. (1)

W. S. Benedict and S. Silverman, Phys. Rev. 95, 752(A) (1954).

Revs. Modern Phys. (1)

A. Adel and E. F. Barker, Revs. Modern Phys. 16, 236 (1944).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1

Error made in direct measurement of line width, peak absorption coefficient, and line intensity as function of ratio of spectral slit width to line half-width for a single Lorentz line with 30% peak absorption and a Gauss slit function.

Fig. 2
Fig. 2

Error made in direct measurement of line half-width as function of ratio of spectral slit width to line half-width, for Lorentz and Doppler lines with 30% peak absorption.

Fig. 3
Fig. 3

Error made in direct measurement of line half-width as function of peak absorption for Lorentz and Doppler lines.

Fig. 4
Fig. 4

Error made in direct measurement of peak absorption coefficient as function of ratio of spectral slit width to line half-width, for Lorentz and Doppler lines with 30% peak absorption.

Fig. 5
Fig. 5

Error made in direct measurement of peak absorption coefficient as function of peak absorption for Lorentz and Doppler lines.

Fig. 6
Fig. 6

Error made in direct measurement of line intensity as function of ratio of spectral slit width to line half-width for Lorentz and Doppler lines with 30% peak absorption.

Fig. 7
Fig. 7

Error made in direct measurement of line intensity as function of peak absorption for a Lorentz line.

Fig. 8
Fig. 8

Error made in direct measurement of line intensity as function of peak absorption for a Doppler line.

Fig. 9
Fig. 9

Curves for determining ratio of spectral slit width to line half-width from direct measurement of line half-widths at pressures of P and 2P. The curves are drawn for Cauchy and Gauss shaped lines of which the width varies linearly with pressure.

Fig. 10
Fig. 10

Curves for determining ratio of spectral slit width to line half-width from direct measurement of line half-widths at spectral slit widths of Δν and Δν/2.

Tables (1)

Tables Icon

Table I Comparison of Cauchy and Gauss slit function effects on line shape parameters.

Equations (4)

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T obs ( ν ) = exp ( - k obs ( ν ) p l ) = σ σ ( ν , x ) exp ( - k ( x ) p l ) d x σ σ ( ν , x ) d x ,
k L ( x ) = S α / π ( x - x 0 ) 2 + α 2 ,
k D ( x ) = S α ( ln 2 π ) 1 2 exp [ - ( ln 2 ) ( x - x 0 ) 2 / α 2 ] .
σ ( ν , x ) = ( Δ ν / 2 ) 2 ( x - ν ) 2 + ( Δ ν + 2 ) 2 .