Abstract

A numerical method has been developed to correct high-resolution infrared spectra for the distortion introduced by the spectrometer. The method involves, first, an accurate determination of the spectrometer response function and, then, deconvolution by a point-successive over-relaxation procedure. The method is applied to portions of the Q branches N2O and CH4 near 3.3 μ. The spectra are observed at pressures below 1.0 torr with spectrometer response-function half-widths less than 0.02 cm−1. The deconvolved spectra show an improvement of resolution which approaches the limit set by the Doppler widths of the lines. Line separations measured from the deconvolved spectra are within 0.001 cm−1 of the calculated values. The reduction of line overlap in the deconvolved spectra considerably increases the number of lines whose positions may be accurately measured.

© 1970 Optical Society of America

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References

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1970 (1)

1969 (2)

1968 (1)

1967 (2)

1966 (1)

1964 (1)

A. Savitsky and M. J. E. Golay, Anal. Chem. 36, 1627 (1964).
[Crossref]

1962 (1)

1960 (2)

1931 (1)

P. H. van Cittert, Z. Physik 69, 298 (1931).
[Crossref]

Benedict, W. S.

Deeds, W. E.

Gailar, N. M.

Golay, M. J. E.

A. Savitsky and M. J. E. Golay, Anal. Chem. 36, 1627 (1964).
[Crossref]

Hecht, K. T.

K. T. Hecht, J. Mol. Spectrosc. 5, 390 (1960).
[Crossref]

Herget, W. F.

Hunt, R. H.

Izatt, J. R.

Jansson, P. A.

Jones, R. N.

Lovell, R. J.

Mielenz, K. D.

Mireles, R.

Nielsen, A. H.

Plyler, E. K.

Robertson, C. W.

Sakai, H.

Savitsky, A.

A. Savitsky and M. J. E. Golay, Anal. Chem. 36, 1627 (1964).
[Crossref]

Tidwell, E. D.

van Cittert, P. H.

P. H. van Cittert, Z. Physik 69, 298 (1931).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Curve A; the Q branch of N2O near 2798 cm−1 observed with a sample pressure- of 0.27 torr, a 7.5-sec time constant, slit widths of 150 μ (0.019 cm−1), and a path of 35 m. Curve B; the same spectrum after deconvolution.

Fig. 2
Fig. 2

Curve A; a portion of the Q branch of the ν3 band of CH4 as observed with slit widths of 100 μ (0.0165 cm−1), a 7.5-sec time constant, a pressure of 0.4 torr, and a path of 23 cm. Curve B; the result of deconvolution with the measured response function. Curve C; the result of deconvolution with the response function approximated by a gaussian function of the same half-width (0.0165 cm−1).

Fig. 3
Fig. 3

Curve A; a portion of the Q branch of the ν3 band of CH4 observed under the same conditions as in Fig. 2. Curve B; the deconvolved spectrum.

Fig. 4
Fig. 4

A comparison of the measured instrument-response function near 3000 cm−1 (solid curve) with a gaussian function of the same half-width (0.019 cm−1).

Tables (1)

Tables Icon

Table I Separations between various absorption lines of N2O near 2798 cm−1 as obtained from deconvolved spectra by centroid determination.

Equations (5)

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Ā m ( ν ) = - R ¯ ( ν - ν ) Ā t ( ν ) d ν ,
( A m ) i = l R ¯ i l ( Ā t ) l ,
[ A t ( k + 1 ) ] i = [ Ā t ( k ) ] i + { ( Ā m ) i - l = 1 n R ¯ i l [ Ā t ( k ) ] l } .
( Ā t ( k + 1 ) ) i = ( A t ( k ) ) i + κ R 00 { ( Ā m ) i - l = 1 i - 1 R ¯ i l [ Ā t ( k + 1 ) ] l - l = i n R i l [ A t ( k ) ] l } .
κ i = κ 0 { 1 - 2 [ Ā t ( k ) ] i - 1 2 } ,