Abstract

It is shown that the deconvolution method of Van Cittert can be used reliably to enhance the effective spectral resolution by a factor of ∼3 with data that exhibit a high SNR (∼103) and in which base line variations have been eliminated. Deconvolution of a Doppler-limited spectrum of C6H6 measured on a difference-frequency laser system yielded linewidths of ∼1.2 × 10−3 cm−1 (compared with the Doppler width of 3.6 × 10−3 cm−1 at 203 K). Extensive reliability tests of the deconvolution technique have been performed.

© 1980 Optical Society of America

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References

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  1. P. H. Van Cittert, Phys Z. 69, 298 (1931).
    [Crossref]
  2. H. C. Burger, P. H. Van Cittert, Phys Z. 79, 722 (1932);Phys Z. 81, 428 (1933).
    [Crossref]
  3. P. A. Jansson, J. Opt. Soc. Am. 60, 184 (1970).
    [Crossref]
  4. P. A. Jansson, R. H. Hunt, E. K. Plyler, J. Opt. Soc. Am. 60, 596 (1970).
    [Crossref]
  5. P. D. Willson, J. R. Hanratty, T. H. Edwards, presented at 1972 Symposium on Molecular Spectroscopy, Columbus, Ohio.
  6. P. D. Willson, Ph.D. Dissertation, Michigan State U. (1973).
  7. G. Halsey, W. E. Blass, Appl. Opt. 16, 286 (1977).
    [Crossref] [PubMed]
  8. A. S. Pine, J. Opt. Soc. Am. 64, 1683 (1974);J. Opt. Soc. Am. 66, 97 (1976).
    [Crossref]
  9. S. R. Polo, P. D. Willson, to be published.

1977 (1)

1974 (1)

1970 (2)

1932 (1)

H. C. Burger, P. H. Van Cittert, Phys Z. 79, 722 (1932);Phys Z. 81, 428 (1933).
[Crossref]

1931 (1)

P. H. Van Cittert, Phys Z. 69, 298 (1931).
[Crossref]

Blass, W. E.

Burger, H. C.

H. C. Burger, P. H. Van Cittert, Phys Z. 79, 722 (1932);Phys Z. 81, 428 (1933).
[Crossref]

Edwards, T. H.

P. D. Willson, J. R. Hanratty, T. H. Edwards, presented at 1972 Symposium on Molecular Spectroscopy, Columbus, Ohio.

Halsey, G.

Hanratty, J. R.

P. D. Willson, J. R. Hanratty, T. H. Edwards, presented at 1972 Symposium on Molecular Spectroscopy, Columbus, Ohio.

Hunt, R. H.

Jansson, P. A.

Pine, A. S.

Plyler, E. K.

Polo, S. R.

S. R. Polo, P. D. Willson, to be published.

Van Cittert, P. H.

H. C. Burger, P. H. Van Cittert, Phys Z. 79, 722 (1932);Phys Z. 81, 428 (1933).
[Crossref]

P. H. Van Cittert, Phys Z. 69, 298 (1931).
[Crossref]

Willson, P. D.

P. D. Willson, J. R. Hanratty, T. H. Edwards, presented at 1972 Symposium on Molecular Spectroscopy, Columbus, Ohio.

S. R. Polo, P. D. Willson, to be published.

P. D. Willson, Ph.D. Dissertation, Michigan State U. (1973).

Appl. Opt. (1)

J. Opt. Soc. Am. (3)

Phys Z. (2)

P. H. Van Cittert, Phys Z. 69, 298 (1931).
[Crossref]

H. C. Burger, P. H. Van Cittert, Phys Z. 79, 722 (1932);Phys Z. 81, 428 (1933).
[Crossref]

Other (3)

S. R. Polo, P. D. Willson, to be published.

P. D. Willson, J. R. Hanratty, T. H. Edwards, presented at 1972 Symposium on Molecular Spectroscopy, Columbus, Ohio.

P. D. Willson, Ph.D. Dissertation, Michigan State U. (1973).

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Figures (6)

Fig. 1
Fig. 1

(A) Section of a Doppler-limited IR spectrum of C6H6 (T = 203 K, p = 0.15 Torr, path 40 m); (B) same spectrum after deconvolution using a Gaussian apparatus function with wG = 3.6 × 10−3 cm−1 (absorbance scale multiplied by 0.3).

Fig. 2
Fig. 2

(A) R(5) lines of ν3 band of CH4 measured on a grating spectrometer; (B) same lines after deconvolution using line at 3076.7255 cm−1 as apparatus function (absorbance scale multiplied by 0.3); (C) same lines measured at Doppler-limited resolution on a difference-frequency laser system.

Fig. 3
Fig. 3

(A) Section of a grating IR spectrum of C6H6 (T = 300 K, p = 0.5 Torr, path 2 m); (B) same spectrum after deconvolution using a Gaussian apparatus function with wA= 16 × 10−3 cm−1 (absorbance scale multiplied by 0.3) (line denoted by * is an atmospheric H2O line at 3031.732 cm−1); (C) same section measured at Doppler-limited resolution on a difference-frequency laser system.

Fig. 4
Fig. 4

Synthetic RR branches of a symmetric top molecule: the δ function stick spectrum (curve C) was convolved with a Gaussian five points wide on the digital wave number scale (curve B) and with a Gaussian fifteen points wide (curve A).

Fig. 5
Fig. 5

(A) Deconvolved synthetic fifteen-point spectrum (from curve A of Fig. 4); (b) synthetic five-point spectrum (curve B of Fig. 4); (C) result of deconvolution of the fifteen-point synthetic spectrum (curve A of Fig. 4), to which a slowly varying background had been added.

Fig. 6
Fig. 6

(A) Gaussian lines on a nonzero background; (B) deconvolved curve A (vertical scale multiplied by 0.3).

Equations (4)

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L ( ν ) = + M ( ν ) A ( ν ν ) d ν .
M n ( ν ) = M n 1 ( ν ) + α [ L ( ν ) + M n 1 ( ν ) A ( ν ν ) d ν ] ,
w D = 7.16 × 10 7 ω ( T / M ) 1 / 2 ( cm 1 ) ,
L ( ν ) = + R ( ν ) D ( ν ν ) d ν .

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