Abstract

A recovery procedure has been developed to correct instrument line-shape distortions observed in Fourier transform spectroscopy. The procedure can be described as a phase-error correction performed in the spectral domain to correct for path-difference-dependent phase errors observed in sharp spectral features. The technique has been applied successfully to high-resolution atmospheric emission spectra. The inherent broadening of the real features has been separated accurately from instrumental distortions. Using models for the path-difference-dependent error sources and data from two narrow window regions at 50 and 118 cm-1, we show that the distortion has a simple dependence on the spectral frequency.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Mertz, Transformation in Optics (Wiley, New York, 1966).
  2. J. Connes, “Recherches sur la spectroscopie par transformation de Fourier,” Rev. Opt. 40, 171–183 (1961).
  3. M. L. Forman, W. H. Steel, and G. A. Vanasse, “Correction of asymmetric interferograms obtained in Fourier spectroscopy,” J. Opt. Soc. Am. 56, 59–63 (1966).
    [CrossRef]
  4. R. C. M. Learner, A. P. Thorne, I. Wynne-Jones, J. W. Brault, and M. C. Abrams, “Phase correction of emission line Fourier transform spectra,” J. Opt. Soc. Am. A 12, 2165–2171 (1995).
    [CrossRef]
  5. B. Carli, F. Forni, and F. Mencaraglia, “Phase error correction in FT spectroscopy of spectra with positive and negative intensities,” Int. J. Infrared Millimeter Waves 3, 529–540 (1982).
    [CrossRef]
  6. H. E. Revercomb, H. Buijs, H. B. Howell, D. D. LaPorte, W. L. Smith, and L. A. Sromovsky, “Radiometric calibration of an IR Fourier transform spectrometer: solution to a problem with the High-Resolution Interferometer Sounder,” Appl. Opt. 27, 3210–3218 (1988).
    [CrossRef] [PubMed]
  7. C. E. Blom, M. Höpfner, and C. Weddigen, “Correction of phase anomalies of atmospheric emission spectra by the double-differencing method,” Appl. Opt. 35, 2649–2652 (1996).
    [CrossRef] [PubMed]
  8. D. G. Johnson, W. A. Traub, and K. W. Jucks, “Phase determination from mostly one-sided interferograms,” Appl. Opt. 35, 2955–2959 (1996).
    [CrossRef] [PubMed]
  9. P. Jacquinot, “New developments in interference spectroscopy,” Rep. Prog. Phys. 23, 268–272 (1960).
    [CrossRef]
  10. M. V. R. K. Murty, “Some more aspects of the Michelson interferometer with cube corners,” J. Opt. Soc. Am. 50, 7–10 (1960).
    [CrossRef]
  11. D. H. Martin and E. Puplett, “Polarized interferometric spectrometer for the millimetre and sub-millimetre spectrum,” Infrared Phys. 10, 105–107 (1969).
    [CrossRef]
  12. B. Carli, F. Mencaraglia, and A. Bonetti, “Submillimiter high-resolution FT spectrometer for atmospheric studies,” Appl. Opt. 23, 2594–2603 (1984).
    [CrossRef] [PubMed]
  13. G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
    [CrossRef]

1997 (1)

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

1996 (2)

1995 (1)

1988 (1)

1984 (1)

1982 (1)

B. Carli, F. Forni, and F. Mencaraglia, “Phase error correction in FT spectroscopy of spectra with positive and negative intensities,” Int. J. Infrared Millimeter Waves 3, 529–540 (1982).
[CrossRef]

1969 (1)

D. H. Martin and E. Puplett, “Polarized interferometric spectrometer for the millimetre and sub-millimetre spectrum,” Infrared Phys. 10, 105–107 (1969).
[CrossRef]

1966 (1)

1961 (1)

J. Connes, “Recherches sur la spectroscopie par transformation de Fourier,” Rev. Opt. 40, 171–183 (1961).

1960 (2)

P. Jacquinot, “New developments in interference spectroscopy,” Rep. Prog. Phys. 23, 268–272 (1960).
[CrossRef]

M. V. R. K. Murty, “Some more aspects of the Michelson interferometer with cube corners,” J. Opt. Soc. Am. 50, 7–10 (1960).
[CrossRef]

Abrams, M. C.

Ade, P. A. R.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Alboni, F.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Blom, C. E.

Bonetti, A.

Brault, J. W.

Buijs, H.

Carli, B.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

B. Carli, F. Mencaraglia, and A. Bonetti, “Submillimiter high-resolution FT spectrometer for atmospheric studies,” Appl. Opt. 23, 2594–2603 (1984).
[CrossRef] [PubMed]

B. Carli, F. Forni, and F. Mencaraglia, “Phase error correction in FT spectroscopy of spectra with positive and negative intensities,” Int. J. Infrared Millimeter Waves 3, 529–540 (1982).
[CrossRef]

Carlotti, M.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Connes, J.

J. Connes, “Recherches sur la spectroscopie par transformation de Fourier,” Rev. Opt. 40, 171–183 (1961).

Cortesi, U.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Epifani, M.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Forman, M. L.

Forni, F.

B. Carli, F. Forni, and F. Mencaraglia, “Phase error correction in FT spectroscopy of spectra with positive and negative intensities,” Int. J. Infrared Millimeter Waves 3, 529–540 (1982).
[CrossRef]

Griffin, M. J.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Hamilton, P. A.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Höpfner, M.

Howell, H. B.

Jacquinot, P.

P. Jacquinot, “New developments in interference spectroscopy,” Rep. Prog. Phys. 23, 268–272 (1960).
[CrossRef]

Johnson, D. G.

Jucks, K. W.

LaPorte, D. D.

Learner, R. C. M.

Lee, C.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Lepri, G.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Martin, D. H.

D. H. Martin and E. Puplett, “Polarized interferometric spectrometer for the millimetre and sub-millimetre spectrum,” Infrared Phys. 10, 105–107 (1969).
[CrossRef]

Mencaraglia, F.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

B. Carli, F. Mencaraglia, and A. Bonetti, “Submillimiter high-resolution FT spectrometer for atmospheric studies,” Appl. Opt. 23, 2594–2603 (1984).
[CrossRef] [PubMed]

B. Carli, F. Forni, and F. Mencaraglia, “Phase error correction in FT spectroscopy of spectra with positive and negative intensities,” Int. J. Infrared Millimeter Waves 3, 529–540 (1982).
[CrossRef]

Mertz, L.

L. Mertz, Transformation in Optics (Wiley, New York, 1966).

Murray, A. G.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Murty, M. V. R. K.

Nolt, G.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Park, J. H.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Puplett, E.

D. H. Martin and E. Puplett, “Polarized interferometric spectrometer for the millimetre and sub-millimetre spectrum,” Infrared Phys. 10, 105–107 (1969).
[CrossRef]

Raspollini, P.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Revercomb, H. E.

Ridolfi, M.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Smith, W. L.

Sromovsky, L. A.

Steel, W. H.

Thorne, A. P.

Traub, W. A.

Vanasse, G. A.

Vanek, M. D.

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Weddigen, C.

Wynne-Jones, I.

Appl. Opt. (4)

Geophys. Res. Lett. (1)

G. Nolt, P. A. R. Ade, F. Alboni, B. Carli, M. Carlotti, U. Cortesi, M. Epifani, M. J. Griffin, P. A. Hamilton, C. Lee, G. Lepri, F. Mencaraglia, A. G. Murray, J. H. Park, P. Raspollini, M. Ridolfi, and M. D. Vanek, “Stratospheric HBr concentration profile obtained from far-infrared emission spectroscopy,” Geophys. Res. Lett. 24, 281–284 (1997).
[CrossRef]

Infrared Phys. (1)

D. H. Martin and E. Puplett, “Polarized interferometric spectrometer for the millimetre and sub-millimetre spectrum,” Infrared Phys. 10, 105–107 (1969).
[CrossRef]

Int. J. Infrared Millimeter Waves (1)

B. Carli, F. Forni, and F. Mencaraglia, “Phase error correction in FT spectroscopy of spectra with positive and negative intensities,” Int. J. Infrared Millimeter Waves 3, 529–540 (1982).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Rep. Prog. Phys. (1)

P. Jacquinot, “New developments in interference spectroscopy,” Rep. Prog. Phys. 23, 268–272 (1960).
[CrossRef]

Rev. Opt. (1)

J. Connes, “Recherches sur la spectroscopie par transformation de Fourier,” Rev. Opt. 40, 171–183 (1961).

Other (1)

L. Mertz, Transformation in Optics (Wiley, New York, 1966).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Atmospheric emission spectra at five different limb angles in the 118-cm-1 region. A distorted ILS is clearly observed at the base of strong narrow lines.

Fig. 2
Fig. 2

Zenith emission lines of ozone that can be used for deriving the instrumental distortion function. The strongest line near 117 cm-1 was selected for deriving the ILS.

Fig. 3
Fig. 3

Normalized modulus Λ(x) (left-hand axis, starting from unity) and phase Φ(x) (right-hand axis) of the Fourier transformation of the 117-cm-1 line shown in Fig. 2. The complex function Λ(x)exp[iΦ(x)] is the product of the distortion function A(x)exp[iϕ(x)] with a function that depends on only the inherent width of the line, the instrument resolution, and the frequency shift with which the line is sampled by the spectral grid. The dashed curves in the plot represent the fitted functions that model these interfering effects [exp(-αx - βx 2) for the modulus and a slope mx for the phase].

Fig. 4
Fig. 4

Modulus {A(x) = Λ(x)/[exp(-αx - βx 2)]} (left-hand axis, top curve) and phase [ϕ(x) = Φ(x) - mx] (right-hand axis) of the distortion function.

Fig. 5
Fig. 5

Modulus [1/A(x)] (left-hand axis, top curve) and phase [-ϕ(x)] (right-hand axis) of the inverse distortion function for the three lines reported in Fig. 2: line centered at 117 cm-1 (solid curves), line centered at 12.3 cm-1 (dashed curves), line centered at 12.6 cm-1 (dotted curves).

Fig. 6
Fig. 6

Inverse ILS of the line centered at 117 cm-1 equal to the Fourier transform of the complex function shown in Fig. 5.

Fig. 7
Fig. 7

Corrected spectra obtained by convolution of the features of Fig. 2 with the inverse ILS of Fig. 6.

Fig. 8
Fig. 8

Dashed lines represent independent estimates of the modulus (left-hand axis, top curves) and phase (right-hand axis) of the inverse distortion function obtained from different calibration spectra by use of the feature at 117 cm-1. The solid curve represents the function obtained from the average spectrum.

Fig. 9
Fig. 9

Atmospheric emission spectra of Fig. 1 after the correction.

Fig. 10
Fig. 10

Line of the average calibration spectrum recorded by the 49–51-cm-1 channel before the correction (plot above) and after the correction (plot below) by use of the correction function obtained from this line.

Fig. 11
Fig. 11

Left-hand axis (upper plots): comparison of the modulus of the inverse ILS at 50 cm-1 (dashed curve) and at 117 cm-1, with the latter scaled with the square of the frequency. Right-hand axis (lower plots): comparison of the phase of the inverse ILS at 50 cm-1 (dashed curve) and at 117 cm-1, with the latter scaled with the frequency.

Equations (20)

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

I x = 0   S σ cos 2 π σ x d σ ,
I m x = 0   S σ cos 2 π σ x + ψ d σ .
I z x = 0   S σ cos 2 π σ x + α x z d σ .
I m x = 1 S b S b 0   S σ cos 2 π σ x + α x z d σ d s .
I m x = 1 l - z 0 l - z 0 0   S σ cos 2 π σ x + α x z d σ d z ,
I m x = 0   A x ,   σ S σ cos 2 π σ x + ϕ x ,   σ d σ ,
A x ,   σ = sinc π σ α x l , ϕ x ,   σ = 2 π σ α x z 0 x - l / 2 ,
I θ x = 0   S σ cos 2 π σ x + θ δ - 1 2 x θ 2 d σ ,
I m x = 1 Ω Ω 0   S σ cos 2 π σ x + θ δ - 1 2 x θ 2 d σ d ω .
I m x = 1 Θ θ 0 - Θ / 2 θ 0 + Θ / 2 0   S σ cos 2 π σ x + δ θ d σ d θ ,
I m x = 0   A x ,   σ S σ cos 2 π σ x + ϕ x ,   σ d σ ,
A x ,   σ = sinc π σ δ x Θ ,     ϕ x ,   σ = 2 π σ δ x θ 0 .
ϕ x ,   σ = 2 π σ Δ x ,
I m x = 0   A σ ,   x S σ cos 2 π σ x + ϕ σ ,   x d σ .
I m x = A x 0   S σ cos 2 π σ x + ϕ x d σ .
S m σ = FT I m x = S σ   *   L σ ,
L σ = FT A x exp i ϕ x .
ϕ - x = - ϕ x ,     A x = A - x .
L - 1 σ = FT 1 A x exp - i ϕ x ,
S m σ   *   L - 1 σ = S σ   *   L σ   *   L - 1 σ = S σ   *   FT A x exp i ϕ x 1 A x × exp - i ϕ x = S σ   *   FT 1 = S σ   *   sinc π σ / D ,

Metrics