Abstract

An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.

© 1984 Optical Society of America

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References

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  1. J. H. Park, “Effect of Interferogram Smearing on Atmospheric Limb Sounding by Fourier Transform Spectroscopy,” Appl. Opt. 21, 1356 (1982).
    [CrossRef] [PubMed]
  2. J. H. Park, “Analysis Method for Fourier Transform Spectroscopy,” Appl. Opt. 22, 835 (1983).
    [CrossRef] [PubMed]
  3. G. Guelachvili, “Distortions in Fourier Spectra and Diagnosis,” in Spectrometric Techniques, Vol. 2, G. A. Vanasse, Ed. (Academic, New York, 1981).
  4. E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratospheric NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
    [CrossRef]
  5. P. R. Griffiths, Chemical Infrared Fourier Transform Spectroscopy (Wiley-Interscience, New York, 1975).
  6. J. B. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972).
  7. C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl, and HF at Northern and Southern Mid-latitudes,” J. Geophys. Res. 85, 1621 (1980).
    [CrossRef]
  8. L. S. Rothman, “AFGL Atmospheric Absorption Line Parameters Compilation: 1980 Version,” Appl. Opt. 20, 791 (1981).
    [CrossRef] [PubMed]
  9. C. Rinsland, C. Benner, College of William & Mary; private communication (1982).
  10. A. Baldacci, C. P. Rinsland, M. A. H. Smith, K. N. Rao, “Spectrum of 13C16O2 at 2.8 μm,” J. Mol. Spectrosc. 94, 351 (1982).
    [CrossRef]
  11. D. J. W. Kendall, H. L. Buijs, Bomem, Inc. Report, MCA contract 77–156 (1979).
  12. The Stratosphere 1981, WMO Global Ozone Research and Monitoring Project, Report No. 11 (NASA Goddard Space Flight Center, 1981).
  13. J. M. Russell, J. C. Gille, E. E. Remsberg, L. L. Gordley, P. L. Bailey, H. Fischer, A. Girard, S. R. Drayson, W. F. J. Evans, J. E. Harries, “Validation of Water Vapor Results Measured by the Limb Infrared Monitor of the Stratosphere (LIMS) Experiment on Nimbus 7,” J. Geophys. Res. in press (1984).
  14. L. S. Rothman, R. R. Gamache, A. Barbe, A. Goldman, J. R. Gillis, L. R. Brown, R. A. Toth, J.-M. Flaud, C. Camy-Peyret, “AFGL Atmospheric Absorption Line Parameters Compilation: 1982 Edition,” Appl. Opt. 22, 2247 (1983).
    [CrossRef] [PubMed]
  15. C. P. Rinsland, College of William & Mary; private communication (1982).
  16. J. H. Park, L. S. Rothman, C. P. Rinsland, M. A. H. Smith, D. J. Richardson, J. C. Larsen, “Atlas of Absorption Lines from 0 to 17,900 cm−1,” NASA RP-1084 (1981).

1983 (2)

1982 (2)

J. H. Park, “Effect of Interferogram Smearing on Atmospheric Limb Sounding by Fourier Transform Spectroscopy,” Appl. Opt. 21, 1356 (1982).
[CrossRef] [PubMed]

A. Baldacci, C. P. Rinsland, M. A. H. Smith, K. N. Rao, “Spectrum of 13C16O2 at 2.8 μm,” J. Mol. Spectrosc. 94, 351 (1982).
[CrossRef]

1981 (1)

1980 (2)

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratospheric NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl, and HF at Northern and Southern Mid-latitudes,” J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

Bailey, P. L.

J. M. Russell, J. C. Gille, E. E. Remsberg, L. L. Gordley, P. L. Bailey, H. Fischer, A. Girard, S. R. Drayson, W. F. J. Evans, J. E. Harries, “Validation of Water Vapor Results Measured by the Limb Infrared Monitor of the Stratosphere (LIMS) Experiment on Nimbus 7,” J. Geophys. Res. in press (1984).

Baldacci, A.

A. Baldacci, C. P. Rinsland, M. A. H. Smith, K. N. Rao, “Spectrum of 13C16O2 at 2.8 μm,” J. Mol. Spectrosc. 94, 351 (1982).
[CrossRef]

Barbe, A.

Bell, J. B.

J. B. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972).

Benner, C.

C. Rinsland, C. Benner, College of William & Mary; private communication (1982).

Brown, L. R.

Buijs, H. L.

D. J. W. Kendall, H. L. Buijs, Bomem, Inc. Report, MCA contract 77–156 (1979).

Camy-Peyret, C.

Drayson, S. R.

J. M. Russell, J. C. Gille, E. E. Remsberg, L. L. Gordley, P. L. Bailey, H. Fischer, A. Girard, S. R. Drayson, W. F. J. Evans, J. E. Harries, “Validation of Water Vapor Results Measured by the Limb Infrared Monitor of the Stratosphere (LIMS) Experiment on Nimbus 7,” J. Geophys. Res. in press (1984).

Evans, W. F. J.

J. M. Russell, J. C. Gille, E. E. Remsberg, L. L. Gordley, P. L. Bailey, H. Fischer, A. Girard, S. R. Drayson, W. F. J. Evans, J. E. Harries, “Validation of Water Vapor Results Measured by the Limb Infrared Monitor of the Stratosphere (LIMS) Experiment on Nimbus 7,” J. Geophys. Res. in press (1984).

Farmer, C. B.

C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl, and HF at Northern and Southern Mid-latitudes,” J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

Fischer, H.

J. M. Russell, J. C. Gille, E. E. Remsberg, L. L. Gordley, P. L. Bailey, H. Fischer, A. Girard, S. R. Drayson, W. F. J. Evans, J. E. Harries, “Validation of Water Vapor Results Measured by the Limb Infrared Monitor of the Stratosphere (LIMS) Experiment on Nimbus 7,” J. Geophys. Res. in press (1984).

Flaud, J.-M.

Gamache, R. R.

Gille, J. C.

J. M. Russell, J. C. Gille, E. E. Remsberg, L. L. Gordley, P. L. Bailey, H. Fischer, A. Girard, S. R. Drayson, W. F. J. Evans, J. E. Harries, “Validation of Water Vapor Results Measured by the Limb Infrared Monitor of the Stratosphere (LIMS) Experiment on Nimbus 7,” J. Geophys. Res. in press (1984).

Gillis, J. R.

Girard, A.

J. M. Russell, J. C. Gille, E. E. Remsberg, L. L. Gordley, P. L. Bailey, H. Fischer, A. Girard, S. R. Drayson, W. F. J. Evans, J. E. Harries, “Validation of Water Vapor Results Measured by the Limb Infrared Monitor of the Stratosphere (LIMS) Experiment on Nimbus 7,” J. Geophys. Res. in press (1984).

Goldman, A.

L. S. Rothman, R. R. Gamache, A. Barbe, A. Goldman, J. R. Gillis, L. R. Brown, R. A. Toth, J.-M. Flaud, C. Camy-Peyret, “AFGL Atmospheric Absorption Line Parameters Compilation: 1982 Edition,” Appl. Opt. 22, 2247 (1983).
[CrossRef] [PubMed]

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratospheric NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

Gordley, L. L.

J. M. Russell, J. C. Gille, E. E. Remsberg, L. L. Gordley, P. L. Bailey, H. Fischer, A. Girard, S. R. Drayson, W. F. J. Evans, J. E. Harries, “Validation of Water Vapor Results Measured by the Limb Infrared Monitor of the Stratosphere (LIMS) Experiment on Nimbus 7,” J. Geophys. Res. in press (1984).

Griffiths, P. R.

P. R. Griffiths, Chemical Infrared Fourier Transform Spectroscopy (Wiley-Interscience, New York, 1975).

Guelachvili, G.

G. Guelachvili, “Distortions in Fourier Spectra and Diagnosis,” in Spectrometric Techniques, Vol. 2, G. A. Vanasse, Ed. (Academic, New York, 1981).

Harries, J. E.

J. M. Russell, J. C. Gille, E. E. Remsberg, L. L. Gordley, P. L. Bailey, H. Fischer, A. Girard, S. R. Drayson, W. F. J. Evans, J. E. Harries, “Validation of Water Vapor Results Measured by the Limb Infrared Monitor of the Stratosphere (LIMS) Experiment on Nimbus 7,” J. Geophys. Res. in press (1984).

Kendall, D. J. W.

D. J. W. Kendall, H. L. Buijs, Bomem, Inc. Report, MCA contract 77–156 (1979).

Larsen, J. C.

J. H. Park, L. S. Rothman, C. P. Rinsland, M. A. H. Smith, D. J. Richardson, J. C. Larsen, “Atlas of Absorption Lines from 0 to 17,900 cm−1,” NASA RP-1084 (1981).

Mankin, W. G.

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratospheric NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

Muller, C.

C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl, and HF at Northern and Southern Mid-latitudes,” J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

Murcray, D. G.

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratospheric NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

Murcray, F. J.

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratospheric NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

Niple, E.

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratospheric NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

Park, J. H.

Rao, K. N.

A. Baldacci, C. P. Rinsland, M. A. H. Smith, K. N. Rao, “Spectrum of 13C16O2 at 2.8 μm,” J. Mol. Spectrosc. 94, 351 (1982).
[CrossRef]

Raper, O. F.

C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl, and HF at Northern and Southern Mid-latitudes,” J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

Remsberg, E. E.

J. M. Russell, J. C. Gille, E. E. Remsberg, L. L. Gordley, P. L. Bailey, H. Fischer, A. Girard, S. R. Drayson, W. F. J. Evans, J. E. Harries, “Validation of Water Vapor Results Measured by the Limb Infrared Monitor of the Stratosphere (LIMS) Experiment on Nimbus 7,” J. Geophys. Res. in press (1984).

Richardson, D. J.

J. H. Park, L. S. Rothman, C. P. Rinsland, M. A. H. Smith, D. J. Richardson, J. C. Larsen, “Atlas of Absorption Lines from 0 to 17,900 cm−1,” NASA RP-1084 (1981).

Rinsland, C.

C. Rinsland, C. Benner, College of William & Mary; private communication (1982).

Rinsland, C. P.

A. Baldacci, C. P. Rinsland, M. A. H. Smith, K. N. Rao, “Spectrum of 13C16O2 at 2.8 μm,” J. Mol. Spectrosc. 94, 351 (1982).
[CrossRef]

C. P. Rinsland, College of William & Mary; private communication (1982).

J. H. Park, L. S. Rothman, C. P. Rinsland, M. A. H. Smith, D. J. Richardson, J. C. Larsen, “Atlas of Absorption Lines from 0 to 17,900 cm−1,” NASA RP-1084 (1981).

Robbins, B. D.

C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl, and HF at Northern and Southern Mid-latitudes,” J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

Rothman, L. S.

Russell, J. M.

J. M. Russell, J. C. Gille, E. E. Remsberg, L. L. Gordley, P. L. Bailey, H. Fischer, A. Girard, S. R. Drayson, W. F. J. Evans, J. E. Harries, “Validation of Water Vapor Results Measured by the Limb Infrared Monitor of the Stratosphere (LIMS) Experiment on Nimbus 7,” J. Geophys. Res. in press (1984).

Smith, M. A. H.

A. Baldacci, C. P. Rinsland, M. A. H. Smith, K. N. Rao, “Spectrum of 13C16O2 at 2.8 μm,” J. Mol. Spectrosc. 94, 351 (1982).
[CrossRef]

J. H. Park, L. S. Rothman, C. P. Rinsland, M. A. H. Smith, D. J. Richardson, J. C. Larsen, “Atlas of Absorption Lines from 0 to 17,900 cm−1,” NASA RP-1084 (1981).

Toth, R. A.

L. S. Rothman, R. R. Gamache, A. Barbe, A. Goldman, J. R. Gillis, L. R. Brown, R. A. Toth, J.-M. Flaud, C. Camy-Peyret, “AFGL Atmospheric Absorption Line Parameters Compilation: 1982 Edition,” Appl. Opt. 22, 2247 (1983).
[CrossRef] [PubMed]

C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl, and HF at Northern and Southern Mid-latitudes,” J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

Appl. Opt. (4)

Geophys. Res. Lett. (1)

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, “Stratospheric NO2 and H2O Mixing Ratio Profiles from High Resolution Infrared Solar Spectra Using Nonlinear Least Squares,” Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

J. Geophys. Res. (1)

C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Muller, “Simultaneous Spectroscopic Measurements of Stratospheric Species: O3, CH4, CO, CO2, N2O, H2O, HCl, and HF at Northern and Southern Mid-latitudes,” J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

J. Mol. Spectrosc. (1)

A. Baldacci, C. P. Rinsland, M. A. H. Smith, K. N. Rao, “Spectrum of 13C16O2 at 2.8 μm,” J. Mol. Spectrosc. 94, 351 (1982).
[CrossRef]

Other (9)

D. J. W. Kendall, H. L. Buijs, Bomem, Inc. Report, MCA contract 77–156 (1979).

The Stratosphere 1981, WMO Global Ozone Research and Monitoring Project, Report No. 11 (NASA Goddard Space Flight Center, 1981).

J. M. Russell, J. C. Gille, E. E. Remsberg, L. L. Gordley, P. L. Bailey, H. Fischer, A. Girard, S. R. Drayson, W. F. J. Evans, J. E. Harries, “Validation of Water Vapor Results Measured by the Limb Infrared Monitor of the Stratosphere (LIMS) Experiment on Nimbus 7,” J. Geophys. Res. in press (1984).

C. P. Rinsland, College of William & Mary; private communication (1982).

J. H. Park, L. S. Rothman, C. P. Rinsland, M. A. H. Smith, D. J. Richardson, J. C. Larsen, “Atlas of Absorption Lines from 0 to 17,900 cm−1,” NASA RP-1084 (1981).

C. Rinsland, C. Benner, College of William & Mary; private communication (1982).

P. R. Griffiths, Chemical Infrared Fourier Transform Spectroscopy (Wiley-Interscience, New York, 1975).

J. B. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972).

G. Guelachvili, “Distortions in Fourier Spectra and Diagnosis,” in Spectrometric Techniques, Vol. 2, G. A. Vanasse, Ed. (Academic, New York, 1981).

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Figures (9)

Fig. 1
Fig. 1

Simulations of the CO2 absorption spectra (solid line) for z = 30 km using segmented-lines approximation of feff(δ) for (a) 3505–3509 cm−1 and (b) 3514.5–3518.5 cm−1, and using straight-line approximation of feff(δ) for (c) 3505–3509 cm−1 and (d) 3514.5–3518.5 cm−1. Note: measured spectrum (dotted line) is normalized by the background level, and differences between spectra are shown at the 0.6 level on the transmittance scale. The rms value should not be directly related to the uncertainty in the retrieved CO2 mixing ratio value (see Sec. II). The uncertainty in the retrieved CO2 mixing ratio value is ±5% for (a) and (b).

Fig. 2
Fig. 2

Simulations of H2O absorption spectra (solid line) for z = 38 km for 3949.25–3951.25 cm−1: (a) using segmented-lines approximation of feff(δ); (b) using straight-line approximation of feff(δ). Note: measured spectrum (dotted line) is normalized by the background level, and differences between spectra are shown at the 0.6 level on the transmittance scale. The uncertainty in the retrieved H2O mixing ratio value is ±5% for (a).

Fig. 3
Fig. 3

Same as Fig. 2 except for z = 36 km. The uncertainty in the retrieved H2O mixing ratio value is ±10% for (a).

Fig. 4
Fig. 4

Same as Fig. 2 except for z = 37 km. The uncertainty in the retrieved H2O mixing ratio value is ±15% for (a).

Fig. 5
Fig. 5

Results of segmented-lines approximation for the CO2 absorption spectrum [shown in Fig. 1(a)]: (a) values of feff(δi) as a function of optical path difference, and (b) variations of gas mixing ratio for each segment j of the interferogram.

Fig. 6
Fig. 6

Same as Fig. 5 except for the CO2 spectrum [shown in Fig. 1(b)].

Fig. 7
Fig. 7

Same as Fig. 5 except for the H2O spectrum [shown in Fig. 2(a)].

Fig. 8
Fig. 8

Same as Fig. 5 except for the H2O spectrum [shown in Fig. 3(a)].

Fig. 9
Fig. 9

Same as Fig. 2 [Fig. 2(a) is for j = 102 and Fig. 2(b) is for j = 0] but the simulations are for the various interferogram segments: (a) j = 10, (b) j = 20, (c) j = 30, (d) j = 40, (e) j = 50, and (f) j = 60.

Equations (14)

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τ ¯ m ( ν ) = [ B ¯ ( ν ) - Q ] / [ B ¯ 0 ( ν ) - Q ] ,
τ ¯ t h ( ν ) = - τ t h ( ν ) Φ ( ν - ν ) d v ,
F ( ν i ) = τ ¯ m ( ν i ) - τ ¯ t h ( ν i ) ,
τ ¯ t h ( ν ) = 1 - a ¯ t h ( ν ) ,
a ¯ t h ( ν ) = 2 0 L I f ( δ ) f eff ( δ ) exp ( - i 2 π ν δ ) d δ ,
I f ( δ ) = - a t h ( v ) exp ( i 2 π ν 0 ɛ 0 ) exp ( i 2 π ν δ ) d ν .
Φ ( ν - ν ) = 2 0 L f eff ( δ ) exp ( i 2 π ν 0 ɛ 0 ) exp [ - i 2 π δ ( ν - ν ) ] d δ ,
a ¯ t h ( ν ) = 2 0 L [ I f ( δ ) f eff ( δ ) + g eff ( δ ) ] exp ( - i 2 π ν δ ) d δ .
Δ δ = 1 / Δ σ .
N = L / Δ δ = K Δ ν L ,
f eff ( δ i ) = f 0 ( δ i ) = 1 + c 0 ( δ i / L ) ,
f eff ( δ i ) = f j ( δ i ) = f 0 ( δ k ) + c j ( δ i - δ k ) ,
f eff ( δ i ) = 1 + d 0 sin ( 2 π γ δ + ϕ 0 ) ,
exp ( i 2 π ν 0 ɛ 0 ) = exp [ i 2 π ν 0 ɛ 0 sin ( 2 π β δ + ϕ 0 ) ] ,

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