Abstract

Phase correction is a critical procedure for most space-borne Fourier transform spectrometers (FTSs) whose accuracy (owing to often poor signal-to-noise ratio, SNR) can be jeopardized from many uncontrollable environmental conditions. This work considers the phase correction in an FTS working under significant temperature change during the measurement and affected by mechanical disturbances. The implemented method is based on the identification of an instrumental phase that is dependent on the interferometer temperature and on the extraction of a linear phase component through a least-squares approach. The use of an instrumental phase parameterized with the interferometer temperature eases the determination of the linear phase that can be extracted using only a narrow spectral region selected to be immune from disturbances. The procedure, in this way, is made robust against phase errors arising from instrumental effects, a key feature to reduce the disturbances through spectra averaging. The method was specifically developed for the Mars IR Mapper spectrometer, that was designed for operation onboard a rover on the Mars surface; the validation was performed using ground and in-flight measurements of the Fourier transform IR spectrometer planetary Fourier spectrometer, onboard the MarsExpress mission. The symmetrization has been exploited also for the spectra calibration, highlighting the issues deriving from the cases of relevant beamsplitter emission. The applicability of this procedure to other instruments is conditional to the presence in the spectra of at least one spectral region with a large SNR along with a negligible (or known) beamsplitter emission. For the PFS instrument, the processing of data with relevant beamsplitter emission has been performed exploiting the absorption carbon dioxide bands present in Martian spectra.

© 2011 Optical Society of America

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References

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  1. M. L. Forman, W. H. Steel, and G. A. Vanasse, “Correction of asymmetric interferograms obtained in Fourier spectroscopy,” J. Opt. Soc. Am. 56, 59–61 (1966).
    [CrossRef]
  2. L. Mertz, “Auxiliary computation for Fourier spectrometry,” Infrared Phys. 7, 17–23 (1967).
    [CrossRef]
  3. A. Kleinert and O. Trieschmann, “Phase determination for a Fourier transform infrared spectrometer in emission mode,” Appl. Opt. 46, 2307–2319 (2007).
    [CrossRef] [PubMed]
  4. C. V. Cox, P. Green, J. Pickering, J. Murray, J. E. Harries, and A. Last, “Modelling of the beamsplitter properties within the tropospheric airborne Fourier transform spectrometer (TAFTS) and associated effect on instrument calibration,” in Fourier Transform Spectroscopy, OSA Technical Digest (Optical Society of America, 2009), paper FMC4.
  5. S. Turbide and T. Smithson, “Calibration algorithm for Fourier transform spectrometer with thermal instabilities,” Appl. Opt. 49, 3411–3417 (2010).
    [CrossRef] [PubMed]
  6. K. Rahmelow and W. Hübner, “Phase correction in Fourier transform spectroscopy: subsequent displacement correction and error limit,” Appl. Opt. 36, 6678–6686 (1997).
    [CrossRef]
  7. D. B. Chase, “Phase correction in FT-IR,” Appl. Spectrosc. 36, 240–244 (1982).
    [CrossRef]
  8. R. C. M. Learner, A. P. Thorne, and J. W. Brault, “Ghosts and artifacts in Fourier-transform spectrometry,” Appl. Opt. 35, 2947–2954 (1996).
    [CrossRef] [PubMed]
  9. C. A. McCoy and J. A. de Haseth, “Modified phase correction algorithms in VCD/FT-IR spectrometry,” Mikrochim. Acta 94, 97–100 (1988).
    [CrossRef]
  10. T. P. Sheahen, “Chirped Fourier spectroscopy. 1: Dynamic range improvement and phase correction,” Appl. Opt. 13, 2907–2912 (1974).
    [CrossRef] [PubMed]
  11. H. E. Revercomb, H. Buijs, H. B. Howell, D. D. LaPorte, W. L. Smith, and L. A. Sromovsky, “Radiometric calibration of IR Fourier transform spectrometers: solution to a problem with the high-resolution interferometer sounder,” Appl. Opt. 27, 3210–3218 (1988).
    [CrossRef] [PubMed]
  12. S. P. Davis, Fourier Transform Spectrometry (Academic, 2001).
  13. B. Saggin, L. Comolli, and V. Formisano, “Mechanical disturbances in Fourier spectrometers,” Appl. Opt. 46, 5248–5256(2007).
    [CrossRef] [PubMed]
  14. B. Carli, L. Palchetti, and P. Raspollini, “Effect of beam-splitter emission in Fourier-transform emission spectroscopy,” Appl. Opt. 38, 7475–7480 (1999).
    [CrossRef]
  15. 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]

2010

2007

1999

1997

1996

1988

1982

1974

1967

L. Mertz, “Auxiliary computation for Fourier spectrometry,” Infrared Phys. 7, 17–23 (1967).
[CrossRef]

1966

Blom, C. E.

Brault, J. W.

Buijs, H.

Carli, B.

Chase, D. B.

Comolli, L.

Cox, C. V.

C. V. Cox, P. Green, J. Pickering, J. Murray, J. E. Harries, and A. Last, “Modelling of the beamsplitter properties within the tropospheric airborne Fourier transform spectrometer (TAFTS) and associated effect on instrument calibration,” in Fourier Transform Spectroscopy, OSA Technical Digest (Optical Society of America, 2009), paper FMC4.

Davis, S. P.

S. P. Davis, Fourier Transform Spectrometry (Academic, 2001).

de Haseth, J. A.

C. A. McCoy and J. A. de Haseth, “Modified phase correction algorithms in VCD/FT-IR spectrometry,” Mikrochim. Acta 94, 97–100 (1988).
[CrossRef]

Forman, M. L.

Formisano, V.

Green, P.

C. V. Cox, P. Green, J. Pickering, J. Murray, J. E. Harries, and A. Last, “Modelling of the beamsplitter properties within the tropospheric airborne Fourier transform spectrometer (TAFTS) and associated effect on instrument calibration,” in Fourier Transform Spectroscopy, OSA Technical Digest (Optical Society of America, 2009), paper FMC4.

Harries, J. E.

C. V. Cox, P. Green, J. Pickering, J. Murray, J. E. Harries, and A. Last, “Modelling of the beamsplitter properties within the tropospheric airborne Fourier transform spectrometer (TAFTS) and associated effect on instrument calibration,” in Fourier Transform Spectroscopy, OSA Technical Digest (Optical Society of America, 2009), paper FMC4.

Höpfner, M.

Howell, H. B.

Hübner, W.

Kleinert, A.

LaPorte, D. D.

Last, A.

C. V. Cox, P. Green, J. Pickering, J. Murray, J. E. Harries, and A. Last, “Modelling of the beamsplitter properties within the tropospheric airborne Fourier transform spectrometer (TAFTS) and associated effect on instrument calibration,” in Fourier Transform Spectroscopy, OSA Technical Digest (Optical Society of America, 2009), paper FMC4.

Learner, R. C. M.

McCoy, C. A.

C. A. McCoy and J. A. de Haseth, “Modified phase correction algorithms in VCD/FT-IR spectrometry,” Mikrochim. Acta 94, 97–100 (1988).
[CrossRef]

Mertz, L.

L. Mertz, “Auxiliary computation for Fourier spectrometry,” Infrared Phys. 7, 17–23 (1967).
[CrossRef]

Murray, J.

C. V. Cox, P. Green, J. Pickering, J. Murray, J. E. Harries, and A. Last, “Modelling of the beamsplitter properties within the tropospheric airborne Fourier transform spectrometer (TAFTS) and associated effect on instrument calibration,” in Fourier Transform Spectroscopy, OSA Technical Digest (Optical Society of America, 2009), paper FMC4.

Palchetti, L.

Pickering, J.

C. V. Cox, P. Green, J. Pickering, J. Murray, J. E. Harries, and A. Last, “Modelling of the beamsplitter properties within the tropospheric airborne Fourier transform spectrometer (TAFTS) and associated effect on instrument calibration,” in Fourier Transform Spectroscopy, OSA Technical Digest (Optical Society of America, 2009), paper FMC4.

Rahmelow, K.

Raspollini, P.

Revercomb, H. E.

Saggin, B.

Sheahen, T. P.

Smith, W. L.

Smithson, T.

Sromovsky, L. A.

Steel, W. H.

Thorne, A. P.

Trieschmann, O.

Turbide, S.

Vanasse, G. A.

Weddigen, C.

Appl. Opt.

T. P. Sheahen, “Chirped Fourier spectroscopy. 1: Dynamic range improvement and phase correction,” Appl. Opt. 13, 2907–2912 (1974).
[CrossRef] [PubMed]

H. E. Revercomb, H. Buijs, H. B. Howell, D. D. LaPorte, W. L. Smith, and L. A. Sromovsky, “Radiometric calibration of IR Fourier transform spectrometers: solution to a problem with the high-resolution interferometer sounder,” Appl. Opt. 27, 3210–3218 (1988).
[CrossRef] [PubMed]

K. Rahmelow and W. Hübner, “Phase correction in Fourier transform spectroscopy: subsequent displacement correction and error limit,” Appl. Opt. 36, 6678–6686 (1997).
[CrossRef]

B. Carli, L. Palchetti, and P. Raspollini, “Effect of beam-splitter emission in Fourier-transform emission spectroscopy,” Appl. Opt. 38, 7475–7480 (1999).
[CrossRef]

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]

R. C. M. Learner, A. P. Thorne, and J. W. Brault, “Ghosts and artifacts in Fourier-transform spectrometry,” Appl. Opt. 35, 2947–2954 (1996).
[CrossRef] [PubMed]

A. Kleinert and O. Trieschmann, “Phase determination for a Fourier transform infrared spectrometer in emission mode,” Appl. Opt. 46, 2307–2319 (2007).
[CrossRef] [PubMed]

B. Saggin, L. Comolli, and V. Formisano, “Mechanical disturbances in Fourier spectrometers,” Appl. Opt. 46, 5248–5256(2007).
[CrossRef] [PubMed]

S. Turbide and T. Smithson, “Calibration algorithm for Fourier transform spectrometer with thermal instabilities,” Appl. Opt. 49, 3411–3417 (2010).
[CrossRef] [PubMed]

Appl. Spectrosc.

Infrared Phys.

L. Mertz, “Auxiliary computation for Fourier spectrometry,” Infrared Phys. 7, 17–23 (1967).
[CrossRef]

J. Opt. Soc. Am.

Mikrochim. Acta

C. A. McCoy and J. A. de Haseth, “Modified phase correction algorithms in VCD/FT-IR spectrometry,” Mikrochim. Acta 94, 97–100 (1988).
[CrossRef]

Other

S. P. Davis, Fourier Transform Spectrometry (Academic, 2001).

C. V. Cox, P. Green, J. Pickering, J. Murray, J. E. Harries, and A. Last, “Modelling of the beamsplitter properties within the tropospheric airborne Fourier transform spectrometer (TAFTS) and associated effect on instrument calibration,” in Fourier Transform Spectroscopy, OSA Technical Digest (Optical Society of America, 2009), paper FMC4.

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Figures (6)

Fig. 1
Fig. 1

(a) Ceramic lamp based PFS calibration, spectral modulus, and phase of one measured interferogram. (b) Phases of calibration spectra (scattered points) with regression curves of 3rd (black), 4th (dark gray), and 5th order (light gray) (10 forward motion interferograms). (c) The regression residuals reported with the same color code.

Fig. 2
Fig. 2

Phase regression residuals with the 4th order polynomial of the correction procedure as a function of temperature: the black, dark gray, and light gray lines are the residuals of the 300 K , 282 K , and 290 K calibration data using the natural phase estimated at 300 K , respectively.

Fig. 3
Fig. 3

(a) Interferogram 91, forward pendulum motion, orbit 726, Mars observation. The dark gray, light gray, and black lines are respectively the modulus, the Mertz method, and the proposed method spectra. (b) Zoom of the three different spectra in the frequency range of 1800 3800 cm 1 .

Fig. 4
Fig. 4

(a) Average spectra from 10 interferograms in the frequency range 1800 3800 cm 1 . The dark gray, light gray, and black lines are the mean modulus spectrum, the mean Mertz real spectrum, and the real mean spectrum recovered with the proposed method, respectively. (b) Raw phase of the spectra of three interferograms in the frequency range 1800 3000 cm 1 .

Fig. 5
Fig. 5

Correction phases in the spectral region mostly affected by ghosts with three different procedures: dashed curve, Mertz with 20 points, light gray continuous Mertz with 100 points, thick continuous the proposed one.

Fig. 6
Fig. 6

(a) PFS deep space phase residuals assuming only detector emission. (b) Residuals after phase correction using the correct emission phase. (c) The black, dark gray, and light gray lines show the calibrated mean spectrum with the proposed method, the modulus, and the Mertz approach, respectively.

Tables (2)

Tables Icon

Table 1 Regression Mean Square Errors and Radiometric Errors for the Calibration Data

Tables Icon

Table 2 Regression Uncertainties and Radiometric Errors for 282 K and 290 K Calibration Data

Equations (11)

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M sym ( σ ) = M ( σ ) e i ϕ ( σ ) ,
M ( σ ) = ( R ( σ ) E d ( σ ) + E op ( σ ) ) | S ( σ ) | · e i ( 2 π σ ( δ ( t ) + Δ x ( σ , T ) ) + φ ( σ · v ) ) ,
ϕ ( σ , t , T , v ) = 2 π σ δ ( t ) + 2 π σ Δ x ( σ , T ) + φ ( σ · v ) .
M ( σ ) = S ( σ ) · ( R ( σ ) E d ( σ ) + E op ( σ ) ) .
{ M 1 ( σ ) = S ( σ ) · ( R 1 ( σ ) E d ( σ ) + E op ( σ ) ) M 2 ( σ ) = S ( σ ) · ( R 2 ( σ ) E d ( σ ) + E op ( σ ) ) ,
{ S ( σ ) = M 2 ( σ ) M 1 ( σ ) R 2 ( σ ) R 1 ( σ ) E E ( σ ) = E d ( σ ) E op ( σ ) = R 1 ( σ ) M 1 ( σ ) S ( σ ) .
R ( σ ) = Re ( M ( σ ) S ( σ ) ) + E E ( σ ) .
R ( σ ) = Re ( M ( σ ) M 1 ( σ ) S ( σ ) ) .
M sym ( σ ) = Re [ S ( σ ) · e i ( ϕ + δ ( t ) ) · ( R ( σ ) E d ( σ ) + E op ( σ ) ) ] .
M ds ( σ ) = | S ( σ ) | e i [ 2 π σ ( δ ( t ) + Δ x ( σ , T ) ) + φ ( σ · v ) ] · ( E d ( σ ) + i · E bs ( σ ) + E f o ( σ ) ) ,
ϕ r = 2 π σ δ ( t ) + atan [ E bs ( σ ) E fo ( σ ) E d ( σ ) ] .

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