Abstract

A method is developed to demodulate (velocity correct) Fourier transform spectrometer data that are taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low-cost, high-resolution audio digitizers to record high-quality data without the need for an event timer or quadrature laser hardware and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simple implementation make it an attractive alternative in space-based applications when compared to previous methods such as the Brault algorithm.

© 2008 Optical Society of America

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  1. N. S. Pougatchev, J. F. Campbell, C. R. Regan, M. C. Abrams, J. W. Brault, C. B. Farmer, and D. E. Hinton, “Advanced technologies high resolution Fourier transform spectrometer for atmospheric studies,” in Aerospace Conference Proceedings (IEEE, 2000), Vol. 3, pp. 237-243.
  2. J. W. Brault, “New approach to high-precision Fourier transform spectrometer design,” Appl. Opt. 35, 2891-2896 (1996).
    [CrossRef] [PubMed]
  3. U. Griesmann, R. Kling, J. H. Burnett, and L. Bratasz, “The NIST FT700 Vacuum Ultraviolet Fourier Transform Spectrometer: applications in ultraviolet spectrometry and radiometry,” Proc. SPIE 3818, 180-188 (1999).
    [CrossRef]
  4. S. P. Davis, M. C. Abrams, and J. W. Brault, Fourier Transform Spectrometry, 1st ed. (Academic, 2001), p. 181.
  5. L. Palchetti and D. Lastrucci, “Spectral noise due to sampling errors in Fourier-transform spectroscopy,” Appl. Opt. 40, 3235-3243 (2001).
    [CrossRef]
  6. J. J. Murray, “The GIFTS satellite project--enabling the NAS of the future with high resolution soundings and imagery,” 41st Aerospace Sciences Meeting and Exhibit, AIAA 2003-385 (American Institute of Aeronautics and Astronautics, 2003).
  7. L. Genzel and J. Kuhl, “Tilt-compensated Michelson interferometer for Fourier transform spectroscopy,” Appl. Opt. 17, 3304-3308 (1978).
    [CrossRef] [PubMed]
  8. D. E. Hinton, I. G. Nolt, J. H. Park, W. L. Smith, and M. C. Abrams, “Applications of advanced technologies to spacebased Fourier transform spectrometers for atmospheric remote sensing,” in Aerospace Conference Proceedings (IEEE, 1998), Vol. 2, pp. 499-504.
  9. E. Fischer, E. Dalhoff, S. Heim, U. Hofbauer, and H. J. Tiziani, “Absolute interferometric distance measurement using a FM-demodulation technique,” Appl. Opt. 35, 5589-5594 (1995).
    [CrossRef]
  10. Y. C. Agrawal, “Quadrature demodulation in laser Doppler velocimetry,” Appl. Opt. 23, 1685-1686 (1984).
    [CrossRef] [PubMed]
  11. M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Fringe pattern demodulation with a two-dimensional digital phase-locked loop algorithm,” Appl. Opt. 41, 5479-5487 (2002).
    [CrossRef] [PubMed]
  12. R. Beer, Remote Sensing by Fourier Transform Spectroscopy (Wiley, 1992), p. 20.

2002 (1)

2001 (1)

1999 (1)

U. Griesmann, R. Kling, J. H. Burnett, and L. Bratasz, “The NIST FT700 Vacuum Ultraviolet Fourier Transform Spectrometer: applications in ultraviolet spectrometry and radiometry,” Proc. SPIE 3818, 180-188 (1999).
[CrossRef]

1996 (1)

1995 (1)

E. Fischer, E. Dalhoff, S. Heim, U. Hofbauer, and H. J. Tiziani, “Absolute interferometric distance measurement using a FM-demodulation technique,” Appl. Opt. 35, 5589-5594 (1995).
[CrossRef]

1984 (1)

1978 (1)

Abrams, M. C.

N. S. Pougatchev, J. F. Campbell, C. R. Regan, M. C. Abrams, J. W. Brault, C. B. Farmer, and D. E. Hinton, “Advanced technologies high resolution Fourier transform spectrometer for atmospheric studies,” in Aerospace Conference Proceedings (IEEE, 2000), Vol. 3, pp. 237-243.

S. P. Davis, M. C. Abrams, and J. W. Brault, Fourier Transform Spectrometry, 1st ed. (Academic, 2001), p. 181.

D. E. Hinton, I. G. Nolt, J. H. Park, W. L. Smith, and M. C. Abrams, “Applications of advanced technologies to spacebased Fourier transform spectrometers for atmospheric remote sensing,” in Aerospace Conference Proceedings (IEEE, 1998), Vol. 2, pp. 499-504.

Agrawal, Y. C.

Beer, R.

R. Beer, Remote Sensing by Fourier Transform Spectroscopy (Wiley, 1992), p. 20.

Bratasz, L.

U. Griesmann, R. Kling, J. H. Burnett, and L. Bratasz, “The NIST FT700 Vacuum Ultraviolet Fourier Transform Spectrometer: applications in ultraviolet spectrometry and radiometry,” Proc. SPIE 3818, 180-188 (1999).
[CrossRef]

Brault, J. W.

J. W. Brault, “New approach to high-precision Fourier transform spectrometer design,” Appl. Opt. 35, 2891-2896 (1996).
[CrossRef] [PubMed]

S. P. Davis, M. C. Abrams, and J. W. Brault, Fourier Transform Spectrometry, 1st ed. (Academic, 2001), p. 181.

N. S. Pougatchev, J. F. Campbell, C. R. Regan, M. C. Abrams, J. W. Brault, C. B. Farmer, and D. E. Hinton, “Advanced technologies high resolution Fourier transform spectrometer for atmospheric studies,” in Aerospace Conference Proceedings (IEEE, 2000), Vol. 3, pp. 237-243.

Burnett, J. H.

U. Griesmann, R. Kling, J. H. Burnett, and L. Bratasz, “The NIST FT700 Vacuum Ultraviolet Fourier Transform Spectrometer: applications in ultraviolet spectrometry and radiometry,” Proc. SPIE 3818, 180-188 (1999).
[CrossRef]

Burton, D. R.

Campbell, J. F.

N. S. Pougatchev, J. F. Campbell, C. R. Regan, M. C. Abrams, J. W. Brault, C. B. Farmer, and D. E. Hinton, “Advanced technologies high resolution Fourier transform spectrometer for atmospheric studies,” in Aerospace Conference Proceedings (IEEE, 2000), Vol. 3, pp. 237-243.

Dalhoff, E.

E. Fischer, E. Dalhoff, S. Heim, U. Hofbauer, and H. J. Tiziani, “Absolute interferometric distance measurement using a FM-demodulation technique,” Appl. Opt. 35, 5589-5594 (1995).
[CrossRef]

Davis, S. P.

S. P. Davis, M. C. Abrams, and J. W. Brault, Fourier Transform Spectrometry, 1st ed. (Academic, 2001), p. 181.

Farmer, C. B.

N. S. Pougatchev, J. F. Campbell, C. R. Regan, M. C. Abrams, J. W. Brault, C. B. Farmer, and D. E. Hinton, “Advanced technologies high resolution Fourier transform spectrometer for atmospheric studies,” in Aerospace Conference Proceedings (IEEE, 2000), Vol. 3, pp. 237-243.

Fischer, E.

E. Fischer, E. Dalhoff, S. Heim, U. Hofbauer, and H. J. Tiziani, “Absolute interferometric distance measurement using a FM-demodulation technique,” Appl. Opt. 35, 5589-5594 (1995).
[CrossRef]

Gdeisat, M. A.

Genzel, L.

Griesmann, U.

U. Griesmann, R. Kling, J. H. Burnett, and L. Bratasz, “The NIST FT700 Vacuum Ultraviolet Fourier Transform Spectrometer: applications in ultraviolet spectrometry and radiometry,” Proc. SPIE 3818, 180-188 (1999).
[CrossRef]

Heim, S.

E. Fischer, E. Dalhoff, S. Heim, U. Hofbauer, and H. J. Tiziani, “Absolute interferometric distance measurement using a FM-demodulation technique,” Appl. Opt. 35, 5589-5594 (1995).
[CrossRef]

Hinton, D. E.

N. S. Pougatchev, J. F. Campbell, C. R. Regan, M. C. Abrams, J. W. Brault, C. B. Farmer, and D. E. Hinton, “Advanced technologies high resolution Fourier transform spectrometer for atmospheric studies,” in Aerospace Conference Proceedings (IEEE, 2000), Vol. 3, pp. 237-243.

D. E. Hinton, I. G. Nolt, J. H. Park, W. L. Smith, and M. C. Abrams, “Applications of advanced technologies to spacebased Fourier transform spectrometers for atmospheric remote sensing,” in Aerospace Conference Proceedings (IEEE, 1998), Vol. 2, pp. 499-504.

Hofbauer, U.

E. Fischer, E. Dalhoff, S. Heim, U. Hofbauer, and H. J. Tiziani, “Absolute interferometric distance measurement using a FM-demodulation technique,” Appl. Opt. 35, 5589-5594 (1995).
[CrossRef]

Kling, R.

U. Griesmann, R. Kling, J. H. Burnett, and L. Bratasz, “The NIST FT700 Vacuum Ultraviolet Fourier Transform Spectrometer: applications in ultraviolet spectrometry and radiometry,” Proc. SPIE 3818, 180-188 (1999).
[CrossRef]

Kuhl, J.

Lalor, M. J.

Lastrucci, D.

Murray, J. J.

J. J. Murray, “The GIFTS satellite project--enabling the NAS of the future with high resolution soundings and imagery,” 41st Aerospace Sciences Meeting and Exhibit, AIAA 2003-385 (American Institute of Aeronautics and Astronautics, 2003).

Nolt, I. G.

D. E. Hinton, I. G. Nolt, J. H. Park, W. L. Smith, and M. C. Abrams, “Applications of advanced technologies to spacebased Fourier transform spectrometers for atmospheric remote sensing,” in Aerospace Conference Proceedings (IEEE, 1998), Vol. 2, pp. 499-504.

Palchetti, L.

Park, J. H.

D. E. Hinton, I. G. Nolt, J. H. Park, W. L. Smith, and M. C. Abrams, “Applications of advanced technologies to spacebased Fourier transform spectrometers for atmospheric remote sensing,” in Aerospace Conference Proceedings (IEEE, 1998), Vol. 2, pp. 499-504.

Pougatchev, N. S.

N. S. Pougatchev, J. F. Campbell, C. R. Regan, M. C. Abrams, J. W. Brault, C. B. Farmer, and D. E. Hinton, “Advanced technologies high resolution Fourier transform spectrometer for atmospheric studies,” in Aerospace Conference Proceedings (IEEE, 2000), Vol. 3, pp. 237-243.

Regan, C. R.

N. S. Pougatchev, J. F. Campbell, C. R. Regan, M. C. Abrams, J. W. Brault, C. B. Farmer, and D. E. Hinton, “Advanced technologies high resolution Fourier transform spectrometer for atmospheric studies,” in Aerospace Conference Proceedings (IEEE, 2000), Vol. 3, pp. 237-243.

Smith, W. L.

D. E. Hinton, I. G. Nolt, J. H. Park, W. L. Smith, and M. C. Abrams, “Applications of advanced technologies to spacebased Fourier transform spectrometers for atmospheric remote sensing,” in Aerospace Conference Proceedings (IEEE, 1998), Vol. 2, pp. 499-504.

Tiziani, H. J.

E. Fischer, E. Dalhoff, S. Heim, U. Hofbauer, and H. J. Tiziani, “Absolute interferometric distance measurement using a FM-demodulation technique,” Appl. Opt. 35, 5589-5594 (1995).
[CrossRef]

Appl. Opt. (6)

Proc. SPIE (1)

U. Griesmann, R. Kling, J. H. Burnett, and L. Bratasz, “The NIST FT700 Vacuum Ultraviolet Fourier Transform Spectrometer: applications in ultraviolet spectrometry and radiometry,” Proc. SPIE 3818, 180-188 (1999).
[CrossRef]

Other (5)

S. P. Davis, M. C. Abrams, and J. W. Brault, Fourier Transform Spectrometry, 1st ed. (Academic, 2001), p. 181.

D. E. Hinton, I. G. Nolt, J. H. Park, W. L. Smith, and M. C. Abrams, “Applications of advanced technologies to spacebased Fourier transform spectrometers for atmospheric remote sensing,” in Aerospace Conference Proceedings (IEEE, 1998), Vol. 2, pp. 499-504.

J. J. Murray, “The GIFTS satellite project--enabling the NAS of the future with high resolution soundings and imagery,” 41st Aerospace Sciences Meeting and Exhibit, AIAA 2003-385 (American Institute of Aeronautics and Astronautics, 2003).

R. Beer, Remote Sensing by Fourier Transform Spectroscopy (Wiley, 1992), p. 20.

N. S. Pougatchev, J. F. Campbell, C. R. Regan, M. C. Abrams, J. W. Brault, C. B. Farmer, and D. E. Hinton, “Advanced technologies high resolution Fourier transform spectrometer for atmospheric studies,” in Aerospace Conference Proceedings (IEEE, 2000), Vol. 3, pp. 237-243.

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Figures (6)

Fig. 1
Fig. 1

Optical layout of “The Web.” This instrument has 8 × folding and is similar in concept to the Genzel interferometer.

Fig. 2
Fig. 2

Synthetic quadrature phase detector using a synthetic reference derived from the average laser fringe frequency to demodulate the laser fringe signal and velocity correct the spectral signal by resampling the spectral signal evenly in space.

Fig. 3
Fig. 3

Derived phase error and displacement as a function of sample number. The phase error in the left graph is the deviation from the phase derived from the average frequency— ( f ( t ) f a ) t . The right graph is the phase error plus f a t .

Fig. 4
Fig. 4

Derived fringe/sample rate obtained from differencing the displacement with respect to sample number. This is directly proportional to the velocity. The left graph shows the profile over the entire scan, and the right graph shows the fine detail.

Fig. 5
Fig. 5

Fourier transform of a laser interforogram before and after processing. Since we can resample at any rate we can even velocity correct the reference metrology laser. The above correction was done by resampling at 3 times per fringe, which is the approximate original data acquisition rate. Since the data are captured evenly spaced in time and corrected evenly space in distance, the units along the x axis must be different.

Fig. 6
Fig. 6

Fourier transform of a spectral interferogram before and after processing. Before correction the absorption spectra are barely visible. After correction one can clearly see the characteristic CO absorption lines. Since the data are captured evenly spaced in time and corrected evenly space in distance, the units along the x axis must be different.

Equations (8)

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S ( t ) = A ( t ) sin ( 2 π f ( t ) t + ϕ ) ,
S 1 ( t ) = A ( t ) sin ( 2 π f ( t ) t + ϕ ) sin ( 2 π f a t ) , S 2 ( t ) = A ( t ) sin ( 2 π f ( t ) t + ϕ ) cos ( 2 π f a t ) .
S 1 ( t ) = A ( t ) 2 cos ( 2 π ( f ( t ) f a ) t + ϕ ) A ( t ) 2 cos ( 2 π ( f ( t ) + f a ) t + ϕ ) , S 2 ( t ) = A ( t ) 2 cos ( 2 π ( f ( t ) f a ) t + ϕ ) A ( t ) 2 cos ( 2 π ( f ( t ) + f a ) t + ϕ ) .
S 1 = A ( t ) 2 cos ( 2 π ( f ( t ) f a ) t + ϕ ) , S 2 = A ( t ) 2 sin ( 2 π ( f ( t ) f a ) t + ϕ ) .
tan ( 2 π ( f ( t ) f a ) t + ϕ ) = S 2 S 1 .
d n = f a t n + 1 2 π arctan ( S 2 ( t n ) S 1 ( t n ) ) ϕ 2 π ± j .
d n + 1 d n = f a Δ t + 1 2 π arctan ( S 2 ( t n + 1 ) S 1 ( t n + 1 ) ) 1 2 π arctan ( S 2 ( t n ) S 1 ( t n ) ) ± k .
S 1 2 + S 2 2 = 1 4 A 2 ( t ) .

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