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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 21 — Jul. 20, 2006
  • pp: 5270–5280

Correction of instrument line shape in Fourier transform spectrometry using matrix inversion

Raphaël Desbiens, Jérôme Genest, Pierre Tremblay, and Jean-Pierre Bouchard  »View Author Affiliations

Applied Optics, Vol. 45, Issue 21, pp. 5270-5280 (2006)

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A novel matrix inversion approach is proposed to correct several contributions to the instrument line shape (ILS) of a Fourier transform spectrometer. The matrix formalism for the ILS is first quickly reviewed. Formal inversion of the ILS matrix is next discussed, along with its limitations. The stability of the inversion process for large field-of view- (FOV-) limited and highly off-axis line shapes is investigated. The effect of inversion on the noise that is present in the spectrum is also presented. Use of classical iterative inversion methods, coupled with efficient synthesis algorithms, is proposed as a way to drastically speed up the inversion process. The method is applied to correct HBr spectra obtained from a laboratory spectrometer that has an adjustable field of view. ILSS from six FOVs are brought to the same spectral axis and to the same ideal sinc shape.

© 2006 Optical Society of America

OCIS Codes
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation
(300.6300) Spectroscopy : Spectroscopy, Fourier transforms

ToC Category:

Original Manuscript: September 7, 2005
Revised Manuscript: January 27, 2006
Manuscript Accepted: February 10, 2006

Raphaël Desbiens, Jérôme Genest, Pierre Tremblay, and Jean-Pierre Bouchard, "Correction of instrument line shape in Fourier transform spectrometry using matrix inversion," Appl. Opt. 45, 5270-5280 (2006)

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  1. J. Connes, "Domaine d'utilisation de la méthode par transformée de Fourier," J. Phys. Radium 19, 197-208 (1958). [CrossRef]
  2. E. Niple, A. Pires, and K. Poultney, "Exact modeling of lineshape and wavenumber variations for off-axis detectors in Fourier transform spectrometer (FTS) sensor systems," in Technologies of Cryogenically Cooled Sensors and Fourier Transform Spectrometers II, R.J.Huppi, ed., Proc. SPIE 364, 11-20 (1982).
  3. J. Kauppinen and P. Saarinen, "Line-shape distortions in misaligned cube corner interferometers," Appl. Opt. 31, 69-74 (1992). [CrossRef] [PubMed]
  4. J. Genest and P. Tremblay, "Impact of the optical aberrations on the line shape of Fourier-transform spectrometers," Vibr. Spectrosc. 29, 3-13 (2002). [CrossRef]
  5. R. Desbiens, J. Genest, and P. Tremblay, "Radiometry in line-shape modeling of Fourier-transform spectrometers," Appl. Opt. 41, 1424-1432 (2002). [CrossRef] [PubMed]
  6. R. Desbiens, P. Tremblay, and J. Genest, "Matrix algorithm for integration and inversion of instrument line shape," in Fourier Transform Spectroscopy (Optical Society of America, 2003), pp. 42-44.
  7. R. Desbiens, P. Tremblay, J. Genest, and J. P. Bouchard, "A matrix form for the instrument line shape of Fourier transform spectrometers yielding a fast integration algorithm to theoretical spectra," Appl. Opt. 45,546-557 (2006). [CrossRef] [PubMed]
  8. C. L. Bennett, M. R. Carter, and D. J. Fields, "Hyperspectral imaging in the infrared using LIFTIRS," in Infrared Technology XXI, B.F.Andresen and M.Strojnik, eds., Proc. SPIE 2552,274-283 (1995).
  9. L. M. Moreau and F. Grandmont, "Review of imaging spectrometers at ABB Bomem," in Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery IX, S.S.Shen and P.E.Lewis, eds., Proc. SPIE 5093, 82-93 (2003).
  10. F. Grandmont, L. Drissen, and G. Joncas, "Development of an imaging Fourier transform spectrometer for astronomy," in Specialized Optical Developments in Astronomy, E.Atad-Ettedgui and S.D'Odorico, eds., Proc. SPIE 4842,392-401 (2003).
  11. J. Genest, A. Villemaire, and P. Tremblay, "Making the most of the through-put advantage in imaging Fourier transform spectrometers," in Fourier Transform Spectroscopy: 11th International Conference, J.A.de Haseth, ed. (American Institute of Physics, 1998).
  12. J. Genest and P. Tremblay, "Instrument line shape of Fourier-transform spectrometers: analytic solutions for nonuniformly illuminated off-axis detectors," Appl. Opt. 38, 5438-5446 (1999). [CrossRef]
  13. K. W. Bowman, H. M. Worden, and R. Beer, "Instrument line-shape modeling and correction for off-axis detectors in Fourier-transform spectrometry," Appl. Opt. 39, 3765-3773 (2000). [CrossRef]
  14. C. Cohen-Tannoudji, F. Laloe, and B. Diu, Mécanique Quantique (Hermann, 1996), Vol. 1.
  15. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, 1992).
  16. Y. Viniotis, Probability and Random Processes for Electrical Engineers (McGraw-Hill, 1998).
  17. 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]
  18. L. A. Sromovsky, "Radiometric errors in complex Fourier transform," Appl. Opt. 42, 1779-1787 (2003). [CrossRef] [PubMed]
  19. V. Pan and J. Reif, "Efficient parallel solution of linear systems," in Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing (Association for Computing Machinery, 1985), pp. 143-153. [CrossRef]
  20. R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. Van der Vorst, "Templates for the Solution of Linear Systems Building Blocks for Iterative Methods," SIAM, Philadelphia, 1994. anon@www.netlib.org/templates/templates.ps.
  21. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, 1996).
  22. S. Barnett, Matrices--Methods and Applications, Oxford Applied Mathematics and Computing Sciences Series (Oxford U. Press, 1990).
  23. J. P. Bouchard, "Étude expérimentale de la forme de raie des spectromètres par transformation de Fourier," Ph.D. dissertation (Université Laval, 2004).
  24. J.-P. Bouchard and P. Tremblay, "Experimental study of the instrument line-shape of Fourier-transform spectrometers using a high divergence, high resolution interferometer," in Fourier Transform Spectroscopy (Optical Society of America, 2005).

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