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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN 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)
http://dx.doi.org/10.1364/AO.45.005270


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Abstract

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:
Spectroscopy

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

Citation
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)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-45-21-5270

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