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

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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