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Applied Optics

Applied Optics


  • Vol. 42, Iss. 10 — Apr. 1, 2003
  • pp: 1779–1787

Radiometric errors in complex Fourier transform spectrometry

Lawrence A. Sromovsky  »View Author Affiliations

Applied Optics, Vol. 42, Issue 10, pp. 1779-1787 (2003)

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A complex spectrum arises from the Fourier transform of an asymmetric interferogram. A rigorous derivation shows that the rms noise in the real part of that spectrum is indeed given by the commonly used relation σ R = 2X ×NEP/(ηAΩ τN), where NEP is the delay-independent and uncorrelated detector noise-equivalent power per unit bandwidth, ±X is the delay range measured with N samples averaging for a time τ per sample, η is the system optical efficiency, and AΩ is the system throughput. A real spectrum produced by complex calibration with two complex reference spectra [Appl. Opt. 27, 3210 (1988)] has a variance σ L 2 = σ R 2 + σ c 2(L h - L s )2/(L h - L c )2 + σ h 2(L s - L c )2/(L h - L c )2, valid for σ R , σ c , and σ h small compared with L h - L c , where L s , L h , and L c are scene, hot reference, and cold reference spectra, respectively, and σ c and σ h are the respective combined uncertainties in knowledge and measurement of the hot and cold reference spectra.

© 2003 Optical Society of America

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation

Original Manuscript: March 29, 2002
Revised Manuscript: October 23, 2002
Published: April 1, 2003

Lawrence A. Sromovsky, "Radiometric errors in complex Fourier transform spectrometry," Appl. Opt. 42, 1779-1787 (2003)

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