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Applied Optics

Applied Optics


  • Vol. 38, Iss. 3 — Jan. 20, 1999
  • pp: 462–475

Simple Monte Carlo methods to estimate the spectra evaluation error in differential-optical-absorption spectroscopy

Martin Hausmann, Uwe Brandenburger, Theo Brauers, and Hans-Peter Dorn  »View Author Affiliations

Applied Optics, Vol. 38, Issue 3, pp. 462-475 (1999)

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Differential-optical-absorption spectroscopy (DOAS) permits the sensitive measurement of concentrations of trace gases in the atmosphere. DOAS is a technique of well-defined accuracy; however, the calculation of a statistically sound measurement precision is still an unsolved problem. Usually one evaluates DOAS spectra by performing least-squares fits of reference absorption spectra to the measured atmospheric absorption spectra. Inasmuch as the absorbance from atmospheric trace gases is usually very weak, with optical densities in the range from 10-5 to 10-3, interference caused by the occurrence of nonreproducible spectral artifacts often determines the detection limit and the measurement precision. These spectral artifacts bias the least-squares fitting result in two respects. First, spectral artifacts to some extent are falsely interpreted as real absorption, and second, spectral artifacts add nonstatistical noise to spectral residuals, which results in a significant misestimation of the least-squares fitting error. We introduce two new approaches to investigate the evaluation errors of DOAS spectra accurately. The first method, residual inspection by cyclic displacement, estimates the effect of false interpretation of the artifact structures. The second method applies a statistical bootstrap algorithm to estimate properly the error of fitting, even in cases when the condition of random and independent scatter of the residual signal is not fulfilled. Evaluation of simulated atmospheric measurement spectra shows that a combination of the results of both methods yields a good estimate of the spectra evaluation error to within an uncertainty of ∼10%.

© 1999 Optical Society of America

OCIS Codes
(010.1280) Atmospheric and oceanic optics : Atmospheric composition
(030.6600) Coherence and statistical optics : Statistical optics
(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation
(280.1120) Remote sensing and sensors : Air pollution monitoring
(300.1030) Spectroscopy : Absorption

Original Manuscript: April 13, 1998
Revised Manuscript: September 21, 1998
Published: January 20, 1999

Martin Hausmann, Uwe Brandenburger, Theo Brauers, and Hans-Peter Dorn, "Simple Monte Carlo methods to estimate the spectra evaluation error in differential-optical-absorption spectroscopy," Appl. Opt. 38, 462-475 (1999)

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