Cepstral analysis for baseline-insensitive absorption spectroscopy using light sources with pronounced intensity variations

Abstract

This paper presents a data-processing technique that improves the accuracy and precision of absorption-spectroscopy measurements by isolating the molecular absorbance signal from errors in the baseline light intensity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>I</mml:mi> <mml:mi>o</mml:mi> </mml:msub> </mml:mrow> </mml:math> ) using cepstral analysis. Recently, cepstral analysis has been used with traditional absorption spectrometers to create a modified form of the time-domain molecular free-induction decay (m-FID) signal, which can be analyzed independently from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>I</mml:mi> <mml:mi>o</mml:mi> </mml:msub> </mml:mrow> </mml:math> . However, independent analysis of the molecular signature is not possible when the baseline intensity and molecular response do not separate well in the time domain, which is typical when using injection-current-tuned lasers [e.g., tunable diode and quantum cascade lasers (QCLs)] and other light sources with pronounced intensity tuning. In contrast, the method presented here is applicable to virtually all light sources since it determines gas properties by least-squares fitting a simulated m-FID signal (comprising an estimated <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>I</mml:mi> <mml:mi>o</mml:mi> </mml:msub> </mml:mrow> </mml:math> and simulated absorbance spectrum) to the measured m-FID signal in the time domain. This method is insensitive to errors in the estimated <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>I</mml:mi> <mml:mi>o</mml:mi> </mml:msub> </mml:mrow> </mml:math> , which vary slowly with optical frequency and, therefore, decay rapidly in the time domain. The benefits provided by this method are demonstrated via scanned-wavelength direct-absorption-spectroscopy measurements acquired with a distributed-feedback (DFB) QCL. The wavelength of a DFB QCL was scanned across the CO P(0,20) and P(1,14) absorption transitions at 1 kHz to measure the gas temperature and concentration of CO. Measurements were acquired in a gas cell and in a laminar ethylene–air diffusion flame at 1 atm. The measured spectra were processed using the new m-FID-based method and two traditional methods, which rely on inferring (instead of rejecting) the baseline error within the spectral-fitting routine. The m-FID-based method demonstrated superior accuracy in all cases and a measurement precision that was <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo>≈</mml:mo> <mml:mspace width="negativethinmathspace"/> <mml:mn>1.5</mml:mn> </mml:math> to 10 times smaller than that provided using traditional methods.

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