An adaptive singular value decomposition (SVD) algorithm for analysis of wavelength modulation spectra

Optical interference fringes due to unwanted etalons are often the limiting uncertainty in diode laser spectroscopic trace gas measurements. Temporal variations in the fringe spacings, phases, and amplitudes introduce systematic baseline changes that limit useful signal averaging times to ∼1000 s, and constrain minimum detectable absorbances to between one and three orders of magnitude worse than the fundamental limiting noise sources (shot noise and/or detector thermal noise). We describe an adaptive numerical filtering method based on singular value decomposition (SVD) that shows, for the system studied, a fivefold reduction in baseline drift due to unwanted etalons over a one-week-measurement period. The adaptive algorithm is fast (<1 ms per computation), robust, and uses linear methods. It is computationally equivalent to principal component analysis (PCA). The test system was acetylene detected using a near-infrared telecommunications laser operating at 6541.96 cm^-1. The gas detection limit was 20 ppb (1σ) over the one-week measurement. PACS 07.05.Kf; 07.07.Df; 07.60.-j; 42.60.-v; 42.62.-b; 42.62.Fi