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The sensitivity of laser absorption spectroscopy (LAS) system is usually determined by the level of unwanted optical fringe (etalon) noise arising from back reflections of the incident light upon parallel surfaces. The difference in travelled distance generates destructive and constructive interference pattern as the laser
frequency is being modulated, which is often observed as high-frequency oscillations riding on the slower tuning of laser light. To mitigate measurement uncertainty from such noise, Wavelet transform can be utilized as an inexpensive digital signal processing technique for signal de-noising.
Problem
The etalon fringe noise is obvious in the measurements of scanned direction absorption on nitric oxide near 1912.075 cm-1, with a mode-hop-free ECQCL laser applied in a static optical cell. The absorption spectrum can be calculated from the incident/transmitted light intensity profiles using the Beer-Lambert relation, with additional efforts for wavelength calibration.
But the etalon noise gets amplified through subtraction and inhibits accurate determination of the gas concentration. This is a common but serious problem that is usually tied to an imperfect design of the cell or poor alignment of the laser beam.
Strategy: separation of noise from signal via Discrete Wavelet Transform
Like Fourier transform, in which sine and cosine are the basic function for data analysis, Wavelet transform uses a family of basic function (multi-resolution wavelets) that are well localized in both time and frequency domains. DWT is accomplished by decomposition of the signal with repeating linear transformations, a low-pass filter and a high-pass filter. For each layer, the signal is decomposed into a high-frequency component, details coefficients (cDi), and a low-frequency component, approximation coefficients (cAi). The approximation coefficients will be used for the decomposition at the next layer, and 15 layers were used in this example.
"fk18" wavelet function well isolates the etalon noise (2nd to 6th layers) from laser tuning signals (deeper layers). Using appropriate thresholding technique would help remove the etalon noise from the signal, which will improve the fitting quality of the results.
Before denoising
Below is a theoretical fit against the experimental data and it becomes obvious that the residual percentage from the theoretical fit is dominated by the etalon noise (RMS 7.40%). The etalon noise also conceals the curvature of the fitting residuals.
After denoising
The intensity profiles are reconstructed from the details and approximation coefficients after crudely replacing the 2nd to 6th layers with zero. The residual RMS is now 3.07% and clearly reveals a drift in laser intensity on the left wing of the curve.
This is an individual project for my graduate course Signal Processing for Machine Learning (EE 269) at Stanford University. This project was supported by Wey-Wey Su for the collection of experimental data.
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