This paper proposes a novel and rapid calibration-free wavelength modulation spectroscopy algorithm based on even-order harmonics. The proposed algorithm, analytically deduced from Voigt line-shape function, only involves simple algebraic operations to describe the actual gas absorption spectra, thus eliminating the time-consuming simulations and line-shape fitting procedures adopted in traditional algorithms. Instead of acquiring the entirely scanned absorption line-shape, the proposed technique only requires extraction of the peak values of the harmonics. This characteristic significantly benefits gas diagnosis at elevated pressure and/or temperature, in which the entirely scanned absorption is very difficult to be obtained due to the broadened line-shapes. The proposed algorithm is validated by both numerical simulation and condition-controlled experiment, indicating millisecond-level calculation of gas parameters with the relative error less than 4% in the experiments.

A regularization approach of iterative algorithms was proposed to reconstruct the two-dimensional temperature and concentration distributions based on linear multispectral absorption tomography (MAT). This method introduces a secondary prior into a classical iterative algorithmviaregularization to improve the reconstruction accuracy. Numerical studies revealed that the regularized iteration outperformed the classical and superiorized versions under various noisy conditions and with different number of spectral lines. The algorithms were also tested with the existing experimental data of a premixed flat flame produced by a McKenna burner. The comparison between the reconstructions and the measured temperature profile using thermocouples confirmed the superiority of our proposed regularized iterative method.

Accurate ranging and real-time temperature monitoring are essential for metrology and safety in electrical conduit applications. This paper proposes an acoustic time-of-flight (TOF) estimation method based on the digital lock-in filtering (DLF) technique for conduit ranging and thermometry. The method establishes the relationship between the frequency and the time domain by applying a linear frequency modulated Chirp signal as the sound source and using the DLF technique to extract the first harmonic of the characteristic frequencies of the transmitted and received signals. Acoustic TOF estimation in the conduit is then achieved by calculating the mathematical expectation of the time difference between each characteristic frequency in the time-frequency relationship of the two signals. The experimental results with enhanced noise interference on different conduit lengths and various temperature conditions, proved that the proposed DLF method can establish a robust linear time-frequency relationship according to the characteristics of the Chirp signal, and the measurement accuracy of TOF has also been confirmed. Compared to the conventional method, the DLF method provides the lowest absolute error and standard deviation for both distance and temperature measurements with an enhanced robustness.

A simple approximation scheme to describe the half width of the Voigt profile as a function of the relative contributions of Gaussian and Lorentzian broadening is presented. The proposed approximation scheme is highly accurate and provides an accuracy better than 10⁻¹⁷ for arbitrary α_L/α_G ratios. In particular, the accuracy reaches an astonishing 10⁻³⁴ (quadruple precision) in the domain 0 ≤ α_L/α_G ≤ 0.2371 ∪ α_L/α_G ≥ 33.8786.