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This paper presents the optical design of a high-resolution double-grating spectrometer for extracting the multiple lines in the Stokes or anti-Stokes branch of the pure rotational Raman spectra of nitrogen. The spectrometer is composed of collimating and focusing mirrors, two reflective gratings, and a linear detector. The structural parameters were calculated using geometric configuration, dispersion, and aberrational theory, and conditions for first-order correction of keystone distortion with divergent grating illumination were derived. Based on this method, we simulated a spectrometer with a 16-channel linear array photomultiplier tube, resulting in uniformly distributed single-branch lines on each detector channel. The resolution reached 0.225 nm per channel, and the keystone distortion was less than 0.7%. The spectrometer avoids the interference of elastic signals by not detecting them, enabling the extraction of atmospheric temperature profiles via separated single-branch lines with high precision. Our design provides a promising solution to extract atmospheric temperature profiles for pure rotational Raman lidar.

The performance of the laser-induced fluorescence (LIF) technique is greatly affected by the excitation wavelength (EW). This study aims to find an appropriate EW that can be used for analyzing extra virgin olive oil (EVOO) adulteration quantification by comparing the effect of different EWs. The EWs of 405 nm, 450 nm, and 532 nm were selected to perform the comparative experiments. By using the three EWs in the experiments, the LIF spectra of EVOO samples adulterated with peanut oil (PO) or soybean oil (SO) in different proportions, as well as the prediction models established through different multivariate analysis algorithms were analyzed. The linear discriminant analysis (LDA) was applied for qualitative analysis, while the partial least squares regression (PLSR), backpropagation neural network, and k-nearest neighbor were employed for quantitative analysis. The results show that the performance of 450 nm EW is always superior to that of 405 and 532 nm EWs in any model, with a smaller root mean square error (RMSE). Using the LDA-PLSR model, the RMSE is 1.35% for SO adulterants and 1.36% for PO adulterants, respectively.

Since the periodogram maximum (PM) algorithm fails to provide consistent estimates, more robust techniques are developed, especially in a low signal-to-noise ratio (SNR) regime. The methods are formulated in a subspace fitting-based framework, such as the eigenvector (EV) method and the proposed weighted subspace fitting (WSF) method by introducing an optimal weighting matrix, which exploits the low-rank properties of the covariance matrix of the coherent Doppler lidar echo data. Simulation results reveal that the number of the reliable estimates by the WSF method is more than the other two methods, and the standard deviation is the smallest. Furthermore, the predicted best-fit Gaussian model for the probability density function of the estimates has a narrower spectral width than that of PM and EV methods. Experimental results also validate the simulation results, which show that the WSF approach outperforms the PM and EV algorithms in the furthest detectable range. The proposed method improves the detection range approximately up to 14.2% and 26.6% when compared to the EV method and the PM method, respectively. In conclusion, the proposed method can reduce the statistical uncertainties and enhance the accuracy in wind estimation specifically for a low SNR regime.

Auto-adaptive background subtraction (AABS) is proposed as a denoising method for data processing of the coherent Doppler lidar (CDL). The method is proposed specifically for a low-signal-to-noise-ratio regime, in which the drifting power spectral density of CDL data occurs. Unlike the periodogram maximum (PM) and adaptive iteratively reweighted penalized least squares (airPLS), the proposed method presents reliable peaks and is thus advantageous in identifying peak locations. According to the analysis results of simulated and actually measured data, the proposed method outperforms the airPLS method and the PM algorithm in the furthest detectable range. The proposed method improves the detection range approximately up to 16.7% and 40% when compared to the airPLS method and the PM method, respectively. It also has smaller mean wind velocity and standard error values than the airPLS and PM methods. The AABS approach improves the quality of Doppler shift estimates and can be applied to obtain the whole wind profiling by the CDL.

An advanced optical design for a low-cost and astigmatism-corrected spectrometer with a high resolution is presented. The theory and method of astigmatism correction are determined with the use of a concave toroidal mirror. The performances of a modified spectrometer and a traditional spectrometer are compared, and the analysis is verified. Experimentally, the limiting resolution of our spectrometer is 0.1 nm full width at half-maximum, as measured for 579.1 nm.

Apodization is a mathematical tool used in Fourier transform spectrometry to reduce the spurious oscillation in the output spectrum. We investigate Norton-Beer apodizing functions and take advantage of the main series to introduce a family of new functions. They weigh the interferogram to zero continuously within the same optical path difference and, accordingly, improve the convergence property of the instrumental line shape (ILS) for the apodized spectrum. In the meantime, the range of spectral smearing is well reduced. Compared with the Norton-Beer functions, the new functions are more flexible in practice and are more applicable with regard to distinguishing the spectral lines, especially the weak lines, which are not too close to the center of a strong line but are still susceptible to the ringing of ILS.