A comparison of different methods of separation of continuous overlapping spectral lines

Several methods of separation of continuous overlapping spectral lines are compared. In the majority of methods, the profile of each line is modeled by a Gaussian or Lorentzian, and total measured spectrum $z$ is processed. Number of lines $N$ and their parameters are usually estimated by the method of derivatives; however, the differentiation of noisy spectrum $z$ causes large errors. To improve the differentiation accuracy, it is proposed to use smoothing splines. In the Fourier-self-deconvolution method, apodization (artificial truncation of the interferogram) is used to resolve overlapping lines, which makes it possible to resolve lines, but at the expense of a significant decrease in their widths. In this work, reducing the widths of lines is not used for their resolution, but rather, true line profiles are reconstructed by minimizing the residual functional with the modified coordinate-descent method using the decremental-constraint technique, and also, for comparison, with the Nelder–Mead simplex method. In the Manoilov method, the parameters of lines (peaks) are determined from convolutions of spectrum derivatives with individual peaks. In that method, the notion of the degree of overlap has been also introduced. In this work, we introduce a generalized degree of overlap for the case in which the amplitudes, widths, and spacings between neighboring lines are different. Numerical illustrations are presented.