Context. The reliability of physical parameters describing the solar atmosphere inferred from observed spectral line profiles depends on the accuracy of the involved atomic parameters. For many transitions, atomic data, such as the oscillator strength (log(gf)) and the central wavelength of the line, are poorly constrained or even unknown. Aims. We present and test a new inversion method that infers atomic line parameters and the height stratification of the atmospheric parameters from spatially resolved spectropolarimetric observations of the Sun. This method is implemented in the new inversion code globin. Methods. The new method employs a global minimization algorithm enabling the coupling of inversion parameters common to all pixels, such as the atomic parameters of the observed spectral lines. At the same time, it permits the optimum atmospheric parameters to be retrieved individually for each spatial pixel. The uniqueness of this method lies in its ability to retrieve reliable atomic parameters even for heavily blended spectral lines. We tested the method by applying it to a set of 18 blended spectral lines between 4015 Å and 4017 Å, synthesized from a 3D magnetohydrodynamic simulation containing a sunspot and the quiet Sun region around it. The results were then compared with a previously used inversion method where atomic parameters were determined for every pixel independently (pixel-by-pixel method). For the same spectral region, we also inferred the atomic parameters from the synthesized spatially averaged disc-centre spectrum of the quiet-sun. Results. The new method was able to retrieve the log(gf) values of all lines to an accuracy of 0.004 dex, while the pixel-by-pixel method retrieved the same parameter to an accuracy of only 0.025 dex. The largest differences between the two methods are evident for the heavily blended lines, with the former method performing better than the latter. In addition, the new method is also able to infer reliable atmospheric parameters in all the inverted pixels by successfully disentangling the degeneracies between the atomic and atmospheric parameters. Conclusions. The new method is well suited for the reliable determination of both atomic and atmospheric parameters and works well on all spectral lines, including those that are weak and/or severely blended. This is of high relevance, especially for the analysis of observations of spectral regions with a very high density of spectral lines. An example includes the future near-ultraviolet spectropolarimetric observations of the SUNRISE III stratospheric balloon mission.
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