Not all workable spectrometer systems can be represented by an exact analytical field; furthermore, while traditional design methods typically involve approximating known analytical fields with appropriate electrode/magnet configurations, modern simulation-based approaches do away with analytical representations altogether. Nonetheless, analytical solutions offer several advantages, including the ease of accurately evaluating focusing properties, and the prospect of optimization through mathematical analysis. In this paper, we propose an original and novel data-driven computational method for determining highly-accurate analytical field solutions, applicable to energy analyzers of arbitrary geometry and electrode/magnet configuration. The method encompasses a statistical analysis on a sample numerical field, from which appropriate eigenvalue bases are identified for the construction of an approximate series solution. The proposed method is demonstrated on three instruments-the parallel radial mirror analyzer, radial mirror analyzer, and parallel cylindrical mirror analyzer-illustrating its excellent versatility and accuracy in both the derived analytical fields ( < 1% mean error) and relative energy resolution predictions. We also demonstrate the potential application of automated optimization on the analytical fields through an adaptive Levenberg-Marquardt algorithm, exploiting the dimension-reducing properties of the method to aid in efficiency. Our proposed method is general enough to be applied across other fields of applications.
Keywords: Analytical field; Computational method; Data analytics; Data science; Energy analyzer; Spectrometer.
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