Precision and Resolution in Spectroscopic Model Fitting

摘要

The effects of errors of observation on the solutions of spectroscopic modelfitting are studied. The spectroscopic model consists of a weighted sum of peak shapes of the same nonlinearly parametric family. Three effects were distinguished: displacement of the solution leading to imprecision, interchange of the geometrical proportions of the peaks and coincidence of the solutions preventing resolution of close peak parameters. A hypersurface that divides the space of errors of observation into two parts is defined for each effect. Errors of observation located in the part containing the origin do not cause effects, errors located in the other part do. The distance from the origin to the hypersurface is called the critical norm. Errors of observation having a smaller norm can not cause the effect in question. The hypersurface can be approximated by a hyperplane to help find in which part particular errors of observation are located. If the errors of observation are statistical, the probability of occurrence of the effect can be computed. Numerical experiments with spectroscopic models show that the theory can be used in practice.