PCA-interpolation methods for inversion of solar stokes profiles. I. Inversion of photospheric profiles

We present a method for the analysis of solar Stokes profiles based on the technique of principal component analysis (PCA). We consider the development of a PCA/interpolation technique for obtaining estimates of the solar magnetic field vector when the underlying physical parameter distribution is not well determined. Unlike previous applications of PCA, we consider separate distributions of the PCA components as applied to the source of the underlying plasma, namely, the umbra, penumbra, and quiet photosphere. We also isolate the PCA for the Fe I lambda6301.5 line. In some previous work, PCA was applied to the entire 6300-6305 Angstrom spectral region that includes the telluric lines. The method is tested on photospheric (Fe I lambda6301.5) observations of NOAA Active Region 9240 and compared with the results of the traditional High Altitude Observatory Milne-Eddington inversion code. We also consider a PCA-perturbation analysis of the data and how it can assist the interpretation of the results, discuss current challenges faced by the inversion codes, and suggest important areas for future development.