An orthonormal set of Stokes profiles

Abstract

A family of well-known orthonormal functions, the set of Hermite functions, is proposed as a suitable basis for expanding the Stokes profiles of any spectral line. An expansion series thus provides different degrees of approximation to the Stokes spectrum, depending on the number of basis elements used (or on the number of coefficients). Hence, an usually large number of wavelength samples, may be substituted by a few such coefficients, thus reducing considerably the size of data files and the analysis of observable information. Moreover, since the set of Hermite functions is an universal basis, it promises to help in modern inversion techniques of the radiative transfer equation that infer the solar physical quantities from previously compiled look-up tables or artificial neural networks. These features appear to be particularly important in modern solar applications producing huge amounts of spectropolarimetric data and on near-future, on-line applications aboard spacecrafts.