Future of Inversion Tools

Since the early 1970's, inversion techniques have become the most useful tool for inferring the magnetic, dynamic and thermodynamic properties of the solar atmosphere. They have evolved with model dependence as a driver: astrophysical inferences do not only depend on measurements but also on the physics assumed to prevail both on the formation of the spectral line Stokes profiles and on their detection with the instrument. Such an intrinsic model dependence makes it necessary to formulate specific means that include the physics in a proper quantitative way. The core of this physics is in the radiative transfer equation (RTE), where the properties of the atmosphere are assumed to be known while the unknowns are the four Stokes profiles. The solution of the (differential) RTE is known as the direct or forward problem. From an observational point of view, the problem is rather the opposite: the data are made up of the observed Stokes profiles and the unknowns are the solar physical quantities. Inverting the RTE is therefore mandatory. Indeed, the formal solution of this equation can be considered an integral equation. The solution of such an integral equation is called the inverse problem. Inversion techniques are automated codes aimed at solving the inverse problem. The foundations of inversion techniques are critically revisited with an emphasis on making explicit the many assumptions underlying each of them. An incremental complexity procedure is advised for the implementation in practice. Coarse details of the profiles or coarsely sampled profiles should be reproduced first with simple model atmospheres (with, for example, a few physical quantities that are constant with optical depth). If the Stokes profiles are well sampled and differences between synthetic and observed ones are larger than the noise, then the inversion should proceed by using more complex models (that is, models where physical quantities vary with depth or, eventually, with more than one component). Significant improvements are expected as well from the use of new inversion techniques that take the spatial degradation by the instruments into account.