Merits and limitations are discussed of using an inferential inverse, as opposed to the usual model-fitting, approach to diagnose stellar wind structure. We aspire to encourage the stellar wind community to use inversion rather than forward modelling by making it clear what inversion means, when and why it is valuable, and by giving examples of successful applications.

A sub-discipline of astrophysics advances beyond the discovery era as the quality of data moves from single numbers (flux, colour, size) to well measured functions or data strings g(y) (e.g., light curves or spectra where g is flux and y is time or wavelength). As the precision δg/g and the resolution δy/y improve, we progress from data gathering and qualitative description to quantitative modelling in terms of some relevant source model function f(x), describing source “structure” in some sense. In general g(y) and f(x) do not correspond one-to-one but rather f maps to g in a “convolved” (sometimes complex and non-linear) way through the radiation processes, while f itself may be a combination of important source properties. Here we consider only the simplest situation (though our arguments can be generalised) where the relationship is of the linear integral form

where the operator function K, represents the emission physics which we assume known. The diagnostic problem is to determine as much as possible about f(x) within the noise and resolution limits of the data g(y) and the smearing effect of K(x, y).