Dynamic background subtraction and the retrieval of threshold signals

Abstract

An approach is outlined for handling the general experimental problem of retrieving characteristic signals from the presence of large backgrounds. The method consists of n th‐order differentiation followed by multiple integration of the same order. It is shown that this procedure results in a function which has the form of the remainder of the (n ‐ 1)th‐order Taylor series for the background plus characteristic signals. If the function is one with a very large radius of convergence, then an order can be found such that the remainder is arbitrarily close to zero over the region of interest. Threshold functions, which are characterized by having very small convergence radii and which asymptotically approach zero on one or both sides of the point corresponding to the minimum radius of convergence, are shown to be accurately retrieved if the minimum convergence radius is contained in the region of integration. The particular advantages of the technique are demonstrated by its application to soft x‐ray appearance potential spectroscopy.