Analytical Representation of Angular Distribution Data

Abstract

A simple method is presented for obtaining an analytical curve fitted to data points. The requirements in least squares analysis that yield a single best curve are relaxed to the extent that it is only necessary to choose one of many possible good fits. The subsequent analytical determination of this good curve may be obtained with relatively little computational effort. Specifically, the method is applied to an analytical representation of angular distribution data by means of a Legendre polynomial series. A smooth curve which one feels is statistically justified is drawn through the data points. The values of this curve at eleven points are chosen as the coefficients in a Lagrange interpolation function series. The intermediate points give back approximately the drawn curve and are also statistically adequate. Subsequent use of a transformation matrix between the Lagrange interpolation basis and the Legendre polynomial basis yields the desired expansion. The transformation matrix is presented for the case in which an 11-point fit adequately characterizes the data curve. Error estimates also are given.