Correction of instrumental distortion by analytical deconvolution of data

A general analytical theorem developed by van de Hulst (1946) for inverting the convolution integral is reviewed and illustrated both with synthetic data and with experimental data from time-of-flight measurements. If the undesired influence of an instrument used in an experimental measurement can be represented by the convolution integral, the original undistorted or true distribution may sometimes be recovered in postprocessing the data by means of deconvolution. Analytical deconvolution is achieved by using the coefficients from a power series representation of the distorted output distribution and a set of 'solving polynomials' which may be readily derived from the response function of the instrument.