A general, analytical theorem developed by van de Hulst for inverting the convolution integral is reviewed and illustrated both with synthetic data and with experimental data from timehyphen;ofhyphen;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 rsquo;rsquo;truersquo;rsquo; distribution may sometimes be recovered in posthyphen;processing the data by means of deconvolution. Analytic deconvolution is achieved by using the coefficients from a power series representation of the distorted output distribution and a set of rsquo;rsquo;solving polynomialsrsquo;rsquo; which may be readily derived from the response function of the instrument. The distortion due to the excitation pulse duration in timehyphen;ofhyphen;flight molecular beam data has been removed by application of the theorem. Some possible advantages of this analytical method over conventional deconvolution techniques are discussed.
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