The problem of error in deconvolution

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Abstract
The subject of this paper is the solution of the convolution integral, which relates the observed line profile to the true profile which is obtained in the absence of instrumental resolution effects. In the case of perfectly accurate data this problem has (by assumption) a well-defined solution. This paper considers the practical problem that results when the experimental curve is subject to error. Estimates are given for the importance of the error and a criterion is developed for optimizing the deconvolution procedure. This leads to a deconvolution function which when convoluted with the experimental curve gives the true solution. Finally the method of solution by iteration is examined and the effect of error upon it studied.