Correction functions for optimizing the reconstructed image in transverse section scan

Two correction functions are derived for one- and two-dimensional convolution methods for reconstructing a section image from multiple projections. The functions are optimized to yield a maximum 'signal-to-noise power ratio' for a given RMS resolution width, where 'signal power' is the integrated squared line spread function (signal power regarding one-dimensional position information per count) and 'noise power' is the variance of the image density at the centre of a locally uniform source. The point spread function of the reconstructed image is Gaussian, and the standard deivation of noise associated with a locally uniform image is found to be proportional to D-3/2, where D is the RMS resolution width. The autocovariance function for uniform noise is also given.