Deconvolution analysis in membrane diffraction using the modulus of the continuous Fourier transform

A method of deconvolution using the modulus of the continuous Fourier transform of the unit cell is described. This method differs from previous deconvolution methods in membrane diffraction in that calculations are carried out in reciprocal space. The modulus profile is obtained from the continuous intensity transform which is itself the Fourier transform of the autocorrelation function. Sampling theorem methods are used to reconstruct the continuous Fourier transform of the unit cell. The various phase choices are examined and compared. In membrane diffraction, the autocorrelation function is derived in two distinct situations: when the interference function is broad as in the case of a few unit cells and when the membrane systems contain wide regions of constant electron density. It is concluded that, in the first situation, the derived autocorrelation function contains missing information and is incorrect. On the other hand, in the second situation, the derived autocorrelation function is a good representation of the true autocorrelation function.