Lissage d'un profil de raie de diffraction pour analyse de Fourier

The fast Fourier transform algorithm commonly used for line profile analysis requires a list of values of the diffracted intensity with constant sinθ step; raw data are usually obtained at constant 2θ step; to interpolate between the measured values an analytic expression of the profile function is very useful. Statistical estimation is used to fit an analytic function to data; the only assumption made is the continuity of this function and no critical initialization is needed. Three different expressions are used: a Fourier sum for the peak and two polynomials of a suitable variable for the tails; the algorithm provides continuity for the function and its first derivative. Simulated examples using a Lorentzian and a Gaussian function are given and several criteria of goodness of fit are examined. The program runs on a PDP 11/03 Digital computer with only 45 kbytes available memory.