On the extrapolation of the magnitudes |E| of the normalized structure factors E

For each fixed reciprocal-lattice vector , the correlation coefficient, , of the pair , where the magnitudes and are presumed to be known, is itself positively correlated with . Thus, the correlation coefficients serve to mediate the transfer of information from one region of reciprocal space to another. In particular, the calculated values of the correlation coefficients lead to estimates of the unknown magnitudes , even when the latter lie outside the sphere of the experimentally observed s (extrapolation). The applications show that the procedure described here to carry out this extrapolation is superior to existing methods.