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

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