Error matrices in gas-electron diffraction : II. Influence of weight matrix

Abstract

The properties of three different forms of error matrices in electron diffraction are investigated, assuming the presence of stationary, Gaussian, Markovian noise in the primary data. The error matrices studied are Mxp based on the optimum weight matrix P the bona fide error matrix Mxw based on the nonoptimum weight matrix W, and the false error matrix Mxo commonly calculated by diffractionists using the formula for the optimum error matrix while incorporating a nonoptimum weighting. Simple formulae relating the elements of the various matrices are derived in the case where W is the best diagonal weight matrix and where geometric constraints are not imposed on parameters. The influence of geometric constraints is tested. Calculations indicate that diagonal weight matrices in ordinary circumstances give results imperceptibly inferior to the results obtained with the best nondiagonal weight matrices. Elements of Mxw closely approach those of Mxp whereas elements of the false error matrix, taken alone, may be very misleading.