Sampling Error of Texture Approximation by Individual Orientation Measurement

摘要

The reliability of the ODF obtained from individual orientation measurement is usually limited by the finite number of data points rather than by the experimental angular resolution which is usually better than 1°. Hence measures of confidence of relevant distribution parameters are highly demanded for texture interpretation. Starting from the multinominal distribution, estimates of the empirical density distribution function and the C coefficients as well as their variances are given. Furthermore estimates of the optimum 1 value for series truncation and reasonable choices of smoothing parameters can be derived from the standard deviations of the C coefficients. Computer simulations on model textures have been carried out to confirm the results. The empirical distribution parameters as a function of sample number are in good accord with those predicted by theory.