Partial texture analysis by the modified maximum entropy method

Abstract

The orientation distribution function (ODF), being a continuous function of three variables, requires a large number of values or series coefficients for its complete description. A partial texture analysis, using a fixed angle texture analyzer, i.e., less pole figure data, gives a limited number of values of the texture function, i.e., an approximate ODF. This partial texture analysis is very important both for theory and for its application to on-line texture analysis, used to refine a manufacturing process and optimize materials properties. Quite recently, the modified maximum entropy method (MMEM), which improved the primary maximum entropy method with series coefficients as constraints, introduced the maximum entropy principle directly into the least square equation of pole figure inversion proposed by Bunge. Because the positivity condition is automatically satisfied, less data are needed to obtain an accurate solution with the MMEM. In the present paper, the MMEM is used of find the partial ODF from only a few data measured on the pole figure. The validity of the new algorithm will be proved by the partial ODF analysis of cold-rolled copper sheets with moderate-to-strong textures.