Spatial spectroscopic diagnostics of planetary nebulae. IV

A method is described and discussed for the three-dimensional determination of the upper level population of an optically thin line. Preliminary knowledge of the kinematical model of a planetary nebula is assumed. Main difficulties are connected with the inversion of the Fredholm integral equation of the first kind and the problems of physical uniqueness, accuracy and resolution of the obtained solutions. Regularization by the method of best determined terms is examined. Inherent limitations of the method are shown and briefly discussed. (author)