According to the classic harmonic approach, an orientation density function (odf)f is expanded into its corresponding Fourier orthogonal series with respect to generalized spherical harmonics, and a pole density function (pdf)\(\tilde P_h \) into its corresponding Fourier orthogonal series with respect to spherical harmonics. While pdfs are even (antipodally symmetric) functions, odfs are generally not. Therefore, the part\(\tilde \tilde f\) of the odf which cannot be determined from normal diffraction pdfs can be mathematically represented as the odd portion of its series expansion. If the odff is given, the even part\(\tilde f\) can be mathematically represented explicitly in terms off itself. Thus, it is possible to render maps ofharmonic orientation ghosts, and to evaluatevariants of mathematical standard odfs resulting in identical pdfs independent of pdf data. However, if only normal diffraction pdfs are known, the data-dependentvariation width of feasible odfs remained unaccessible, and within the harmonic approach a measure of confidence in a solution of the pdf-to-odf inversion problem does not exist.