Here's a challenge: Suppose I have a powder of a crystal and I look at individual grains, for instance using a micro-XAS beamline. If I have good diffraction data on each grain, I could in principle use it to infer its orientation. With 6 such grains (in the general, triaxial case) I can then infer the whole absorption tensor: mu = e_transpose * Mu * e, where e is the polarization vector and Mu is the tensor which has the whole polarization dependence in it (I assume no magnetic effects and dipole approx). You can think of it as an ellipsoid which, for the general triclinic case, rotates around with respect to the crystal axes as you scan energy. One of my users has actually done this. Here's where the challenge comes in: Suppose I *don't* have any diffraction data, so I just have spectra without orientation labels. How many such spectra would I need to infer all possible data? How would I do it? Of course, it would be ambiguous with respect to rotation, so I'd have to define a set of principle axes at one energy. This job would be sort of like the kinds of reconstructions people do of TEM pix of randomly-oriented objects. Would PCA give it to me? I thought of this while taking Fe K-edge spectra of augite powder (monoclinic) and finding that the XANES spectra on four grains all looked different. mam