[Ifeffit] polarization sampling

[Matthew]

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