  We demonstrate how the mixed dynamic form factor (MDFF) can be interpreted as
a quadratic form. This makes it possible to use matrix diagonalization methods
to reduce the number of terms that need to be taken into account when
calculating the inelastic scattering of electrons in a crystal. It also leads
in a natural way to a new basis that helps elucidate the underlying physics.
The new method is applied to several cases to show its versatility. In
particular, predictions are made for directly imaging atomic orbitals in
crystals.
