As it is indicated by its name, the inverse
pole figure is a sort of 'opposite' to the pole figure.
While the pole figure shows how the specified crystallographic
direction of grains are distributed in the sample reference frame,
the inverse pole figure shows how the selected direction in the
sample reference frame is distributed in the reference frame of
the crystal. For example, normal direction inverse pole figure,
lets us know which crystallographic directions in the polycrystalline
material are most likely parallel to the sample normal direction.
Since the properties of many important engineering materials are
strongly direction-dependent, the inverse pole figure is very
useful in predicting and calculating the average properties of
polycrystalline material along a chosen direction.
Due to the crystal symmetry, a complete inverse pole figure usually
contains many areas where the same information is repeated. For
example, there are 24 symmetric sections in a inverse pole figure
for cubic system, as shown below. Practically, only one section
is used.