Inverse Pole Figure

 

See also: Stereographic projection, gnomonic projection, equal area projection

 

In an inverse pole figure, the axes of the projection sphere are aligned with crystal directions.  The directions plotted are the stereographic projection of crystal directions parallel to either the normal direction (ND), rolling direction (RD) or transverse direction (TD) in the sample.   The inverse pole figure can help visualise certain types of textures.

 

Effect of crystal symmetry on the inverse pole figure

 

The sample crystal symmetry determines the shape of the region of the stereographic projection used for the inverse pole figure.  Any of the crystallographically symmetrical equivalent directions can be assigned to a particular sample direction and the shape of the inverse pole figure is such that  the direction appears only once.  The figure below shows the shape of the inverse pole figure for some crystal symmetries.  In general the shape will be determined by the stereographic projection of the point group of the corresponding Laue class.