In Multi-ROI Analysis module, Dragonfly provides orientation (Phi, Theta) and Aspect Ratio for each isolated ROI.

As indicated below, the Theta angle is equal to the rotation of the X-axis towards the Y-axis. The Phi angle is equal to the rotation of the X-Y plane towards the Z-axis.

Anisotropic versus isotropic orientations can be used to determine if a material has undergone a change. For example, from a random distribution of grains to grains along a particular orientation.

The orientation is found by the eigenvector associated to the smallest eigenvalue of the tensor of inertia, which corresponds to the axis where the rotation is the easiest (or “long” axis).

The aspect ratio is obtained from the inertia tensor by computing the eigenvalues:

**aspect ratio = smallest eigenvalue / largest eigenvalue.**