The indicatrix is a geometric figure, constructed so that the indices of refraction are plotted as radii that are parallel to the vibration direction of light.
In isotropic minerals the indicatrix was a sphere, because the refractive index was the same in all directions.
In uniaxial minerals, because nomega and nepsilon are not equal, the indicatrix is an ellipsoid, the shape of which is dependant on its orientation with respect to the optic axis. In positive uniaxial minerals, the Z indicatrix axis is parallel to the c-crystallographic axis and the indicatrix is a prolate ellipsoid, i.e. it is stretched out along the optic axis.
All light travelling along the Z axis (optic axis), has an index of refraction of nomega, whether it vibrates parallel to the X or Y axis, or any direction in the XY plane.
Light travelling along the X axis is split into two rays, the ordinary and extraordinary rays,
The XZ and the YZ planes through the indicatrix are identical ellipses with nomega and nepsilon as their axes, with the radii of the ellipses equal to the magnitude of the RI for the ray.
Plotting the indices of light travelling in all directions produces the prolate ellipsoid, whose axis of revolution is the optic axis, for uniaxial positive minerals;
For optically negative minerals the X indicatrix axis corresponds to the optic axis and the indicatrix is an oblate ellipsoid, i.e. flattened along the optic axis, and
In each case, for positive and negative minerals the circular section through the indicatrix is perpendicular to the optic axis and has a radius = nomega.
The radius of the indicatrix along the optic axis is always nepsilon.
Any section through the indicatrix which includes the optic axis is called a principal section, and produces an ellipse with axes nomega and nepsilon.
A section through the indicatrix perpendicular to the optic axis produces a circular section with radius nomega.
A random section through the indicatrix will produce an ellipse with axes nomega and nepsilon'.
The indicatrix is oriented so that the optic axis is parallel to the c crystallographic axis.
Light travelling from the origin of the indicatrix outwards, construct a wave normal to the wave front.
A slice through the centre of the indicatrix, perpendicular to the wave normal forms an ellipse with axes of nomega and nepsilon'.
The magnitude of the axes = nomega and nepsilon'.