The prism-coupling systems and methods include using a prism-coupling system to collect a 2D digital mode spectrum of an IOX article. The mode line and critical angle positions and orientations are found by performing a weighted fit to mode line and critical angle images and are used to define a compensated mode spectrum. If mode line tilt is found, it is removed from the 2D digital mode spectrum to define the compensated mode spectrum. The compensated mode spectrum is then processed using techniques known in the art to provide a more accurate estimate of stress-related characteristics of the IOX sample versus using the uncompensated mode spectrum. Derivative-based methods of accurately establishing positions of intensity transitions in a mode spectrum of an IOX sample using a derivative spectrum and curve fitting are also disclosed.