The quartz compensator is a birefringent optical compensator: a retarder of known principal directions. With its principal axes at45degrees to the polarizer and analyser, the previously dark isotropic background acquires the compensator's own interference colour. The crystals are now viewed through two retarders.
When a specimen's slow axis is parallel to the compensator's slow axis, the retardations add. A90degree relative principal-axis rotation pairs the specimen's slow axis with the compensator's fast axis, and the signed retardations subtract:
Thus different crystallites can shift to higher or lower interference orders even if their original hue was similar. In the subtracting orientation, equal magnitudes can compensate and yield extinction. These shifts identify fast and slow specimen directions.
At a general relative angle the full polarization transformation is required; simple scalar addition is only valid for aligned principal axes. The source does not specify the compensator retardation, so no unique list of resulting named colours can be assigned. The robust predictions are a changed background, orientation-dependent addition or subtraction, and possible compensation.