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Rotating a uniform crystallite around a fixed propagation direction changes the crossed-polar intensity factor ${\sin }^2(2\alpha )$. Extinctions repeat every90degrees and maxima occur45degrees away. Similar interference colour can coexist with different brightness if retardation is similar but azimuth differs.

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.

An unstressed glass is optically isotropic, so it does not split incident light into differently phased in-plane components; it remains dark between crossed polars. A natural explanation of the colored regions after heating is devitrification: anisotropic crystallites have nucleated in the glass. Edges and surfaces provide heterogeneous nucleation sites, making their greater concentration there plausible.

Each approximately uniform crystallite can give a nearly uniform interference colour. Regions with similar thickness and effective birefringence have similar retardation and therefore similar spectral colour, while differing azimuths multiply the intensity by ${\sin }^2(2\alpha )$ and change brightness. Identical hue does not prove identical three-dimensional crystallographic orientation.

Stress-induced birefringence is a possible alternative in a heat-treated glass. The observations alone do not uniquely prove crystallinity; rotating-stage extinction, morphology or diffraction could distinguish the explanations. The crystallite interpretation is the straightforward phase-transformation explanation, without inventing a composition or heat-treatment schedule.

At distance $x$ from its tip, the wedge thickness is $t_q=x\tan {\theta }_q$. Its optical path difference is thereforeThe perpendicular slow directions make the two retardances subtract. A white-light black compensation fringe is the zero-order cancellation, so the film retardance has magnitude approximately $393\mathrm{nm}$, with its slow direction along the rods. This interpretation assumes the observed fringe is the white-light compensation fringe; a single monochromatic dark fringe alone would have an integer-order ambiguity. Without the wedge, the wavelength dependence of ${\sin }^2(\pi \Gamma /\lambda )$ selectively transmits visible wavelengths and gives the film its interference colour.

A quartz retarder used to identify specimen fast and slow directions through changes of interference colour or compensation. Its own retardation and orientation must be specified before unique final colours can be predicted.