The multiple internal reflections cause a polarization-dependent phase-lag of the transmitted light, in a manner similar to a Fresnel rhomb.
This must be suppressed by multilayer phase-correction coatings applied to one of the roof surfaces to avoid unwanted interference effects and a loss of contrast in the image.
These phase-correction coating or P-coating on the roof surfaces was developed in 1988 by Adolf Weyrauch at Carl Zeiss[3] Other manufacturers followed soon, and since then phase-correction coatings are used across the board in medium and high-quality roof prism binoculars.
[4] From a technical point of view, the phase-correction coating layer does not correct the actual phase shift, but rather the partial polarization of the light that results from total reflection.
[6] The presence of a phase-correction coating can be checked on unopened binoculars using two polarization filters.