Photochemical quenching in essence means light is efficiently used in photosynthesis, and this occurs when light intensity meets the minimum required by the zoox (the compensation point, where oxygen production meets respiratory requirements( and the maximum required (photosaturation, where an increase of light will not increase the rate of photosynthesis. An analogy would be a car motor at maximum speed and additional fuel will not make the vehicle faster.) Once the photosaturation point is achieved, non-photochemical quenching occurs - this could be the protection offered by the xanthophyll cycle, where light energy is shunted away from Photosystem II, called Dynamic Photoinhibition. If the protective capabilities of xanthophylls are exceeded, Chronic Photoinhibition occurs, leading to damage of the photosynthetic apparatus. If this is minimal, damage is repaired. If Chronic Photoinhibition exceeds a critical state, damage is not repaired and the coral will bleach.
As mentioned, there are 'sun' and 'shade' corals. Montipora capitata is definitely a shade coral, so is Pocillopora molokensis. On the other hand, some Porites corals (or more coreectly) their zoox, are tolerant of light up to about a PAR of 400. Hence, it's a great compromise in an aquarium. Maintaining a PAR value of 100 at the sandbed seems to be about the minimum; higher if SPS corals are at the bottom - 200 seems sufficient. Of course there will be higher light towards the top. Coloration - either through fluorescence, reflection, or acting as anti-oxidants) will help protect corals if light intensity is high. As a footnote, the only photosynthetic animals I've seen that cannot be over-illuminated are Tridacna clams. I could not achieved photosaturation in my experiments, even when using a metal halide lamp. I later found a thesis that confirmed my observation, but the author of that paper had a more intense light source and did not see photosaturation even when PAR approached that of full-strength sunlight (2,000 micromol/m2/sec.)