Here's a cut-and-paste from DrJone's excellent explanation of what dedoming does. This is taken from his BLF thread "Flashlight Optics - Dome, Dedoming and Throw". Tint shift is unavoidable if the dedome is done properly... "As a side effect, there's a tint shift towards lower color temperatures, because the back-reflected blue photons have another chance to be converted into yellow light by the phosphor layer."
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The LED
The LED die consists of a GaN layer which produces blue light. On top of it is a thin Ce:YAG phosphor layer (in the magnitude of 100µm) which converts a part of the blue light into yellow light by fluorescence (actually a very 'broad' yellow including green and red). Mixed together this gives white light. A thicker phosphor layer gives a more yellowish light (i.e. a lower color temperature), while a thinner layer gives cool white. Since the phosphor layer also adds some absorption losses, cool white LEDs can be produced with higher luminous flux [lumens].
What the dome does
The GaN die has a refractive index of about 2.5, which makes getting the blue photons out quite difficult: Light from the die hitting the surface perpendicularly has a good chance to get out, however there's always some fraction of the light reflected. With an increasing angle to the surface normal the reflection gets more, and above the critical angle there's only reflection (total inner reflection, TIR). Tha GaN-to-air surface has a critical angle of only 24°, so most photons get reflected. (The YAG layer doesn't help to increase the effective critical angle.) The reflected photons may bounce up and down a while until they get absorbed or they are lucky to hit a surface patch under a better angle (the surface is often roughened to offer such patches) and finally escape.
A silicone dome has a refractive index of about 1.5, and the GaN-to-dome critical angle is 37°, that means photons have a much better chance to escape the GaN crystal. However there's a second surface then: the dome-to-air surface of course gives some reflection, too. But since the die usually in in the center of the dome hemisphere, all photons hit that surface more or less perpendicularly so there's no TIR and only about 4% reflection there. But even those reflected photons aren't lost, they go back to the die and may be scattered or reflected there again to get another chance to get out, or they get absorbed and maybe re-emitted (called photon recycling) into a better angle.
Result: The total amount of light emitted (luminous flux) is higher. That's why the dome is there.
What dedoming does
As written above, without the dome the photon extraction is reduced, most photons don't get out - at the first try. But those photons aren't lost, TIR bounces them back and gives them more chances to be diffused into a better angle and get out. That TIR back to a the diffuse LED and photon reuse is the reason why the luminance can be increased even though normal optics can't do that. The dome actually is just some normal lens and would have no influence on luminance, but without it we get TIR and photon reuse, and those photons add to luminance.
The same trick is used with the Wavien collar: With an SST90 in an aspheric lens thrower, the light emitted to the side is lost, as it's not caught by the lens. An additional lens as 'pre-collimator' may catch more flux from the LED, but that won't give more throw, since it neither increases luminance nor the front lens area (instead the bigger caught flux is packed into a wider beam with same intensity and throw). However some clever people put a reflective collar around the lower part of the dome, so that the light that wouldn't hit the lens anyway was back-reflected onto the die, where it additionally lights up the diffuse surface (and those photons have another chance to escape into the right direction). This effectively increases the luminance.
As a side effect, there's a tint shift towards lower color temperatures, because the back-reflected blue photons have another chance to be converted into yellow light by the phosphor layer.
The TIR does exactly the same for the dedomed XM-L; it increases the luminance and shifts the tint towards warmer side.
Another observation can be explained by this: XM-Ls have quite some angular tint shift, i.e. the light emitted to the side is substantially more yellowish, while with the dedomed LED this effect is greatly reduced. The YAG phosphor has a refractive index of about 1.8. the critical angle agains the dome (~1.5) is about 55°, which means that such a ray to the very side has traveled a 74% longer distance through the phosphor compared to a perpendicular ray and more blue photons get converted to yellow. Without the dome, the critical angle against air is 33°, resulting in only 19% longer distance in the phosphor and thus much less angular tint shift.
Wrong/incomplete explanations
The die is smaller so the light density is higher - well, if you get about 30% less flux out of about 50% less (apparent) area with similar beam profile (lambertian), that should result in about 50% more luminance. However that's only half of the truth: If you try to get a smaller image of the die by using a diverging lens, or by filling something around the dome to get a flat surface to cancel the magnifying effect of the dome, that would not succeed. To increase luminance the TIR light needs to be reflected back to the die, thus the reflecting surface must be very near to the die. Either you remove the dome completely or you only leave a small layer (<0.5mm).
Due to the collimating dome missing, the light from the LED has a bigger beam angle and thus more light hits the reflector - actually no. First, the beam is about lambertian (i.e. 120° FWHM angle) with or without dome (see Tecmo's images). Second, that wouldn't explain why aspherics get increased throw, too. And third, even if you use a more collimating dome (like XR-E), that won't change luminance, because normal optics can't. (The XR-E doesn't throw so well because of the smaller beam angle, but because the EZ900 has a quite small area, thus more flux per area and thus a high luminance).
Actually the A*W rule does make the beam profile broader, broader than the hemisphere by back reflection that is. That itself doesn't change luminance. Only if that back-reflected light hits the diffuse die again, luminance increases.
