It appears there is some confusion as to the performance and capabilities of our technology. Maybe I can clear things up a bit.
The light recycling retro-reflector redirects light back to the phosphor of the white LED. Some light is re-emitted to the aperture, some to the reflector again and some is absorbed. The result is more light through the aperture and a warmer color temperature.
The output (lumens) of a system such as this narrow beam flashlight is increased by light recycling. If we compare the output of this flashlight with and without the reflector, it's about double. It could be more with a different LED and/or lens but the important thing is, the reflector increases output.
The 50mm lens is about F/1. The LED is a Luminous CBT-90. If we're getting around 800 lumens, that should give you all you need to know about brightness, LUX, radiance, whatever. Technically, this reflector can improve the performance of any LED and lens combination.
I fail to see how your light recycler accomplishes a task more effectively than a TIROS, or how it decreases the color temperature of the light emitted. It seems as though a TIROs would also be more efficient than your light recycler design, as it would surround the LED "dome(as it were)", gathering most of the light emitted, and concentrating it...