A reflective aperture is a front surface concave, or dome shaped mirror in which an aperture effect is created (same thing as in a camera, a “hole” for light passage), along with a reflective effect occuring when a return image of the LED chip is in perfect focus back on the LED chip. The perfect focus occurs at R=1 with R being mirror radius. Since parabolas produce focal points further than R=1, they do not capture as much light. Also, radius is not constant in a parabola, so only part of the mirror can be in focus if this shape were used.
Our eyes are not good enough to see an image in perfect focus on an LED die surface to use the die itself as the only method for alignment/focus. At R=0.9 focus, or R=1.1 focus, you wouldn’t be able to notice that the image was slightly out of focus, since a die is so small, it will look identical and still like a clear square, but not all light will be collimated onto the die. Tilt of the mirror is a problem, even a couple degrees. Centering of the mirror is extremely important, as is mirror distance from the die.
Two methods exist for checking focus and centering of the reflective aperture. Once you have devised a method to mount and center the mirror, method one would be to check lux at the center of the output circle. The output spot is uncollimated, so wash is fairly smooth and even looking to your eye, but try to be sure things are lined up so the meter lands in the same place in the output spot on each test. You do not want other optics involved at this point, since it is another variable. Since the light output spreads rapidly from the aperture, lux would be checked using a highly repeatable setup (so that the test measure distance remains a constant), at a range of 1/4 to a 1/2 meter, before intensity grows too weak for accurate measurement.
Before you begin checking the lux though, the reflective aperture must be mounted, over and over to check height, until you know the exact real-value required. Centering should also be practiced with height adjustment, this is not done with lux reading, but a laser (coherent light source).
Centering and height (FL) must be checked by reflection. For this, I use a laser with small beam diameter (at the usage distance), mounted in a mill or CNC, using a digital readout in 100ths mm, or 1000ths inch, aimed down at the die through the aperture hole. The laser dot, green or red, should be used, with green being preferred, and not at a high power either (5mW to 8mW is more than sufficient). You must be able to observe the effect of return reflection of the laser while aiming it into the aperture hole (wear safety shades, this is bright), which is far easier than viewing the return image of an entire LED square while moving the mirror around. Since it is a concave mirror and not a flat mirror, the reflection image jumps to the opposite quadrant of the die. If a tiny needle-focused laser is used, and -X/+Y quadrant corner of the die is struck to begin, the same image will appear in the same location on the +X/-Y quadrant of the die if mirror is aligned right. If the aperture mirror is centered, the laser can get extremely close to touching its return reflection at the die center until two dot halves exist, but the halves can never touch each other in reality—an imaginary boundary line will exist neither reflection can cross. If the images cannot butt up against each other at the die center like this to make a virtual appearance of one single dot when the two halves meet, but rather a line gap of area on the die exists where the two beams cannot meet but may come close, the die is not at the correct focal length from the mirror. If the input laser dot is tight and crisp on the die, the second returning dot should be of equal size and shape/look (again, in exact opposite die quadrant position). If the input laser dot is crisp, and the return beam strikes the die but does not look of equal size but larger and more blurred, the die is at the wrong focal length from the mirror. If these previous details can simply never be met no matter at what height or centering position, this means the mirror you are using is not capable of working effectively, either due to curvature being poor or wrong, or surface being non-optical grade, such as bare metal, which will highly distort a laser reflection typically. If the mirror shape is a few percent off in some areas of curvature, it may look like a great mirror to the eye, but at the macro scale of actual use, it is probably highly inadequate. This is why optical grade surface quality is the most important feature of the mirror.
When these things are done right, lux will approach 80-110% of original LED intensity, and nearly all available excess light will be used to produce the return image on the die.
I have created a 3-axis adjustment spacer for my mirrors, so that I can make minute adjustments via set screw, laser check the adjustment, and when I feel I have reached the closest adjustment I can using a laser, I then test lux for the final, extremely small adjustments. These small adjustments account for another 10-25% intensity gain depending on the LED. Also, when lux testing is initiated, the die should be powered by an accurate DC supply at a constant current, being sure conditions are repeated and heat sagging output is not occurring during the test too quickly, which would be creating another variable to deal with. So, lux should be checked quickly after LED power-on. If the supply is not highly accurate, it may make sense to run the LED at bumped up wattage, to minimize supply variance per test. Intensity should never be checked with batteries when lux testing, or in a light that has rapid heating taking place, therefore it makes the most sense to test lux at very low, consistent wattage levels just high enough to obtain some lux reading that is comparible (200-300 starting lux for example). Move the LED closer to the meter if you want to run even lower LED testing wattages, just be sure a spacer is used between them. Do test maximum lux possible first before adding the mirror, and maximum lux to end with, to realize actual total gain in usage conditions.
Since gain can reach 100% or more, gains are simply massive, and there is no reason not to use one of these aperture types, especially if your goal is maximum throw. As I say, it’s like moving 10+ intensity bins into the future, and many jump when only one higher new bin becomes available (I.E., U3 to U4). Just remember that adjustment is everything, along with mirror material/grade. Similar gains can be seen with a dome still on the LED, but this makes alignment much harder and more time consuming, as you must work through a lens instead of open air. With the dome, no the gains will not be as high, but they can still get way up there.
I hope this helps some figure it all out. Producing the mirrors is far more effort and labor, and requires careful glass grinding.