to elaborate, (I'm in agreement with what has been said, just going to throw in a few tidbits to think about)
Most 1AA lights use a boost regulation circuit that works "well" down to around 1V give or take, but they do get slightly brighter as you provide more voltage. A great example is taking a 1AA light that also has a 2AA body available, the regulation circuit can run more efficiently with the extra voltage from the 2 AA cells and you get a little more light, and most especially more consistent output through the discharge (flatter regulation). Moving from a 1.2V NIMH to a 1.5V Lithium primary will have a very minor effect on brightness and "flat" regulation, (as lithium primaries actually do hold around 1.5V through the discharge, unlike alkalines, that fall on their face if you look at them wrong). As others have said though, it's probably not enough to see with the naked eye, and even if you can see a difference, it won't be enough to make a practical difference in a real world application.. In other words, it's not like the light is suddenly going to seem any more useful or capable in actual use.
The reason for the improvement with higher input voltages on these boost circuits has to do with the maximum inlet current that the driver can "pull." As the voltage drops on the supply side, the amount of current needed to maintain constant output increases, but if you can imagine, it's not easy to get MORE current to flow into a circuit with LESS voltage pushing it, the circuit can keep trying to lower the effective resistance on the supply side, but there's a bottom end limit of resistance on the circuit having a lot to do with component sizing. You *could* theoretically make a high power boost driver that could maintain constant output all the way down to say, 0.7V, but lets say, just for the sake of this concept, that the output current of the driver is 500mA on high, it would have to draw well over 3 amps on the supply side after efficiency losses to to maintain that 500mA to the LED with only 0.7V supply voltage. This would mean that the supply side of the regulator, combined with the resistance of the contacts in the flashlight, and the cell, and the switch, would all have to add up to less than 0.25ohm to accomplish. This would require huge wiring, large inductors, gold plated contacts etc etc etc... not practical for a compact flashlight.
So bottom line is, boost circuits that run from 1.2V sources and push high flux LEDs rarely have flat regulation. They do a good job of staying above 50% output through most of the discharge though. And they will almost always benefit from higher supply voltage. (but do not exceed the Vf of the LED by too much, else fry the LED when the driver goes into direct drive)
The Jet beam boost circuit is compatible with the higher input voltages of a single 3.7V 14500, this will increase output much more noticeably (about double). As I understand, when driven by a fresh 3.7V cell, it's basically direct driving the LED though a small amount of resistance in the driver to keep things in order.
Eric
