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You can *sometimes* pulse LED's at a higher than rated current. How much higher and for how long are the questions to answer. In order to answer these, one has to know about the thermal design of the part. This is best a question for the manufacturer of the device.
In this regard, you can think of the LED the way you think of power transistors. You can run them at much higher currents in a time varying fashion provided there is a low enough thermal *impedance* to remove that heat from the die. Of course, ultimately if the current level gets too high, the bond wires will melt and destroy the device - just like a power transistor.
As a first order guess, I would say it would be safe to run them at twice the current level for half the time (50% duty cycle) If you want to push it higher, you'll need to think about the thermal properties of the device as mentioned above.
Wouldn't the LED be off 50% of the time, and appear half as bright? Twice the current doesn't mean twice as bright. For an IR remote transmitter pulsing at high current (38 kHz), works great to increase range, because the individual pulses are being read at the reciever.
You could always use a switched capacitor approach... You'd actually get some efficiancy gains if you were stuck with a higher voltage than the LED could handle.
Look at the datasheet for the LED. It has a max continuous current rating and a higher pulsed current rating with the max length of the pulse specified.
If the LED blinks for a duration of 20ms or longer then it appears at the same brightness. Less than 20ms then it dims.
If the LED oscillates on and off quickly so it appears to be on continuously then it is dimmed to the duty-cycle percentage. Your vision's response to brightness is to the average brightness.
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