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Here's a proof of concept for doing dark frame subtraction. It takes an image before turning on the LED, then subtracts that image from the one taken when the LED is on.
This results in an extremely clean image. The only disadvantage is that it's very sensitive to anything moving in frame - even sub-pixel movements can become visible.
This managed to accurately detect LEDs in a large room with my (old) Macbook Pro webcam and no exposure adjustments. I think exposure adjustment may still be valuable, but this makes it much less necessary.
This might not be the neatest way of doing it, as I hacked a lot of stuff around on Friday. I've refactored this a bit without testing because I don't actually have any easily-accessible LEDs at home...
I'd recommend giving it a try with your test setup and see how it works.
ref #33