# Noise and ETTR

Started 10 months ago | Questions thread
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 Re: How ETTR and ETTL work mathematically In reply to Andy Crowe, 10 months ago

Andy Crowe wrote:

To help visualise, here's what's happening with noise mathematically.

Lets say you're photographing a completely plain grey wall, which when correctly exposed the grey pixels are 50 brightness. Noise adds +-5 to that.

Thus with noise a line of pixels might be

55, 46, 54, 55, 48, 49, 50, 45, 55, 48, 48, 52, 51, 50, 47, 55, 54, 48, 55, 51

With the noise ranging from 45-55.

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If you underexpose (so the grey pixels are just 25 brightness) you still get +-5 noise, so you have

20, 25, 22, 30, 20, 26, 21, 21, 23, 28, 29, 20, 27, 30, 24, 23, 22, 30, 24, 22

You then double the exposure in post to make 50 and get

40, 50, 44, 60, 40, 52, 42, 42, 46, 56, 58, 40, 54, 60, 48, 46, 44, 60, 48, 44

which if you compare to the correctly exposed pixels is more noisy, ranging from 40-60.

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If you overexpose so the grey pixels are 75 +- 5 noise you get

76, 80, 78, 79, 79, 73, 75, 70, 79, 73, 70, 76, 73, 79, 78, 77, 80, 80, 72, 78

Which if you bring it back down to 50 in post makes

50, 53, 52, 52, 52, 48, 50, 47, 52, 48, 47, 50, 48, 52, 52, 51, 53, 53, 48, 52

With less noise with a range of just 47 - 53

Although you are basically on the right track, that's not quite how it works. The noise does not stay constant as you vary the exposure. If it's originally +-5, as in your example, it will be less than that if you underexpose (before pushing) and more than that if you overexpose (before pulling). After pushing, it would still be higher, and after pulling, it would still be lower, than it was with the exposure you first exemplify.

The only problem with ETTR is if your pixels go over 100% brightness you can't bring them back down in post anymore, so if you go too far to the right you may end up with white or off-coloured patches where the colour channels have clipped.

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