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Clarification on Bit Depth's relationship to Dynamic Range?


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I was recently reading an article explaining how for every added bit of information the dynamic range increases by one stop. This makes sense to me as I understand light is perceived logarithmically, but the one point of confusion for me was in the article it stated that the added stop of dynamic range would always be in the shadows. I understand the last stop of light in the highlights will always take up half of the data, and the dynamic range of the sensor isn't changing (the photosites wells aren't getting any bigger or more sensitive), rather there are now just double  the values to record the data, but I don't quite understand how the added dynamic range always goes to the blacks versus say the midtones or highlights? Any clarification would be greatly appreciated.

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When a lot of people discuss this they confuse the mathematical dynamic range of the signal with the range of light levels that was in the scene we were photographing.

The simplest way to understand this is that we could have, say, a two-bit signal capable of representing four levels (00, 01, 10 and 11). We can take a normal camera image that's thirteen stops or so (no matter what the manufacturers say) and define it such that some reasonable black level is 00, and the sensor saturation point is 11, and then we have a thirteen-stop image represented in four bits.

It'll look awful, of course, with massive quantisation noise ("banding") all over the place, but the point is that the number of stops in the image has nothing necessarily to do with the number of bits in the data.

Assuming a linear relationship between bits and stops is seductive because we know that stops represent a successive doubling of the light level, and adding one bit to a digital word doubles its maximum count (we have all the old combinations with the new bit set, and all the old combinations with the new bit unset).

Only in the case where we're storing something in linear light, where the digital number stored is roughly, more or less, a photon count of light levels, does that work as we'd expect. It's no surprise, therefore, that linear storage like that is very often done at 16 bit.

That's quite wasteful, though, because of our logarithmic eyes, so we use brightness encoding schemes (gamma, log) to make better use of bit space. That's how we get common 10-bit signals with 13-stop images encoded in them at high quality.

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Hi Phil, thanks for the explanation, I understand there is no linear relationship between bits and stops because of your comment, but I still am failing to understand why, when there are more bits, the added dynamic range is typically gained in the shadows instead of the highlights? I understand we can't gain any additional dynamic range past the whitest white because of sensor saturation, but couldn't we get another shade in the whites? why does it go to the blacks?

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Usable information at the high end is controlled by exposure because of the clip point, but information at the low end is controlled by the noise floor -- below which the information isn't of much use. So most increases in dynamic range come from lowering the noise and increasing the range in the low end. With dual gain readouts you can basically combine a signal from the photosite before it gets too much light (to capture more overexposed detail) with a signal that gets full exposure to improve dynamic range, which is what the Alexa does. More or less. I think it has to do with degree of analog amplification since the amount of charge created by a photon hitting a photosite is quite low.

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Isn't the stops of dynamic range dependent on ISO? Like in the native ISO dynamic range is equally spreaded on both Shadow and Highlights . However,as we stop down the ISO we get more stops in shadows rather Highs and opposite result for ISO increment?

I came across this great video by John Hess. He tested with different ISO to measure stops .

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With the Alexa, the dynamic range (14+ stops) is the same at different ISO settings, the only thing that changes is how many stops above and below middle grey are captured -- low ISO means fewer stops above middle grey and more stops below, but the total range is the same. 

However, in practical reality, if you are outside in an open field in the daytime and your shadows are only 4-stops below middle grey at the darkest, then using a low ISO might cause you to lose some highlight detail but without gaining more shadow detail since there isn't anything below 4-stops under anyway -- in other words, if you switch your ISO so that instead of 7-stops above and 7-stops below, you were capturing 9-stops below and 5-stops above but your darkest shadow was only 4-stops below, you're throwing away dynamic range.

Same goes for the reverse situation, like a dim twilight where there are no bright highlights -- a high ISO sacrifices shadow detail for more highlight detail but if the scene has no bright highlight detail, then you've thrown away some of the camera's potential dynamic range.

Dynamic range refers to the total number of stops captured.

 

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  • 2 weeks later...

With this in mind David, is it common practice to just shoot achieving the highest dynamic range possible, and then proper exposure can be achieved in post? Let's say I have a scene where there's a bright sky, but no dark shadows, I underexpose the image, or raise the ISO, so I can retain more highlight information in the sky, but now my actors skin is not exposed as desired, is this fixable in post by a colorist (assuming the skintones still have enough data/ aren't noisy) ? I haven't really had experience working with a colorist on log images and will be for the first time, so I'm unsure about the best way to approach setting exposure (always shoot at native ISO with proper exposure, or pick an ISO that retains the most dynamic range w/o clipping or excessive noise)

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