This is a topic that nothing else makes much sense without. If you don't understand this stuff, you're likely to make mistakes all the time with video - especiallly now that we're into an era of complex raw workflows and grading. Luckly, you're in safe hands. Phil Rhodes is an expert: he's not just a cinematographer but an engineer as well.
While we’ve talked about dynamic range and bit depth before, it seems as if that there’s quite a bit of confusion out there regarding the relationship between the absolute dynamic range of a camera and the bit depth of the recording medium. I’ve even heard manufacturers’ sales reps furthering this association, which just goes to show that you shouldn’t get your information from sales reps. Obviously, you should get your information from Red Shark News.
I think the reason for this confusion comes from the fact that both dynamic range and bit depth increase their range by a factor of two every time an additional index is added. Open up a lens by a stop and you double the amount of light getting in; add one bit to a binary number and you double the range of numbers it can encode.
In binary numbers, this is easy to understand. While practical imaging systems such as the ones we use in cinematography use either eight or ten bits to encode brightness, let’s consider the example of a two-bit word, which is easier to consider as an example. Two bits, each of which may be either 1 or 0, have a total of four unique combinations: 00, 01, 10 and 11. Add another bit, and we can have all of the existing combinations with the new bit at zero, plus all the existing combinations with the new bit at one, for a total of eight. Keep doing this, and you end up with a total of 1,024 combinations for a 10-bit word. Adding one bit doubles the available range of numbers, and therefore makes for more precise greyscale representations.
F-numbers, in terms of photographic exposure, are similarly straightforward. An F number is the ratio between the diameter of the “entrance pupil” – the hole through which the light must pass – and the focal length. As a practical matter this is easy to picture. Looking down a long tube allows less light to hit your eye than looking down a shorter tube of the same diameter, because the shorter tube allows a wider field of view from which light can enter. The reason the F-stops on actual lenses are not evenly numbered is because the amount of light entering the lens is dependent on the area of the entrance pupil, not its diameter. The counterintuitive, fractional numbers are chosen such that the area of the entrance pupil, and thus the amount of light entering and the exposure, doubles for every stop opened up on the lens.
F-stops, therefore, are a measure of relative brightness, whereas bit depth is a measure of precision. These concepts, while both critical to digital cinematography, are strictly speaking unrelated. It would be entirely feasible to consider a camera system with a dynamic range of 20 stops (something we don’t currently have, but would like) which recorde two-bit pictures (which we wouldn’t like). It wouldn’t be terribly usable, much as people occasionally used to shoot on optical-sound origination stock to probably quite similar results. But if it was configured such that the highest binary count of 11 occurred only when the sensor was at maximum level, and the lowest binary count of 00 occurred just above the noise floor, we could correctly describe that as a four bit picture with a dynamic range of 20 stops.
Now, we might not consider that terribly useful – and we’d be right. But it does serve to demonstrate that while it’s highly desirable to have a decent amount of precision, and the amount of precision required to do a decent job certainly does increase with dynamic range, there is no absolute relationship between the two.