Adrian - Can you give us one? (or point to one)
sure. It’s extremely simple. The number of bits equals the stops of dynamic range, assuming a linear gamma. If you change your gamma, you can encode more or less dynamic range in the same number of bits at the expense of having your total number of available tone values redistributed amongst the number of stops that you’re encoding. what that ends up being depends on the gamma you used.
in the practical real world, ADC converters generally have a very linear response except at the extreme ends of the scales they are designed to handle. Good ones minimize that as much as possible in their design so that you can effectively assume the number of bits equals the number of stops. The same goes for digital sensors. Even though they are actually analog devices, their response is incredibly linear except at the extreme ends of the range they are designed to operate at.good ones minimize that as much as possible so that you can effectively assume that it is linear over it’s stated design DR.
so what does this mean? It means if you have a 14 bit ADC you will never get more than 14 linear stops of dynamic range from it. So, if you have a sensor that can cleanly capture 16 stops of range in a linear fashion and you feed that signal to a 14 bit ADC, you’ll get a very clean 14 stops, with the last 2 stops falling into either the upper end where they are clipped off, or falling into the extreme lower end where they are indistinguishable from the ADC noise floor.
the same goes for having a sensor that can only cleanly handle 12 stops of dynamic range. If you feed that into a 14 bit ADC, you’ll get a 14 bit sample that either never has data in the top two stops of its range, or a sample that has the bottom 2-3 stops of its range completely encoding the non linear floor response of the sensor, depending on how the designer decided to feed the sensor response to the ADC.
A good design aligns the maximum voltage that the sensor can produce with the maximum voltage the ADC is designed to handle, and uses an ADC that has an appropriate number of bits to match the sensors linear dynamic range, thus meaning, if you have 14 bits, you have a maximum 14 stops, minus a little noise/non linearity at the extreme ends of the tonal range. Again, a good design will minimize that as much as possible so that you can safely assume 14 bits equals 14 stops.
Where things tend to fall down is reviewers/people on the internet take it upon themselves to determine for the audience how much noise is acceptable, and then subtract that from the available dynamic range and declaring that it’s only 11 stops or whatever the number is. Then people get confused and go, wait a minute, so 14 bits is only 11 stops? Then those people on the internet attempt to explain using a staircase analogy... see where I’m going with this?
it’s very simple. In sensor and ADC land the number of bits equals the total dynamic range. Some of that dynamic range at the extreme ends will not be completely linear, or have some noise, or both, but good designs minimize that as much as realistically possible. How much of that at the extreme ends you choose to accept should be up to you, not to a reviewer. A reviewer who takes it upon themselves to decide that for you is not doing you any favors.
