At what point is bit depth redundant in photography/cinematography?

Question

When thinking of pixel (physical) resolution, I imagine the pixel count as sampling the spatial variations in luminance across the scene. More pixels, the greater ability to sample the undulating pattern of changing luminance values more faithfully (such as when there are high frequency patterns).

I then started thinking about Bit-depth, as the systems ability to sample the changes in the luminance’s values at a single pixel.

Thinking of it in these terms made it more clear to me the relation of bit depth to dynamic range and then I’ve read this article talking about how increasing bit depth just increases the amount of noise one captures. To be fair I don’t think I quite understand the whole of the article, but I understand that increasing bit depth allows for higher dynamic range and that it makes sense that increase bit depth also increases the accuracy at which we quantize the noise deviations. However, surely there must also be a gain of increasing bit depth.

For example, ARRI made sure that it’s 12 bit logC4 encoding has an increased Bit depth code value per exposure stop compared to its previous logC3 10bit curve, while also increasing its dynamic range.

So when does Bit depth become redundant, i.e. not visible to the human eye (just noticeable difference) or just end up recording noise (which might not be even noticed) and where does it still improve image due to improved quantization?

The link to the article I was referring to https://m.dpreview.com/articles/4653441881/bit-depth-is-about-dynamic-range-not-the-number-of-colors-you-get-to-capture

Source about ARRI log curves: Harald Brendel in Colorist meetup podcast https://open.spotify.com/episode/6CvgfAPTC0V4FIkXDXq4iV?si=djxl7cBFR3WDxjtC0MVaew

Thank you for your time and please feel free to let me know if I’ve misunderstood something.

Answer 1

It becomes redundant when it is recording useless data. One example would be when the scene contains fewer stops of dynamic range than the sensor is capable of. And this is typical of when you use an ISO higher than base... i.e. a higher ISO is used because the scene does not contain the maximum brightness recordable. In this case the excess DR capability is only recording noise because the minimum sensitivity is invariable; the minimum recordable light level cannot be reduced.

It also becomes less useful at higher exposures.

The difference between 0 and 2 is one stop (0-1), and the difference between 8192 and 16,384 is also one stop (13-14). And in terms of human perception those stops are equivalent, because human perception is also logarithmic.

The Weber ratio is 0.14 for the cone cells in the human eye. That means the intensity must change at least 14% from where it was before in order to be perceivable. That only requires ~ 7 values measured/recorded within each stop.

So what happens is that you are effectively measuring/recording the linear DR (e.g. 14 stops in linear 1 stop increments) with a logarithmic scale which has increments much finer than a human can perceive... i.e. that last stop of DR only requires 7 values, but it is being measured/recorded with 8,192 values. In this case the excess isn't noise perse; it just isn't useful... and this is where a lot of "visually lossless" compression can be achieved.