# Does small sensor/pixel has an upper limit of dynamic range?

It is from a friend that I heard:

Cellphone cameras, due to their small sensor size, can have at most 11 stops of dynamic range

(I did not ask too much about where that came from or what source is supporting this. I also paraphrased a bit since I cannot remember the exact sentence he said).

The idea does conform to what people commonly say, i.e. larger sensor can have a bigger dynamic range, and also aligns with the experience that cellphone photos produce a lot of blown-out or pure black.

I have seen this post, and most answers under the question seem to agree that theoretically, a larger sensor would have a higher dynamic range. However, using the box and ball example in that post, I wonder what limits the number of balls that fall into the box. Is it because there can only be so much ball in an area (the density of balls falling), or is it because the box has a maximum volume (the size limit of the box).

Say, would it be possible to have a box extremely tall, so that despite the cross area being as small as that 256-ball-box, this tall new box can hold 2048 balls?

I guess another way to ask my question is: would it be possible to make small senors/pixels holding as much light as the bigger ones? Or are there any theortical/physical rules that limit the maximum dynamic range with a given size?

Dynamic range is the difference between the minimum and maximum light (photoelectrons) that can be discerned/detected.

The minimum is determined by the system's noise floor; there must be enough collected for the signal to stand out against/above the noise. The maximum is determined by the photosite's full well capacity; which is just how many electrons it can hold (acting as a capacitor) prior to readout.

A decade ago a photosite's capacity was limited by its' diameter/physical size; and you couldn't really make them deeper due to limitations of the technology/materials.

However, in recent years manufacturers have been adding a second capacitor in parallel with the photodiode. This does increase the photosite's full well capacity (DR potential) without requiring the photosite itself to be larger... it does in effect makes the photosite "deeper." And most manufacturers are disabling it at higher ISOs where it is not needed (lower light levels), or they are making it optional/selectable. In either case, the result is a sensor with dual base ISOs and two levels of maximum DR capability.

You can always improve NR algos and on-chip sensors, but for any given resolution, a larger sensor will exhibit less optical noise.

Consider setting two containers outside to measure rainfall; one a test tube and one a cylindrical pie pan. After the rain, you measure the volume of water in each vessel and divide by the container's surface area to compute height, aka rainfall amount. Let's assume you can measure to the nearest ml.

It's intuitive that the pie pan will produce greater precision and accuracy as measurement and sampling error is relatively diminished in the larger container. Whereas +/-0.49ml (our best precision) might be 10% of the test tube, it could be 0.05% of the pie pan. These numbers are made-up, but they still illustrate how larger samples output better averages.

The more photons you capture, the more info you have. If you have more info, you can spread the dynamic range out more (eg boosting shadows) before noise is significant. There's other factors to consider of course, but all else being equal, a larger sensor provides more accuracy and precision, and thus higher usable dynamic range.