Are electrons on a sensor Poisson-distributed?

1 month ago

To be precise, my question is:

Is the number of electrons 'generated' (released/excited) in a photosite on a sensor in a fixed time interval Poisson-distributed?

I am reading through some articles about image noise on dpreview and other websites.

It is claimed in these articles that the number of photons hitting the sensor and the number of electrons released are both Poisson-distributed.

The statement about photons can be proven by quantum physics, though I cannot follow this fully due to insufficient understanding of quantum physics.

At least, I can comprehend that the limit of binomial distributions of photon arrivals is the Poisson distribution, so I just go with this argument.

For the statement about electrons I could not find a proof on the internet. If one assumes that a photon excites an electron in the photosite with a fixed probability p, and that these electron releases are all independent from each other, then the binomial distribution limit consideration makes it plausible that electron release is Poisson-distributed. But I am not sure if this line of thought is actually valid. (Theoretically, each collected photon might 'charge' somehow the sensor, and for every 1/p photons collected, one electron is released. In this theoretical consideration, the number of electrons would be rather a kind of scalar multiple of a Poisson-distribution.)

So, can someone please confirm and give rough directions on how to explain by physics that the number of electrons released in the sensor is actually Poisson-distributed?

Thank you for your help!

Comments:

- Actually, I have not seen evidence that the number of electrons excited in the sensor is Poisson-distributed. Only digital numbers (DN) after ADC and gain are reported. The calculations of full well capacity (of electrons) that I have seen rely on the assumption of Poisson-distributed electrons. It seems that only camera/sensor producers would have direct information about number of electrons excited, full well capacities, etc. for their sensors, but they seem not share it.

- Of course, I consider the case that the mean value of photon numbers hitting the sensor is constant over time and that the time interval is chosen in a way that the mean number of electrons generated is sufficiently small compared to the full well capacity so that no clipping occurs.

- Let us keep the fact aside that even in this case it cannot be strictly a Poisson distribution because such a distribution has positive (though extremely small) probability for any arbitrarily large number of electrons to be released in this time interval.