I'm currently working to characterize the noise in a CMOS camera. I understand that on top of the read noise and dark noise inherent to the sensor, the data is also subject to photon shot noise.
I've taken some data in uniform lighting conditions and measured the variation of values of a particular pixel over time.
Based on the poisson nature of shot noise, I would expect the variance in the pixel values to be equal to the mean pixel value, however I'm seeing that the noise in the pixel values is proportional to the mean pixel value but significantly smaller than it.
The Wikipedia article on shot noise in optics reflects this relationship, using "$\propto$" rather than "$=$" but does not explain why.
Why is this? If photon shot noise is poisson distributed, why isn't the variance equal to the mean? I suspect the answer has something to do with the area of my pixels - am I somehow effectively taking multiple samples from the poisson distribution and averaging/adding them?
Additional info in response to questions
- The images are at a significantly long shutter speed with light present. Dark noise and read noise are not the major effects here.
- Folks asked to see data. Here's the same effect in a paper (Pagnutti et al 2017) on the Raspberry Pi Camera:
As you can see, at each ISO tested, there was a linear relationship between mean and variance, but the slope differs based on ISO. The unit, DN, is the Digital Number readout of intensity which goes from 0 to 1024 in this camera.