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I'm reading about sources of noise in cameras while taking images - One of them is the dark current. That is, some electrons in the CCD device of a camera are set free due to thermal noise. Those free electrons than indicate that photons have fallen on that pixel - though they haven't. Even with closed shutter, those electrons are set free. The dark current is dependent on the ambient temperature and the exposure time. [Wikipedia: Dark Current]

Now, I wonder why this behaviour is also somewhat pixel dependent. I assume that the number of released electrons should be roughly the same for all all pixels as they should average out over exposure time. In my understading this is an pyhsical application of the central limit theorem, which should result in the same "offest of light" for all pixels.

But my assumptions seem to be wrong, as this dark current stays the same for given pixels and can even be used as a finger print for a camera. A series of pictures show the same noise patterns. [Wikipedia: Fixed-Pattern_Noise]

Can someone explain why my assumptions seem to be wrong and hence why the dark current can be used as a finger print?

Thank you!

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    $\begingroup$ Not all noise is thermal noise. There are low frequency noise components in all semiconductor devices, fittingly called 1/f-noise or pink noise, that have non-thermal origin: en.wikipedia.org/wiki/Pink_noise. This noise originates from a number of different mechanisms, some of which are localized to defects in the semiconductor or on its surface. In a sensor these localized defects will be resolved at the pixel level, while in most other semiconductor elements (like transistors), they will add up to a total noise floor. The level of 1/f noise is technology dependent. $\endgroup$ – CuriousOne Mar 1 '16 at 10:24
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    $\begingroup$ When recording experimental data with a CCD it is prudent to carry out studies of the particular camera performance with the light field blocked. At the minimum you will often find a gradient density across the frame, plus a few bad pixels which can be excluded from any analysis. These defects are independent of the dark currents, and come from manufacturing defects and the operating cycle of the camera's data transfer mechanism. The dark current is reduced by lowering the temperature -- available with peltier cooled devices -- but these other symptoms remain, so the have a different origin. $\endgroup$ – Peter Diehr Mar 1 '16 at 11:25
  • $\begingroup$ @CuriousOne That is the foundation of a pretty good answer. In particular the localization to surface defect goes right to the matter. $\endgroup$ – dmckee Mar 1 '16 at 15:27
  • $\begingroup$ @dmckee: Except that I simply don't know enough about it... I am a device user who knows how to deal with 1/f noise when necessary and I talked to some device technologists in the industry about it. There doesn't seem to be a simple theory nor are there easy ways to characterize the microscopic problems... one guy told me that a lot of it is actually trade secrets, especially how to etch/clean away surface defects... so I don't feel like I am qualified to do anything but handwaving here. $\endgroup$ – CuriousOne Mar 1 '16 at 23:11
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The basic reason is that the bulk material used to create the CCD or CMOS sensor array is not perfectly uniform, either in crystalline structure or foreign element contamination. Similarly, the exact diffusion depths in the pixels, readout layer line widths etc etc vary slightly. All these parameters contribute to the "dark noise" statistics for each pixel. So while each pixel's noise is pretty much constant (ignoring temperature dependence and cosmic ray damage :-) ), the pixels are all slightly different. Their quantum efficiency, aka percent detection of incoming photons, varies as well, so cameras have a built-in set of maps which both remove dark noise and adjust for signal gain.

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