# Is the charge accumulation linear in time for image sensors?

Reformulating the question: Does the rate of charge of the pixels photodiodes in an image sensor depends of the previous accumulated charge?

The pixel sensor integrates light during a specific amount of time called exposure time. Suppose that the image sensor scanning time is in perfect synchronization with a light source that generates square pulses. That is, when the pixel start scanning the light is starting to arrive to its surface (ideal conditions). Now, If the pulse has the same duration as the exposure time of the pixel I will get an integration quantity, q1. Now, if the pulse is on just half of this time, is it my new quantity half of the previous (q2=q1/2). Does the pixel behaves linearly with charge? How can I measure this effect, taking into account that I'm not able to reproduce the ideal conditions of perfect synchronization? Thank you!

• What photosensor? – Andy aka Jan 14 '20 at 9:04
• Any of them as a generic question. I'm interested cause I do a lot of image processing and knowing it's hardware behaviour will be very helpful – CristoJV Jan 14 '20 at 9:08
• Be more specific and explain more about the setup you are contemplating. – Andy aka Jan 14 '20 at 9:27
• @CristoJV there's more than one type of photosensor, so, stating the type at least would be required to pinpoint which physical phenomena are of relevance. – Marcus Müller Jan 14 '20 at 14:44
• You were right, I'm editing the question to address a more specific situation. I'm talking about image sensors (Ej: picamera module) – CristoJV Jan 14 '20 at 17:47

Does the rate of charge of the photosensor after the photon to electron conversion depends of the previous overall charge?

Yes absolutely. If it didn't, your sensor would have infinite dynamic range. At some point all photosensors saturate.

Probably you are asking about image sensors and not any photosensor. Usually the gain will be set such that the highest value (eg 255) is below saturation (so that the device is highly linear), but not always. If you want to test for linearity, you can use the photon transfer method, which check that shot noise scales proportional to exposure time. If the device becomes nonlinear, shot noise will stop being proportional to the exposure time.

Edit:

## Photon Transfer Method

The EMVA 1288 standard provides formalized test procedures for evaluating the SNR and linearity of imaging devices such as CCDs and CMOS image sensors. They have an excellent description of the entire process and the theory behind it:

https://en.wikipedia.org/wiki/EMVA1288