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1st it would be nice to open a section on Computer Vision on this forum

@theodore Thank you very much for interesting in my opinion. I'll try to gain this karma

From Quantum Imaging: Linearity? In an ideal linear camera, doubling the light intensity should result in a doubling of the video signal.

Using my bad English... I never had performed this kind of tests but what I know is that the relation between light intensity and signal is expected to be linear with gain K.

pixel_intensity = dark_signal  + Gain * input_photon

This is theoretical and is close to reality for most featured cameras at least for a sub-range of their resolution. In other words linearity is a quality factor for cameras.

See. Characterization and Presentation of Specification Data for Image Sensors and Cameras EUROPEAN MACHINE VISION ASSOCIATION Standard 1288

The linearity of a camera should be one of the specification provided by camera manufacturer. For example see specs for Basler AcA750-30gm Par 4.3.1 and 4.3.6.

From your point of view, you are guessing to verify the linearity of the camera. In other words to do a Photon Transfer Characterization where the camera is the system the light is the input signal and the pixel value is the system output.

This is not so easy because you need of a controlled diffused light emitter at fixed wavelength (otherwise quantum efficiency will produces artefacts) you have to understand/remove the effects of exposure time, type of shutter (global vs rolling) the effects of spatial noise on sensor and finally you have do deduce the linearity as difference of measured signal to noise ratio as suggested by the PTC method.

It would be interesting to see your result if you would use

• a band pass filter over the lens (choose a band where your cam has max quantum efficiency)
• many pixels (full image or a ROI or large binning) per frame instead just 1 (I never use 1 pixel because of noise)
• just 1 light always on
• change the light received by your camera changing the shutter time

• get at least N>=10 points for your analysis... I means N different light intensity

  • When shutter=0 you are reading the dark signal (read noise)
  • Get maxShutter when your ROI=255 (avoid local saturation)
  • Set your light points using shutter[i] = i * maxShutter / N

  This would give you a more accurate curve for your estimation

As alternative you can use the Photon Transfer Curve (PTC) method. It's well known and you will find a lot of docs like this or this