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Using my Nikon D5100, shooting RAW pictures and using Darktable to disable absolutely all contrast curves, white balancing, sharpening and even the debayering, I've measured the average value of the green pixels of each picutre in a test (by green pixels I mean the actual physical pixels behind the green filters of the bayer filter, the other pixels where ignored).

This test consisted of, using a constant light (in both intensity and spectrum) and varying the exposure time, find the variation of the average value of the green pixels in respect to the total amount of light in each exposure (as everything else was kept constant, the amount of light integrated in each exposure was directly proportional to the exposure time).

I've got the true exposure times from this site, which I checked to be exact in the millisecond range with a microphone recording the shutter sound.

Then, I made a graph of the normalized exposure times VS the normalized average green pixel values for those exposure times.

What I expected was to see a 45º straight line, with the values being directly proportional to the amount of light integrated in each exposure.

But instead I got a way different graph:

enter image description here

This here is quite obviously some particular response function of the CMOS sensor. I didn't find which function makes the best fit on this data yet, logs didn't work very well.

So, what is this response function and why is it like that?

Thanks!

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  • \$\begingroup\$ @jsotola But a constant light intensity should mean a constant charge current in the case, as a constant amount of photons is hitting each sensor over a period of time (and a constant amount of electrons is being acumulated in the well in a period of time). The charging curve of a capacitor for a constant current is a straight line. \$\endgroup\$ – user2934303 Nov 1 '18 at 23:10
  • \$\begingroup\$ my apologies to you. .... i messed up and confused CMOS with CCD ..... i have deleted my comment \$\endgroup\$ – jsotola Nov 1 '18 at 23:22
  • \$\begingroup\$ the curve appears to have the same shape as a capacitor charge curve ..... allaboutcircuits.com/tools/… ...... it may also be a custom designed curve to increase the sensitivity at low light levels \$\endgroup\$ – jsotola Nov 1 '18 at 23:27
  • \$\begingroup\$ deleted and converted to answer \$\endgroup\$ – analogsystemsrf Nov 2 '18 at 3:43
  • \$\begingroup\$ A linear response is what I got (& expected) from extensive characterisation of the Cmosis CMV12000 CMOS image sensor. It's intended for machine-vision applications, so you expect that kind of linear response. Whereas a sensor for a DSLR may well be doing what @analogsystemsrf suggests in his answer, as a wider dynamic range is a more valuable selling feature for a general photography camera. \$\endgroup\$ – Techydude Nov 5 '18 at 1:35
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This looks like a square-root, which may be the current-in/voltage-out of a gate-drain-tied long-channel MOSFET.

This is a cheap way to compress the dynamic range, and greatly expand the shadow details.

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Oh, just found out that the CMOS sensor itself was actually linear. What got me was that there was a gamma compression being applied to the final image when exporting, because the image was written to match sRGB standard, it's not Linear RGB.

The gamma compression does exactly a function Vout=Vin^(0.45), where both Vin and Vout are in the 0-1 range. That's why it looks like a square root.

Once I exported all the images again (I've made measures again with much higher precision) I got ridiculously perfect straight lines when varying both exposure time (and keeping the light fixed) and the light intensity (keeping the same exposure time).

Nothing with the sensor.

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