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To be more precise, let's say we are taking a W&B photograph.

Picture 1 : And let's say we take it once with a 1/1000 shutter speed, so that the values for R/G/B range from 0 to MAXVALUE / 2

Picture 2 : And then, we take the same scene, with a 1/500 shutter speed, so that the values range from 0 to MAXVALUE.

Question : will Picture 1, look as Picture 2 once its brightness has been scaled so that the whole dynamic range is filled ?

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Regarding sensor linearity, the considerations about scientific CCD's in this answer could also be of interest. –  Alberto Aug 23 '13 at 13:11
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3 Answers

Digital sensors are very linear for the vast majority of the response curve, with deviations at the very bottom (due to noise, depending on where the black point is set) and at the very top near saturation. Digital sensors are particularly linear when compared to film, which has a pronounced 'S' shape response curve.

The reason for this is that incoming photons free up electrons in the photodiode generating a charge which is ultimately read out to form the image. The number of freed electrons depends on the number of incident photons hence the linear response to light intensity. However when a photosite is nearing saturation various electrical effects reduce the charge generated by incident photons leading to a roll-off of the response curve (i.e. it becomes shallower). After saturation no further increase in output can be achieved so the curve becomes highly nonlinear.

However it is important to realise that RAW converters, both in software and in camera will probably apply some form of tonecurve to the image to give a more contrasty film-like output.

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(Note: Though you explicitly asked about DSLR sensors, I though that, for completion, this could be of interest)

In CMOS sensors, every sensel has its own amplificator, so the sensor's response can in theory be tuned up on a per-pixel basis. In fact, there are already HDR sensors in the market whose answer is non-linear to allow for higher dynamic range. For example, the OV10630 HDR targeted at the automotive industry.

I could not find any native HDR sensor for consumer cameras, though.

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It is more like an S curve, where the low end is mostly cut off by subtracting the dark current, but it starts saturation before hitting the MAXVAL. In an 8bit image I have sometimes found the true saturation to start around 200 rather than 255.

This is the reason why HDR images is more complicated to make than to sum(Wn*In), where Wn is given by the exposure of In. You first need to calibrate the sensitivity curve.\

Take a look at slide 9.8:

http://www.uio.no/studier/emner/matnat/ifi/INF5440/v10/undervisningsmateriale/F9e.pdf

and response curves here:

http://pages.cs.wisc.edu/~sgallege/P1/index.html

Read more about calibration of response curves here:

http://www.pauldebevec.com/Research/HDR/debevec-siggraph97.pdf

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The tonecurve in the second link is very misleading, as it is unclear how the images have been processed (e.g. in camera RAW conversion applies it's own curve), but more importantly the curve is plotted on a log scale! –  Matt Grum Jan 28 '13 at 10:46
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Here's a very raw curve output V is a function of electrons - you see the snip of the s curve around zero and the pre-maxValue saturation "knee": siliconimaging.com/SI6600%20spec.htm –  Michael Nielsen Jan 28 '13 at 16:03
    
@MichaelNielsen A quote from your link, just below the [V] graph you referred to: "The figure above shows the pixel response curve in linear response mode." –  BBking Jan 29 '13 at 23:57
    
yes, linear mode (normal) versus bi-linear response mode (HDR). and the figure shows that in the setting they chose to name "linear mode", it is not true linear. "The SI-6600 can be used in a dual slope bi-linear mode, extending the useful dynamic range in scenes where detail in bright areas are to be preserved at the same time as maintaining details in darker regions. In normal linear response, a camera requires a short exposure to keep the bright areas from saturation." –  Michael Nielsen Jan 30 '13 at 7:27
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