I wondered what would be better for the signal to noise ratio (i.e. visible noise in the image) if the shooting conditions do not allow us to expose more our shot using aperture nor shutter speed. For example, in very dark indoor pictures like in a church (an old European church I should say), a concert, night photography without tripod,...
To test this I have done the following tests over this scene, ranging all possible ISO values my camera (350D) has:
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Shot at T=1/4, f/13, 50mm
PLEASE NOTE: that shutter speed and aperture were the same for all of them, I just changed the ISO. Of course I balanced exposure in the RAW development to be able to compare the final noise in the shots face to face. The RAW development was done using DCRAW, with absolutely no noise reduction nor unsharp options.
ISO PROGRESSION
From left to right, lighter to darker areas.
Crops at 50% done using nearest neighbour to preserve SNR.
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ISO100 vs ISO1600
Crops at 100%:
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Improvement is so clear that noise manages to alter the general tone (colour) in the darkest areas.
The improvement is higher the darker the areas are. So in the darkest shadows the gap from ISO100 to ISO200 is clearly larger than from any other couple of ISO values. The improvement gets less noticeably once we have reached consiredably high ISO values (we can see differente between ISO800 and ISO1600 is much less than from ISO100 to ISO200).
Conclusion: it is always better (at least with my Canon 350D) to expose to the right, even if we have to use high ISO values to achieve that. So high ISO values are preferred than image underexposure to improve noise at given aperture/shutter speed values.

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