Take a FF sensor and a situation where a minimum DOF requirement forces us to push ISO to achieve proper RAW exposure (it's then assumed we are already using the slowest possible speed to avoid trepidation). Now let's compare noise in the shadows (dynamic range) in two cases:
- A: FF sensor at 24mm, f/4, ISO800
- B: The same FF sensor but using it at 12mm, f/2, ISO200, and cropping it by 2x (1/4 of the original resolution)
(http://www.guillermoluijk.com/misc/ruidorecorte.png)
(http://www.guillermoluijk.com/misc/ruidorecorte.gif)
Framing, DOF and RAW exposure are the same. But what about noise?
- Assuming we have an ISOless sensor (leave Canon apart), pushing ISO by 2 stops in A makes us lose 2 whole stops of DR
- On the other hand having 4 times as many pixels in A statistically halves noise when rescaling A to the B size, hence we gain 1 stop of DR (not 2!)
The combined effect is that the B image once both images are reescaled to the same output size will still hold 1 extra stop of DR over A, i.e. half the noise in the shadows. Of course we are losing a lot of resolution, but if noise becomes a problem this can be secondary.
The conclusion is that when a DOF requirement forces us to push ISO to achieve proper exposure, thanks to the statistical trick of noise using a lower focal length + crop (with the consequent wider aperture and lower ISO), can provide a noise improvement in the shadows. This can become of practical use with those new cameras having tons of Mpx.
This is also the explanation why noise advantage in larger sensors vanishes when pushing ISO is needed to achieve a minimum DOF.
Regards
I did a test to demonstrate what was explained here. In an application where ISO3200 was needed to achieve a good exposure with certain DOF requirement, using half the focal length with a 2 stops wider aperture at ISO800, and cropping by 2X the resulting image provides the following improvement in noise in the final image (the ISO3200 image has fairly been rescaled 50% to model the statistical SNR improvement for having twice as many Mpx):
(http://www.guillermoluijk.com/misc/recortes.png)
(upper half in correctly exposed areas, lower half in the shadows -3EV, Sony A7 II over a uniform colour wall)
Greater improvement in the deep shadows (dynamic range) was totally expected since SNR improves much quicker in those areas when increasing exposure (photons) than in good exposure areas. Nevertheless there is improvement in the whole range.
Regards