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F/0.9 on APS-C equals f/1.2 on FF, both for DOF and collecting of light per time. I really don't get why this is so hard to understand and thus comes up every time different formats are compared and discussed.
A sensor with the area X will have to get twice the exposure compared to a sensor with the area 2X, to get the same noise per image height. Forget about ISO. What you want is photons.
It's not hard to understand at all. The reason this stupid argument comes up is because people are arguing two different things when they bring this up, and unfortunately one of those things is completely irrelevant to the discussion when practically applied to photography, however technically correct it may be (with certain assumptions). Because of the difference in "vocabulary", this argument perpetuates.
The first "thing" one could be arguing is referring to resultant shutter speeds from various apertures. This is a relevant argument. Shutter speed is a known parameter as displayed by the camera and can be altered by the photographer through a variety of means, one of which is to alter the aperture of a lens.
The second "thing" is this completely irrelevant "photos per unit time" and its association with differing sensor sizes and performances. I say irrelevant because there are a hell of a lot assumptions made when talking this point (and the assumed conclusion, then, that the FF sensor is always better)
1) The sensor ISO steps are calibrated exactly the same between the sensors,
2) The sensors are equally efficient at gathering light in the first place
3) The sensors have exact the same noise read characteristics from underlying electronics, etc.
4) The camera metering performance and algorithms are exactly the same.
Unfortunately, there is no such thing as a "photos per unit time" parameter to alter in the camera. Furthermore, because of differences in items 1-4 above, to equate FF camera as "better" in light vs a crop is folly.
While yes, on a purely technical level the FF sensor area "catches" more photos in, say 1/60s than a crop camera, that doesn't really mean much. The items 1-4 can be varying wildly, such that the crop sensor is so much advanced over the FF that given the same shutter speeds and ISOs, it's still better than the FF.
An example of this would be something like the Canon 5D vs an Olympus OM-D or NEX camera, Fuji, etc.
All cameras are excellent, but on a purely noise performance basis, the crop cameras above are close (if not tied, or ahead) of the 5D.
Yet, per the second irrelevant item of argument (photons per unit time), this shouldn't be possible...because the 5D's sensor receives much more photos per unit time!
This argument is ridiculous - there is no setting at all which a photographer can change in the camera that would directly modify this parameter - it is a useless, "false argument" parameter.
Instead, we can look at resultant noise (as modified through the changing of ISO), we can look at aperture (or effective aperture), we can look at depth of field, and we can look at shutter speeds, when talking various apertures.
In effect, I just metered a lamp on my desk using a Canon S95 and an OM-D at the same apertures and ISOs. These photos, framed exactly, gave the same shutter speeds.
I know at f/5.6, metered this way at this ISO, I get this shutter speed. I don't get, in an operationally relevant way, "8x photons" from the OMD (or whatever the number is).
I can say, knowing the noise characteristics of my S95 vs my OM-D, that pushing my ISOs is much easier for acceptable levels of noise on the OM-D vs the S95 -- because of performance characteristics 1-4.
That's not to say in the future, the Canon S950 won't actually be better at resultant noise than my ancient Olympus OM-D, regardless of the photos utilized. That is why I believe people have an argument about this - photos/time is not really a field-relevant parameter.