It is critical to remember
that the "out of focusness" of a crop image will be enlarged more to
achieve a given print size than the "out of focusness" of a full
frame image, since the latter starts larger.
Does this mean that the background blur of the image from the crop
sensor will look the same as the background blur from the FF image
(when the image is printed at the same size)?
For the same FOV and DOF, yes.
Anyway, your asking hypothetical questions about hypothetical systems, which, of course, is all fine and dandy, as it helps form an understanding about the principles at work, just as working a high school ballistics problem that ignores the effects of wind resistance and a curved surface helps illustrate the principles of Newtonian Mechanics.
But eventually, we must shoot our rocket into orbit though an atmosphere and around a curved Earth. To that end, let's discuss some of the important "real world" differences between crop and FF:
1) Larger sensors have less shot noise and more read noise. What this means is that larger sensor systems produce much cleaner images at low ISOs when there is ample light, but when upping the ISO to maintain the same DOF and shutter speed in a limited light environment, the darker areas of the image from a larger sensor will exhibit more noise.
2) The MTFs of some FF lenses exhibits a sudden drop at the exteme edges. This means that cropped sensor systems using FF glass will not experience this sudden drop, as this portion of the image is cropped out, and the extreme corners (5% of the total image area) may be sharper, even though the rest of the image will be softer.
3) While I know of no example where cropped glass is sharper by a factor of the crop factor, most cropped glass is sharper than their FF counterparts. Thus, while FF will still be sharper overall, the difference is not as exteme as some make it out to be.
4) The fact that glass on 1.6x has to be 1.6x times sharper on FF does not mean that FF images are 1.6x sharper than 1.6x. Remember, as long as the glass is sharp enough to resolve the pixels, being sharper gives no additional advantage. Thus, if the glass can resolve all the pixels on 1.6x, and can also resolve all the pixels on FF, there is no advantage in sharpness for FF, but there is an advantage for whichever sensor has more pixels.
Let's discuss this last point a bit further. Let's say we have FF glass that is sharp enough to resolve 12 MP on 1.6x. Then that lens will produce the same sharpness of image on 1.6x as it does on FF if both sensors have 12 MP. However, if the glass is sharp enough to resolve 12 MP on 1.6x, then it is also sharp enough to resolve 31 MP on FF, so if a FF sensor had 31 MP, then it would obviously have a big advantage.
On the other hand, let's say that the glass is only sharp enough to resolve 12 MP on FF. Then it will not be sharp enough to resolve 12 MP on 1.6x. However, if a 1.6x counterpart is made for 1.6x, and it is 1.6x times sharper than the FF lens, then both the FF sensor and 1.6x sensor will have the same sharpness and be able to resolve the same detail.
In practice, of course, lenses lie somewhere between these two extremes, with interesting twists, such as the sudden MTF falloff at the extreme edges of some FF lenses mentioned earlier.
Lastly, as I've said many times before, none of this matters if your focus is not accurate enough to resolve the pixels, if the camera shake or motion blur is present (and don't think that's an issue only for very low light -- why else would landscape photographers be using a tripod and MLU?). Finally, there's print size. For an 8x12 print, 300 PPI only requires 8.64 MP. On the other hand, 300 PPI for a 12x18 print requires 19.44 MP. So, how big are you printing? Even so, just how big of a difference will 200 PPI, or even 150 PPI vs 300 PPI matter to you?
It's important to understand the advantages/disadvantages of the equipment. But this can all too easily be taken to an extreme where it is well past the point of having any meaningful purpose.
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--joe
http://www.josephjamesphotography.com
http://www.pbase.com/joemama/