Originally posted by Wheatfield You are depending on the red herring of DOF to cloud reality.
Not really; it's just *one* of the things that will necessarily vary in order to get an improvement in noise. Chances are in many cases, it won't be the most field-relevant - size, weight, and price will.
Quote: Let me give you an example of reality:
A friend brought me a file from a Nikon D3. It was shot at our local police academy, under horrid lighting conditions at ISO 1600. When I adjusted the levels to see how much noise was in the dark blue trousers that the cadets were wearing, I was surprised to see the nap of the fabric and the stitching in the seams.
What I did not see was noise.
I know that if I had done a similar picture with my cropped frame Pentax it would have been a noisy mess.
Had you shot at the f-stop, ISO and shutter speed, the noise would have been one stop worse - at least, that's the difference made by the difference in *size* between the sensors. Who knows what difference is made by the sensor technology itself, or different NR algorithms, etc. But the "FF-ness" of the D3 was good for one stop.
The idea of equivalence is to allow you also consider what *else* had to change to get that advantage. In order to get the same FOV between the two cameras means you had to use a lens with 1.5X longer focal length. And in order to get the same f-stop on that longer lens means also larger glass elements. Basically you need a lens 1.5X times as large overall in order to realize that benefit. And depending on what focal length we are talking about, the lens might well be much *more* 1.5 times as expensive, too. Or it might not - some fields of view turn out to be wins on FF, others turn out to be wins on APS-C. the beauty of equivalence is that it gives us a way to figure out which is which.
If you're talking "normal" ranges, FF wins pretty handily. Say you were shooting a 35/2 on APS-C; all you'd need on FF to get that one stop win is a 50/2. Here, the lens required to give a win to FF is no larger, no heavier, and no more expensive than the APS-C lens. You get a shallow DOF at 50/2 on FF than at 35/2 on APS-C, but you are correct to observe that in many cases, this doesn't matter, or would indeed even be a good thing. Of course, there are cases where it *does* mater. We don't mention DOF to cloud the issue; we mention it because it is a necessary part of the equation mathematically, not because anyone assumes it is a term people would always care about. And for the times when DOF *does* matter, it's nice to know the equivalence covers that as well.
On the other hand, at the telephoto end, it is considerably less clear even without taking DOF into consideration. If you were shooting the APS-C camera at 135/2.8, you'd need a 200/2.8 to realize that one stop win in noise. If you were shooting the APS-C at 200/2.8, you'd need a 300/2.8 to realize that same win. I think you'll agree that in both cases, you're looking at a significantly larger, heavier, and more expensive lens, so that's what I mean abut paying a price for the improvement in noise. The fact you *also* pay a price in DOF is, as you observed, not normally the most important issue - and indeed, often, people *want* that shallower DOF. Equivalence isn't about making value judgements - it's about telling you which focal length / aperture combinations will produce the same results between APS-C and FF, and what focal length / aperture you'd need to get less noise, shallower DOF, deeper DOF, faster shutter speed, slower shutter, or whatever effect it is you want.
With equivalence, we can quickly see that a 200/4 on FF is "equivalent" to the 135/2.8 on APS-C - they will provide the same FOV, the same DOF at each click of the aperture ring, and - most importantly - the same amount of nosie for a given shutter speed. That is the fact that the 200/4 is a stop slower thn the 135/2.8 exactly nullifies the one stop advantage of FF in terms of noise. In order to get the same shutter speed out of the 200/4 on FF, you'd need to go one stop higher in ISO than you needed to with the 135/2.8. So if you shoot with a 200/4 - which is *already* a larger and heavier lens than the 135/2.8 - you don't get any benefit from FF at all - you are just needlessly carrying around a bigger and heavier camera and lens.
Conversely, equivalence lets us see that shooting a 135/2 on APS-C would give you the same DOF as the 200/2.8, but more importantly, that it *also* would nullify the noise advantage of FF, because the 135/2 would allow us to shoot the APS-C camera one stop lower in ISO.
Whether or not a 135/2 ends up being cheaper / smaller / lighter than a 200/2.8 is another matter. But that does help illustrate the basic point here. In order to realize a one stop advantage at the telephoto end over what you get with a given lens on APS-C, you need a lens 1.5X times as big. The interesting part is, *it doesn't matter if you also go to FF*. That is, you can *either* go to FF nd a larger 200/2.8, *or* you can stay with APS-C and simply upgrade the lens to 135/2. Either way you get the same one stop advantage over where you were before. The 200/2.8 on FF and 135/2 on APS-C are *equivalent* in this extremely important sense - the 200/2.8 on FF does *not* allow you to enjoy a one stop advantage in noise over the 135/2 on APS-C.
Obviously, getting the faster/larger lens for APS-C is not always a viable option, and that's why FF often makes the difference - because it makes it most feasible to actually get that bigger lens in many cases. But make no mistake - at the telephoto end, you don't get a win in noise from FF without a much bigger lens (and shallower DOF, for whatever that happens to be worth to you).