Originally posted by Digitalis Equivalence is an intellectual attempt to level the playing field - however, in the real world it has little relevance. I'm familiar with the fundamental similarities in sensor performance across formats. But I think it is unrealistic to expect someone to shackle 35mm format with the limitations of APC-C.
Shackle? It's one stop.
Diffraction sets in on both APS-c and FF somewhere between ƒ5.6 and ƒ8.
Quote: Originally posted by Digitalis Equivalence is an intellectual attempt to level the playing field - however, in the real world it has little relevance.
In my real world it has practically no relevance. My philosophy has always been "look through the lens, see what you have, know which format you need to use, if you don't like what you see." Equivalence never became an issue until I start arguing with FF proponents who thought they could use it to prove full frame was "better".
But...
Quote: In a digital camera, diffraction effects interact with the effects of the regular pixel grid. The combined effect of the different parts of an optical system is determined by the convolution of the point spread functions (PSF). The point spread function of a diffraction limited lens is simply the Airy disk. The point spread function of the camera, otherwise called the instrument response function (IRF) can be approximated by a rectangle function, with a width equivalent to the pixel pitch. A more complete derivation of the modulation transfer function (derived from the PSF) of image sensors is given by Fliegel.[3] Whatever the exact instrument response function we may note that it is largely independent of the f-number of the lens. Thus at different f-numbers a camera may operate in three different regimes, as follows:
in the case where the spread of the IRF is small with respect to the spread of the diffraction PSF, in which case the system may be said to be essentially diffraction limited (so long as the lens itself is diffraction limited).
in the case where the spread of the diffraction PSF is small with respect to the IRF, in which case the system is instrument limited.
in the case where the spread of the PSF and IRF are of the same order of magnitude, in which case both impact the available resolution of the system.
The spread of the diffraction-limited PSF is approximated by the diameter of the first null of the Airy disk,
d
2
1.22
λ
N
d/2=1.22\lambda N,\,
where λ is the wavelength of the light and N is the f-number of the imaging optics. For f/8 and green (0.5 μm wavelength) light, d = 9.76 μm. This is of the same order of magnitude as the pixel size for the majority of commercially available 'full frame' (43mm sensor diagonal) cameras and so these will operate in regime 3 for f-numbers around 8 (few lenses are close to diffraction limited at f-numbers smaller than 8). Cameras with smaller sensors will tend to have smaller pixels, but their lenses will be designed for use at smaller f-numbers and it is likely that they will also operate in regime 3 for those f-numbers for which their lenses are diffraction limited.
Clearly when looks at a lens chart.....
Nikon AF-5 ƒ1.4
The lens peaks at 3846 and ƒ5.6 in terms of resolution. By f 11 it's lost roughly 20% of it;s resolution.
Look at the AF-S 35 1.4 on APS_c and its peaks at 2838 and ƒ4 and by ƒ11 about 16% of it's resolution.
IN a practical sense, I don't care much about theoretical limits, I like looking at practical results. Where is the lens sharpest, how much DoF can be achieved before the loss of resolution starts to affect print quality.
SO from my perspective equivalence is irrelevant. Both APS-c and FF start to lose resolution after ƒ5.6, and in that sense they are pretty much identical systems. Further in my own tests, it's very rare that I come upon a situation where the stop blurrier background of FF makes much difference at all. Unless you're shooting with 1 stop of wide open, you can achieve the same with both. That's all we are saying here.
Theoretically, were it not for diffraction, the smallest aperture should be the sharpest and have the most DoF. My one and only concern is that point at which my image starts to be degraded by diffraction, when my over all sharpness will start to be impacted by diffraction.
In both APS-c and FF, it's pretty much the same point, a little bit of difference, not enough to really care about.
That's my beef with equivalence, people discuss it as if it means something it doesn't. As a theory I could care less about it. Ditto with diffraction limits. I don't give a give any credence to all the theory around diffraction limits, only about how the lenses perform.
Just through looking at a lot of charts, you see certain characteristics and theoretical similarities.
I've been using equivalence because it clarifies what I see, both in limited testing and from the theoretical charts.
SO I would argue talking about what lens is diffraction limited and when is irrelevant. You can find all the information you need looking at test charts and by taking a few images. The whole concept and discussion around it has been completely framed by those thinking they can prove some kind of decisive difference exists between APS-c and FF using these theories.
Me, I stick to what I see. All such discussion is pointless. A lens on a camera system does what it does.
A person can like a system because it's large format, another person might like another system because it's small format. That decision can be made without the gobbledygook. If someone wants to use a few formulas etc. to try and explain physical phenom a, i.e.. testing results, go nuts. Thinking it has anything to do with the practice of photography is nonsense. A photographer needs knowledge of the tools he works with. He needs the knowledge of the physic behind it as much as framing carpenter need to theoretically know the laws that govern the efficiency of a framing hammer.
The carpenter just has to swing the hammer, see the effect it has on the nail, and say "that really sucks" or "sweet'.
The photographer with different formats and all this theory is no different. All this theoretical gobbledygook can help you explain what you see, but as a photographer, can't help you change what you see, so in that sense it's meaningless.
The only time theoretical science becomes meaningful to the artisan is when it can be used to change outcomes. A lens it a finished product. There are simply no outcomes that can be changed. Your choice is learn it's characteristics and use it as it is, or don't. The theory is meaningless to the photographer.
There is nothing more irritating than these armchair scientists without a shred of training posting not he internet as if the gobbledygook means some thing.
The gobbledygook is used to explain demonstrable phenomenon. If you don't have the phenomenon that the theory is supposed to describe, you have nothing. I cannot stress enough, or often enough, how pointless it is to discuss theory, as if it means something on its own. Theory describes reality, not the other way around. Theory alters itself to more adequately describe reality all the time. Reality itself doesn't give a flying **** about theory.
One of the most frustrating things on this site is the theoretical nonsense where people delude themselves into thinking they are actually discussing lenses and camera systems by discussing airy discs, diffraction lists and on and on. The scientific properties are one way of describing camera system, but the way least relevant to the photographer. Which approx. 30mm lens gives you the smoothest bokeh? That's what the photographer needs to know. And not one of the geniuses with their knowledge of optical physics has ever worked through a set of equations to that figure that out for me. Talk about useless.
And pullease, don't write a fricken paper on it, just look at a few comparison images, and give us the answer. And if possible post the images. No one cares why.