Diffraction discussion continued

Started Jul 27, 2013 | Discussions thread
The_Suede
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Diffraction + sensor MTF graphs, MTF50 limits
In reply to quadrox, Jul 30, 2013

quadrox wrote:

  1. Diffraction is not a reason to pick one camera/lens system over another, as equivalent photos will have the same amount of diffraction. Lens quality/selection and sensor quality/design are the only reason to go with a specific format when concerned with image quality).
  2. Diffraction has an effect on all images regardless of pixel size (but sometimes it is so small it is not noticeable).
  3. Diffraction will never make images taken with smaller pixel size sensors worse compared to images taken with sensors having larger pixels. Smaller pixels will always yield more detail (at least theoretically).

1. Yes. Diffraction is not the differentiator, in fact it's the OTHER end of the aperture spectrum that makes the difference. A 100mm F2.8 lens will almost unvariably be sharper relative to the format than a 50mm F1.4 lens used on a half-sized sensor. At exactly the same image-related diffraction, though the difference gets close to zero as both systems approach true diffraction limit (where both are well above the Rayleigh limit).

2. Yes. Again, the problem is DEFINITION of "sharp".

3. Yes, though there are practical limits. But they're manufacturing problems, not physics.

When considering viewing an image at 100%, there will be some pixel size for a given sensor format where any further decrease in pixel size (increase in sensor resolution) will not yield any practical increase in detail due to diffraction. Because the effect of diffraction per pixel will increase or decrease smoothly with pixel size, it is difficult to specify a precise threshold for when diffraction makes the picture appear blurry (when viewed at 100%).

Nevertheless one could argue for two specific thresholds - one where the image will definitely appear blurry, and one where it definitely won't (always considering 100% view).

The 'definitely blurry' threshold is probably around the point where the airy disc has the same size as the pixel size, probably even quite a bit earlier. Since the airy discs won't be aligned with sensor pixels, having them be the same size will virtually guarantee that some of them will be projected onto adjacent pixels, which would result in a slightly blurry image.

The 'definitely not blurry' threshold probably requires the airy disc to be quite a bit smaller than a sensor pixel - maybe one half to one quarter of the pixel size. If I understood the Nyquist stuff better, I could probably give a more precise figure. But somewhere around this number should guarantee that most pixels sample more than one airy disc, which will thus look reasonably sharp (I cannot explain it better - I would appreciate it if someone could rephrase this to make sense).

You're kind of right, even though you're wrong...

The Airy disc is much like a Gaussian, it has a well defined "peak" in the PSF. So the real threshold for visibility is when the pixel is the same width as the RADIUS, not the diameter of the Airy disc. That is: Airy diameter = 2*pixel width.

The sensor surface information sampling can be modeled as a sparse box filter, and it has a very well defined MTF in it self (as long as you don't mix in oblique ray angles, then it gets complicated again...). The box filter has a Fourier over area that is approximately a sinc(f) function, and the resulting MTF simulation has a very good correlation with actual measurements. One problem with this is that the response has good response from 0.5f (Nyquist) to 1.0f (2xNyquist) - and also strong side lobes at 1.5f and 2.5f. Those do also induce aliasing and moire, but the 2.5f is so high in resolution that it's largely safe to ignore it.

Diffraction is a very well defined PSF, with a very well defined MTF curve. The correlation between model and reality is extremely high. The function is what you call a chinese hat function chat(x), and after a 2D Fourier it gives the diffraction effect MTF.

Those two can be combined, like this:

D800 pixels, with F8.0 diffraction.

So, if you disregard all "other" sources like camera shake, lens aberrations and so on, you can model most resolution vs diffaction effects. Here you have an aperture step, from F4.0 to F16, D800 pixels (but only the sensor+diffraction result this time, not the individual values).

D800 pixels MTF w. diffraction at F4.0 - F16

If you're not into signal theory, the "cycles per pixel" X-axis is a bit hard to read, so here's the same graph, but with lp/mm X-axis in stead. 106lp/mm is the D800 resolution (4.7µm)

D800 lp/mm MTF w. diffraction at F4.0 - F16

In that graph it's quite easy to see the MTF50-limit for each setting. MTF50 (0.5 on the Y-axis) is a rather strict criteria though, that you often choose when you WANT stuff to give large measurement differences (like in lens tests and so on).

But for this discussion, it might be more interesting to see what difference sensor resolution makes, at different apertures. This is F8.0, but on five different sensor linear resolutions. From D800+20% (56MP) down to D800-20% (25MP).

MTF for F8.0 at 3.8-5.6µm pixel sizes

What's interesting here is that the MTF50-criterion based resolution "only" increases by 18% while pixel resolution increases from 5.6>3.8µm = 50%. On F11 it's even lower, and on F16 it's almost zero difference. -But as you also can see, the MTF at 80lp/mm goes up - from 40% to 50%.

That is certainly a visible improvement, and people usually gladly pay a huge extra sum on lenses to get a 10% better MTF at 80lp/mm (and +5% on 40lp/mm)...

On F5.6 though, where many good lenses are still peaking, the linear difference is much bigger:

MTF for F5.6 at 3.8-5.6µm pixel sizes

Now linear resolution at MTF50 rises from 78lp/mm to 98lp/mm, a change of 26%. The MTF50-limited MP resolution goes from 21MP to 33MP.

So, diffraction does not have much of a "limiting" effect on the resolutions where lenses work best - at least not for another doubling of the MP-count.

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