>Diffraction absolutely doesn't come out as a wash. What matters is the actual diameter of the aperture, not the ratio

It's actually the f stop that matters for diffraction, not the absolute diameter. Roughly, this is because the light spreads more with a longer focal length because it has a longer distance over which to diverge. If you crunch the numbers this exactly compensates for the larger absolute diameter of the aperture. Here is a post with a reference: https://www.dpreview.com/forums/thread/21428

It's amazing how much enthusiast discussion about cameras is based on basic misconceptions about optics.

I'm not talking about linear resolution. I'm talking about angular resolution.

Here, the airy disk diameter is the image size. At the same magnification, the image height is proportional to the object size.

Since when the f number is smaller, at the same magnification, substituting in the thin lens formula with the magnification, you find that the object size is inversely proportional to the focal length.

From this you come to the conclusion that, at the same focus distance, the smallest object you can image is a function of the absolute diameter of the aperture.

Intuitively, this is because even though the airy disk has the same size, the focal length is much smaller, therefore the field of view is much wider for the same sensor size, therefore the angular confusion is much bigger, therefore for the same FoV at the same f number detail goes down.

Or put another way, yes the light spreads more, but the sensor on a camera is bigger, so in the end you have much more detail anyways.

This is why, for example, spy satellites despite operating at f/11 or so can resolve much more detail than a cellphone :)

This is a standard exam question if you ever take a Wave Optics class, by the way. But as you say, enthusiast discussion, such as on DPReview, is often based on basic misconceptions about optics :)

Apologies for the snark. This would probably be a fun discussion in person. In my experience, most apparent disagreements like this just come down to confusion over which factors are being held constant out of field of view, sensor size, focal length, total amount of light gathered, etc. etc.

If the phone was using a slice of a DSLR sensor, then yes, the absolute aperture would be what was relevant, as you obviously cannot improve the resolution of an image merely by cropping it (if you imagine a ultra ultra wide DSLR lens which becomes a normal phone lens after the crop).

But two points:

First, you're then comparing resolution at a focal length that's irrelevant to DSLRs, so in practical terms it's not a like for like comparison.

Second, phones are using sensors with higher pixel density. The question is just whether the phone can use a wide enough fixed aperture to avoid being limited by diffraction at the desired resolution. A fixed aperture of e.g. f1.6 is practical at phone focal lengths but not (as a fixed aperture) at full frame focal lengths. If you calculate the theoretical linear resolution limit imposed by phone camera f-numbers, it's approaching 1000 lp/mm for the better models (e.g. an iPhone with an f1.6 aperture and a ~10mm sensor). I'm sure the real limits are lens aberrations and noise at the moment.

It's not an either-or. Diffraction makes things a lot harder, and some phone lenses are indeed essentially diffraction limted

Secondly, I'm actually comparing resolution at fixed FoV, not a fixed focal length.

Again, the sensor size doesn't matter, what matters is the focal length. The focal length of an iPhone main lens isn't 10mm, the sensor size is 8.5mm but the focal length is actually around 5mm. You find the theoretical maximum linear resolution is more around 300-400 lp/mm. If you run the numbers, at f/1.6 the airy disk diameter is already bigger than the pixel pitch (2.11 microns airy disk and 1.7 micron pixel pitch). The resolution is already being seriously degraded by diffraction, although it's not completely diffraction yet. Lens aberrations make it even worse, of course. All in all, realistically the resolution is pretty much at its limit.

If you work at this regime where the linear resolution is close to equal to the airy disk, you start having a type of abberation where changing the wavelength of the system causes a change in the resolution, which can't be fixed. So pretty much in practice you can't really exceed the resolution we see now even in perfect light with a perfect lens, because you start having unavoidable abberrations that are very significant to the image.

>Again, the sensor size doesn't matter, what matters is the focal length.

Well, yes, but the two are obviously tightly linked if we're comparing a DSLR to a phone camera.

I'm going by the calculation in the 'Cameras' section of https://en.wikipedia.org/wiki/Airy_disk It explains why only the f-number is relevant. If you plug values for an iPhone into the 'x =' equation, you'll see that an iPhone camera is not really close to being limited by diffraction. The minimum separation distance at 500nm wavelength at f1.6 comes out to 976nm. Along an 8mm sensor dimension that's 8188 line pairs. Now sure, that's by the Rayleigh criterion, so you're not resolving 8188 perfectly sharp line pairs. But that's a still a good margin over the sensor resolution, and it's an open question how good sharpening algorithms can get.

I'm afraid that the radius, not the diameter. The diameter of the airy disk at f1.6 for 500nn is of 2 microns, and for a line pair you'd need double that, not a single, so a line pair would fit on 4 microns. Over an 8mm sensor that's 4000 lines, 2000 line pairs. Note that even here contrast is reduced by diffraction as we are operating from the first null. If you use the Rayleigh criterion and relax your standard for resolution you're at 4000 barely distinguishable line pairs. IIRC that would 4000LP at MTF15, so at MTF50 you might be at around 2500-2600?

And this is of course the very best you can do at 26mm equivalent focal lengths, if you want a tighter or wider shot your image quality degrades because once again the optics don't fit and you'll have to reduce your f number.

2000 line pairs in perfect conditions is quite low. Better is expected from cheap DSLR zoom lenses.

>I'm afraid that the radius, not the diameter

Yes: the quantity calculated is the smallest separation two objects can have before they blur together (by the Raleigh criterion).

According to the standard notion of lp/mm, there is no need to halve the reciprocal of this quantity to get lp/mm. See e.g. the table on p.14 here: https://zenodo.org/record/3518178/files/Verhoeven%202019%20-... An airy disc of ~2um radius translates to ~500 lp/mm. The following page also agrees with this usage, as does every other source I can find at the moment. http://www.normankoren.com/Tutorials/MTF1A.html

I think you are basically out by a factor of 4 by using the diameter instead of the radius and requiring line quads rather than line pairs. I believe the lp/mm value obtained is for ~9% MTF, so it's a fairly generous estimate of the available resolution, but not excessively so.

Regardless of the correct definition of lp/mm, the iPhone has plenty of room to increase the sensor resolution at f1.6. And phone cameras could certainly move to somewhat wider apertures and somewhat larger sensors.

Phone cameras are already at the limit of the space they can occupy. You would have to trade off the number of cameras.

As for the rest, lp/mm only makes sense at a given MTF rating. MTF50 is the standard. MTF9 is very, very, very generous. Incredibly so.

But anyways, sure, let's take 900lp/mm on the short edge for 4590lp/mm MTF9 - maybe I misremembered. A 5DSr with a real world zoom lens, the 24-70mm F2.8L, gets 7700lp/mm in the real world, and that's the MTF lens-sensor system, not just the lens. And that's not even close to the maximum possible resolution, nor to the maximum you can actually get in real life as you can. If you take the sharpest full-frame lens I know of whose MTF9 is limited to 400lp/mm because no testing apparatus was available that could go higher, the actual maximum is around 9600lp/mm. In any case, even the highest theoretical resolution of a phone is far lower than the practical resolutions of ILCs in use today, and is actually less than the sharpness of a 90$ lens on the very cheapest full-frame body you can find.

Indeed, take the Canon 50mm EF II, with an MTF50 yielding ~2000-2400lp/mm on the short edge of FF sensor. According to this source (https://www2.uned.es/personal/rosuna/resources/photography/D...), at around f/1.6 we should get around 420lp/mm, on the short edge that's 2142lp on the short edge, which is less than the cheapest EF lens in production right now. I don't know about you, but the best possible performance in theoretically perfect conditions being under the performance of the cheapest EF lens in the real world says something.

In real life, of course, the lens-sensor system will barely get close to the theoretically perfect result, and you will peak at the best possible result being around half the linear resolution of the cheapest production Canon lens.

Keep in mind, if you were to go for a larger sensor, you'd have to increase the focal length to compensate too. So 20% increase in sensor size length would need a 20% increase in focal length and at the same f number you'd need a 20% wider aperture too. And again, you'd be fixed at around 25mm FF eq. focal lengths, if you try more practical focal lengths like 50mm FF eq. you would see a drop in quality. They're already pretty much at their optical limits and have been for a while, actually f/1.6 isn't even the fastest phone lens - but those had smaller sensors still.