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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

by foldr 6y ago

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.

sudosysgen 6y ago
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.
- foldr 6y ago
  >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 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.
  - sudosysgen 6y ago
    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.
    - foldr 6y ago
      >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-%20Resolving%20some%20spatial%20resolution%20issues%20%E2%80%93%20Part%202.pdf?download=1 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 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.

by foldr 6y ago

sudosysgen 6y ago

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.

foldr 6y ago
>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 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.
- sudosysgen 6y ago
  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.
  - foldr 6y ago
    >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-%20Resolving%20some%20spatial%20resolution%20issues%20%E2%80%93%20Part%202.pdf?download=1 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 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.