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So at time of writing a number of high end phones are available with 24 or even 40 megapixel cameras on them.

Assuming good conditions, (good light, still setting, tripod?!) What would be the largest practical size print, for viewing in a gallery, could you make from a 24 or 40 megapixel phone camera?

Note: I can use a rule of thumb and take the number of pixels across divide that 300dpi to give me the number of inches. However once we get down to 40 mp with a lens less than 5mm across, I imagine other artifacts (sensor noise, lens artifacts etc) come to dominate and therefore limit the practical size.

  • If I put the print on the moon, I could make it very big indeed and you couldn't see any artifacts. Or in other words: it's viewing angle that matters, not absolute size. – Philip Kendall Mar 7 at 23:02
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    It's not like there's a hard limit, you might not even notice it's lacking at a very large size unless you see something better right next to it. 600 DPI seems a bit extreme, I'd have no hesitation printing at 200 DPI. – Mark Ransom Mar 7 at 23:23
  • How far away do you expect your viewers to stand? – mattdm Mar 7 at 23:42
  • I don't have a moon printer, so probably closer than the moon. Also it would be an 'art' print so closer than a billboard too. – DarcyThomas Mar 8 at 0:15
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    Possible duplicate of Is there a general formula for image size vs. print size? – xiota Mar 8 at 4:23
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Apple made billboard advertisements using iPhone images. Even for phones with a mere 8 mp, I'd expect lens sharpness to be the limiting factor. You'll have to photograph a resolution chart with your phone and adjust as needed.

The real answer is likely associated with the angular resolution of the human eye. But in practice, about 200-300 ppi is sufficient for viewing pixel-peeping sharp images handheld. Since about 60lpmm on crop sensor (24mm x 16mm) at 6000x4000 is reasonably sharp, a 30in x 20in print should be fine for viewing about a cubit away. You can use the above values (or whatever you find acceptable) as a basis to calculate the print size for different viewing distances, image resolutions, and lens sharpness. The weakest parameter is the limiting factor.

As for artifacts:

  • Compression artifacts stay about constant at the same print resolution because they're pretty much limited to 16x16 blocks.

  • Sensor noise depends on light levels, ISO setting, and other factors. Assuming a clean image in good light, it can pretty much be ignored. Otherwise, treat similarly to lower resolution images taken in poor lighting.

  • Similarly for dynamic range and lens characteristics, such as sharpness and contrast.

  • A cubit? Egyptian or Roman cubit? – mattdm Mar 8 at 3:33
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    @mattdm - Thank you for asking. The long Greek cubit. A short cubit if you're nearsighted. – xiota Mar 8 at 3:41
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The classic rule for computing depth of field considers that at a normal viewing distance (that increases linearly with the size of the print) the good human eye cannot see details smaller than 1/1800th of the diagonal of the picture. This roughly translates to a 3MPix picture, whatever the size (credit card to billboard(*)). Even if you double this for safety you don't need more that 12MPix whatever the print size.

Of course these rules don't apply if people try to look at your pictures at very close range, but then when you pixel-peep the 40Mpix from a smartphone don't look that good.

(*) speaking of billboards, the ones I see up close in the subway are printed at around 5DPI, but at the normal viewing distance (from the opposite platform) you don't see the dots.

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