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> It's easy to see the difference between a page printed at 300 dpi and one printed at 600 dpi This depends entirely on viewer and viewing distance. 300 dpi sh

> It's easy to see the difference between a page printed at 300 dpi and one printed at 600 dpi This depends entirely on viewer and viewing distance. 300 dpi should be roughly at the limit of what someone with 20/20 vision can distinguish from a distance of about a foot. If you get a teenager with 20/15 vision and put them as close as their eyes can focus (say, 4 or 5 inches), they’ll be able to see a clear difference between these. But if you take an average person and look at the two images from a distance of a few feet, it will be all but impossible to tell the difference.

kragen 5y ago
Subjectively, I think it's easy to see the difference between the output of a "300 dpi" laser printer from a "600 dpi" one. But can we justify that mathematically? I think distinguishing the orientation of a set of bars separated by, in ancient Babylonian units, 1 arc minute, is Snellen's definition of 20/20 vision? 290 microradians? You might have, say, a 1-arc-minute-wide line, followed by a 1-arc-minute-wide space, and then another 1-arc-minute-wide line? At a "foot" an arc minute is 88.7 microns, which works out to 286 "dpi". So, I guess you're right: 300 dpi is fairly precisely the limit of what 20/20 vision can distinguish from one "foot". In https://dercuano.github.io/notes/bokeh-pointcasting.html https://dercuano.github.io/notes/bokeh-pointcasting.html I estimated the visual acuity in my good eye experimentally at about 200 μradians, which I guess means I have about 20/15 vision. Too bad I can't focus any closer than a "foot" now that I'm old. I can still see the jaggies on 300-dpi laser prints, though. But if you have 20/20 vision and can focus at 150 mm (as most of us can before we get old, or as we can with reading glasses, or just if we're a bit nearsighted, or if we're reading in bright sunlight so the bokeh is a bit smaller), then you can distinguish lines separated by a single white pixel at 600 dpi. So in theory you should be able to print out http://canonical.org/~kragen/bible-columns.png http://canonical.org/~kragen/bible-columns.png on a regular 600-dpi laser printer and then read it with a magnifying glass—the whole KJV Bible on three pages. Two sheets of paper, if you print double-sided. (So far, I haven't managed to get it to print that clearly, but I think that's probably a matter of printer drivers and pixel grid alignment to avoid resampling.) Now, if you have 20/15 vision, at one foot you should have about 400 dpi of resolution. Or, at the 4 inches you suggest, 1200 dpi! (1145, actually.) You should be able to get the KJV Bible onto one side of one sheet of A4 paper! Anyway, I think there's a big gap between the ambition described by "The World's Most Detailed Print Maps" and "we print our maps using the highest resolution mediums available" and even "no sense printing at a higher resolution than humans are able to perceive", and the standard you describe, "if you take an average person and look at the two images from a distance of a few feet, it will be all but impossible to tell the difference." I mean there are a lot of things that humans are able to perceive, but not from a distance of a few feet: the flavor of pizza, the scent of most kinds of roses, the difference between good wine and bad wine, the individual scales on a butterfly's wing, bad breath, the subtle impatience in an outwardly tender caress—and, perhaps, even the meaning of most printed text. And there are many, many things that humans are able to perceive, but average people are not: the meaning of an English sentence (since 83% of people do not speak English), the difference between love and lust, the historical context of colonialism, the particular version of AutoCAD used to design a building, the form of engine malfunction represented by a particular rattling noise, the shoddiness of Dan Brown's writing, the self-serving dishonesty of those who promote the "Law of Attraction," the abusive nature of proprietary-software licenses, global warming, the difference between a Bristol accent and a London accent. So I think you are redefining the stated goals of this work downward to a really remarkable extent. What an average person can easily see from a distance of a few feet is very far from the limits of human perception.
- jacobolus 5y ago
  Marketing copy exaggerates a bit, film at 11. You are right if they wanted to really push the limits of human perception they could develop custom printers or buy some machines used for physics experiments or integrated circuit fabrication or whatever and try to print at 1200+ pixels/inch. Realistically, what they are doing is making full resolution prints on commercially available large-format photograph printers, with their effort going into tweaking the shaded relief algorithms and applying photoshop filters to boost local contrast.
  - kragen 5y ago
    I think you're being unjustifiably uncharitable by accusing them of intentional fraud. I think they're just fooling themselves because they're carried away by their enthusiasm for what they've created, which is really pretty cool. You don't need custom printers to print at 1200+ pixels per "inch". Most off-the-shelf inkjet printers and some laser printers can do it, though at high resolutions there's a serious tradeoff between precise color and precise position. https://news.ycombinator.com/item?id=27965938 https://news.ycombinator.com/item?id=27965938 points out that standard imagesetters are 2540 "dpi" (and they have been since the 01980s). Photographic processes routinely produce images with a resolution below 10μm (2540 "dpi") and, when desired, below 2μm (12700 "dpi"). I don't mean with some kind of super niche lab equipment; I mean Kodak point-and-shoot cameras with mass-market Kodachrome film. Metal machining routinely hits precisions of 25 μm (1000 "dpi") and has for a century and a half, sometimes using machines made out of junk using nothing but hand tools; when it matters, it gets down to 1 μm (25400 "dpi"), which is roughly the measuring repeatability of any old handheld micrometer. You can buy such a micrometer on eBay for US$30 https://www.ebay.com/itm/363415676100?hash=item549d4324c4:g:7vkAAOSwP2xgsVU4 https://www.ebay.com/itm/363415676100?hash=item549d4324c4:g:... though a quality one probably costs US$60 or more, even used. What made Harrison's achievements with the diffraction-grating ruling engines 70 years ago remarkable was not that he could position the ruling engine in increments of 25 nanometers or better (a million dpi); that, and even 2-nanometer increments, had been achieved for small gratings about a century earlier. His achievement was maintaining a total error under 5 nanometers across a distance of over 200 mm during the weeks necessary to rule a full diffraction grating. (I think the Richardson Grating Lab still uses the Michelson ruling engine he overhauled in the 01940s, though with further improvements.)

kragen 5y ago

Subjectively, I think it's easy to see the difference between the output of a "300 dpi" laser printer from a "600 dpi" one. But can we justify that mathematically? I think distinguishing the orientation of a set of bars separated by, in ancient Babylonian units, 1 arc minute, is Snellen's definition of 20/20 vision? 290 microradians? You might have, say, a 1-arc-minute-wide line, followed by a 1-arc-minute-wide space, and then another 1-arc-minute-wide line? At a "foot" an arc minute is 88.7 microns, which works out to 286 "dpi". So, I guess you're right: 300 dpi is fairly precisely the limit of what 20/20 vision can distinguish from one "foot". In https://dercuano.github.io/notes/bokeh-pointcasting.html https://dercuano.github.io/notes/bokeh-pointcasting.html I estimated the visual acuity in my good eye experimentally at about 200 μradians, which I guess means I have about 20/15 vision. Too bad I can't focus any closer than a "foot" now that I'm old. I can still see the jaggies on 300-dpi laser prints, though. But if you have 20/20 vision and can focus at 150 mm (as most of us can before we get old, or as we can with reading glasses, or just if we're a bit nearsighted, or if we're reading in bright sunlight so the bokeh is a bit smaller), then you can distinguish lines separated by a single white pixel at 600 dpi. So in theory you should be able to print out http://canonical.org/~kragen/bible-columns.png http://canonical.org/~kragen/bible-columns.png on a regular 600-dpi laser printer and then read it with a magnifying glass—the whole KJV Bible on three pages. Two sheets of paper, if you print double-sided. (So far, I haven't managed to get it to print that clearly, but I think that's probably a matter of printer drivers and pixel grid alignment to avoid resampling.) Now, if you have 20/15 vision, at one foot you should have about 400 dpi of resolution. Or, at the 4 inches you suggest, 1200 dpi! (1145, actually.) You should be able to get the KJV Bible onto one side of one sheet of A4 paper! Anyway, I think there's a big gap between the ambition described by "The World's Most Detailed Print Maps" and "we print our maps using the highest resolution mediums available" and even "no sense printing at a higher resolution than humans are able to perceive", and the standard you describe, "if you take an average person and look at the two images from a distance of a few feet, it will be all but impossible to tell the difference." I mean there are a lot of things that humans are able to perceive, but not from a distance of a few feet: the flavor of pizza, the scent of most kinds of roses, the difference between good wine and bad wine, the individual scales on a butterfly's wing, bad breath, the subtle impatience in an outwardly tender caress—and, perhaps, even the meaning of most printed text. And there are many, many things that humans are able to perceive, but average people are not: the meaning of an English sentence (since 83% of people do not speak English), the difference between love and lust, the historical context of colonialism, the particular version of AutoCAD used to design a building, the form of engine malfunction represented by a particular rattling noise, the shoddiness of Dan Brown's writing, the self-serving dishonesty of those who promote the "Law of Attraction," the abusive nature of proprietary-software licenses, global warming, the difference between a Bristol accent and a London accent. So I think you are redefining the stated goals of this work downward to a really remarkable extent. What an average person can easily see from a distance of a few feet is very far from the limits of human perception.

jacobolus 5y ago
Marketing copy exaggerates a bit, film at 11. You are right if they wanted to really push the limits of human perception they could develop custom printers or buy some machines used for physics experiments or integrated circuit fabrication or whatever and try to print at 1200+ pixels/inch. Realistically, what they are doing is making full resolution prints on commercially available large-format photograph printers, with their effort going into tweaking the shaded relief algorithms and applying photoshop filters to boost local contrast.
- kragen 5y ago
  I think you're being unjustifiably uncharitable by accusing them of intentional fraud. I think they're just fooling themselves because they're carried away by their enthusiasm for what they've created, which is really pretty cool. You don't need custom printers to print at 1200+ pixels per "inch". Most off-the-shelf inkjet printers and some laser printers can do it, though at high resolutions there's a serious tradeoff between precise color and precise position. https://news.ycombinator.com/item?id=27965938 https://news.ycombinator.com/item?id=27965938 points out that standard imagesetters are 2540 "dpi" (and they have been since the 01980s). Photographic processes routinely produce images with a resolution below 10μm (2540 "dpi") and, when desired, below 2μm (12700 "dpi"). I don't mean with some kind of super niche lab equipment; I mean Kodak point-and-shoot cameras with mass-market Kodachrome film. Metal machining routinely hits precisions of 25 μm (1000 "dpi") and has for a century and a half, sometimes using machines made out of junk using nothing but hand tools; when it matters, it gets down to 1 μm (25400 "dpi"), which is roughly the measuring repeatability of any old handheld micrometer. You can buy such a micrometer on eBay for US$30 https://www.ebay.com/itm/363415676100?hash=item549d4324c4:g:7vkAAOSwP2xgsVU4 https://www.ebay.com/itm/363415676100?hash=item549d4324c4:g:... though a quality one probably costs US$60 or more, even used. What made Harrison's achievements with the diffraction-grating ruling engines 70 years ago remarkable was not that he could position the ruling engine in increments of 25 nanometers or better (a million dpi); that, and even 2-nanometer increments, had been achieved for small gratings about a century earlier. His achievement was maintaining a total error under 5 nanometers across a distance of over 200 mm during the weeks necessary to rule a full diffraction grating. (I think the Richardson Grating Lab still uses the Michelson ruling engine he overhauled in the 01940s, though with further improvements.)