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Comment by wtallis | Hacker News Reader

1 arc second is 4.8x10^-6 radians. For small angles, sin(x) is approximately x. Thus, sin(1 arc second) = 4.8x10^-6 is the ratio between pixel width and viewing distance. At 3ft this is 5240 dpi, and at 10ft it's 1720 dpi.

I think the 1 arc second threshold is too strict by about an order of magnitude.

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Yeah, I found this:

https://www.quora.com/How-do-you-convert-arc-seconds-to-mete...

"One degree is an angular measurement. 1/60th of a degree is an arc minute. 1/60th of an arc minutes is an arc second, a rather small angle but an angle none the less.

(...)

1 arc second subtends 1 meter at a distance of 205,787 meters (I did say it was a small angle)."

Which should mean that 1 arc second subtends one millimetre at ~200 meters? Do we really have that high visual acuity?

100 pixels per millimeter at 2m? 200 at 1m? That's ~25 * 200 = 5000 pixels per inch at 1m. I would think 1200 dpi would be more than sufficient at 1m...

[ed: missed the bit about: "from standard viewing distances" - still sounds rather extreme]

The theoretical upper limit of the resolving power of the human eye will be given by the Rayleigh criterion. For a pupil diameter of 5mm and a wavelength of 500nm (green light) we can theoretically resolve about 1.22e-4 radians. 1 arcsecond is about 5e-6 radians, i.e. 25 times smaller than we could theoretically resolve without a magic retina.

1 arcminute is a more realistic size for what people can reliably resolve I think. I guess we need significantly better than that to avoid a subjective feeling it is blurry but, that is about what we can actually reliably tell the difference between I think. We cannot tell the difference below 25 arcseconds or so though, it is not possible without larger pupils.

Can you tell us at what distance the theoretical 1.22e-4 radians would apply. I suppose you mean something like regular screen-viewing distance.

The angle in radians apply at any distance - if I understand correctly it is about when light from two adjacent points would have to "hit" the aperture so close as to interference with each other. Another random link from the Internet makes the connection between the definition of 20/20 vision and Rayleigh limit:

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/Raylei.htm...

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