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I know that most problems involving the human eye in my undergrad physics text book tell the student to treat the human eye as a diffraction limited system (ie to assume the only factor limiting human vision is the diameter of the pupil). I was wondering, however, how good of an approximation this assumption is. My question is whether healthy human eyes are arbitrarily close to diffraction-limited systems or if there is another underlying factor that limits our ability to distinguish objects even further. Specifically, I am asking about healthy eyes with no diseases such as astigmatism, and 20/20 vision or better.

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    $\begingroup$ Resolution can be a problem. We have a set number of rods and cones. Also sensitivity; we require a minimum number of photons for each wavelength to trigger a detection $\endgroup$
    – Jim
    Jul 23, 2015 at 15:11
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    $\begingroup$ I always tell students to work this out for themselves, as it is both instructive and tractable. The eye has a focal length of a couple of centimeters; the iris runs from ~1mm to ~1cm and the wavelengths are a few hundred nanometers. The only non-physical input you need is the lateral size of the rods and cones. $\endgroup$ Jul 23, 2015 at 15:57
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    $\begingroup$ @dmckee well done. I'll only add that there's a lot of variation in the quality not only of the lens system but of the retina's rod/cone density. Or ask anyone with nystagmus. $\endgroup$ Jul 23, 2015 at 16:56

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The human eye is close to being fully diffraction-limited, at least for photopic (cone-based) vision at the center of the visual field (i.e. for images wholly within the fovea), though it's not quite there for most people.

According to Yanoff and Duker (Ophthalmology, 3rd ed. (Mosby, 2009), p. 57):

The 20/20 (6/6) Snellen line represents the ability to see 1 minutes of arc, which is close to the theoretical diffraction limit, but the occasional patient can see the 20/15 (6/4.5) or 20/10 (6/3) line.

Four explanations suggest themselves. First, some individuals may have cone outer segment diameters of less than 1.5 μm, which would give a finer-grain mosaic having cone separations of less than 1 minute of arc. Second, longer eyes provide slightly magnified retinal images, thereby tending to yield better acuities. Third, some eyes may have less aberration than others, which would allow them to function optimally with larger pupils having, consequently, better diffraction-limited performance. Finally, the neural image enhancement mechanisms may be slightly more efficient in certain favored individuals.

In other words, the standard benchmark of "essentially perfect vision" is at about 60 arcseconds, with some calculations putting the diffraction limit (at shorter wavelengths, and with a contracted pupil) closer to 20 arcseconds. Some key considerations:

  • Depending on conditions, the diffraction limit on the visual resolution is in competition with the "pixel" resolution, i.e. with the density of cone cell and nerve terminations, which can be at roughly comparable levels.
  • There is also a minor amount of optical aberration, which causes the residual factor of ~2 to ~3 between the ostensible diffraction limit and the average.
  • There is considerable variation in the human eye, both for good and for bad. The 20/10 vision reported above corresponds, given the 20/20 $\leftrightarrow$ 60'' correspondence above (and also here), to a resolution of 30 arcminutes, essentially at the diffraction limit for normal humans $-$ but there's a legitimate question as to whether slight changes in those people's eyes (say, a slight elongation, or a larger-than-average pupil) push the diffraction limit even lower for their eyes.
  • Ultimately, checking the angular resolution for human eyes depends on what humans report that they see, i.e. it is filtered through the human brain's processing (what Yanoff & Duker call "neural image enhancement mechanisms"), and this makes determining the actual resolution in an objective manner quite a hard task to accomplish.
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