# When does the retina fail to recognize images of two closely separated points as distinct?

Our eye is a lens and lenses have a resolving power. The resolving power of a lens, physically speaking, is related to how good two closely separated points A and B can be distinguished as separate. If two such points A and B, separated by a distance $$d$$, are looked at, their images will be created on our retina.

When does the retina fail to recognize them as two separate images? To ask it differently, what sort of image formation at the retina does and does not allow it distinguish the images of A and B as separate?

This matter is agonizing me for a long time. I made Google searches but didn't find the exact answer I'm looking for: What kind of image formation "confuses/fools" the retina? If you answer this, please supplement it with a figure/drawing for a clearer picture. I am happy to assume that the points emit monochromatic light of wavelength $$\lambda$$. Thanks!

• There may be several layers to this answer. I can think of at least three: (1) It's a question about the ability of the eye's optical system to focus a sufficiently sharp image on the retina. (2) It's a question about how closely the receptor cells are spaced in the retina and, how well they are isolated from their neigbors. (3) it's a question about image processing functions that are performed in deeper layers of the retina and in the visual cortex. – Solomon Slow Apr 23 '19 at 15:52

There are two main features that give, e.g., eagles much better visual acuity than humans: a greater density of retinal cells (~1,000,000 per mm^2 vs ~200,000 per mm^2), and continuously adjustable corneal curvature (whereas in human eyes only the lens shape is adjustable). Of the two, the density of retinal cells is the most important limitation in human visual acuity. It is analogous to the pixel spacing in a digital camera: although a camera lens might be able to form diffraction-limited images with ~ 1 micron resolution, if the pixels in the detector array are 10 microns apart then the best resolution the camera can obtain is 10 microns.

• Thanks but my question is given a person, with a given eye-lens, given retina, what really happens. I think my question is a geometrical optics question. Sorry if my question sound foolish – mithusengupta123 Apr 23 '19 at 14:28
• Are you asking how an image is formed in the eye? The point of my answer is that even if the optics of the eye forms a "perfect" diffraction-limited image, the spacing of retinal cells determines the net resolution of the eye. – S. McGrew Apr 23 '19 at 15:49
• @muthusengupta the answer is correct. It clearly points out that the limit is not determined by geometrical optics but by retina pixel density. If you want a different answer you should ask a different question. – my2cts Apr 23 '19 at 19:23
• @S.McGrew We can see things of linear dimension $d$ if we use waves of $\lambda\lesssim d$. I think I needed an answer to this. – mithusengupta123 Apr 24 '19 at 15:17
• I would suggest that you consider all the answers and reference links given here, then ask a new question aimed specifically at the issue you would like to have clarified. – S. McGrew Apr 24 '19 at 15:41

I believe you are looking for Rayleigh Criterion and more generally Angular Resolution

Resolution limitations occur because of the density of photo sensitive cells on the retina. There are some geometric considerations dependent on wavelength which also yield a limit on being able to tell distant objects apart, even given perfect resolution. This is called diffraction limited resolution.

The Rayleigh Criterion is a gauge for the ability of an optical system to discern distant objects even with perfect resolution. For example, stellar parallax, comparing the observed distance of a star at different parts of the year, can gauge how far away objects are, but only for a certain range. Far enough away, this process cannot tell two stars apart even if they are very far away from each other. The range of effectiveness of parallax is proportional to the length of semi-major axis of an elliptical orbit.

The resolution is given by the separation of the rods and the cones which can be about 1-2 um apart. Assuming the eye diameter is 20 mm, this is also the distance from the lens to the retina, we get 0.5-1 arcmin angular resolution just by geometric optics. At 25cm normal vision you will be able to see objects as separate if they are about 75um apart.

This is the best scenario when the lens operates fine.

The wavelength is not a variable here because the diffraction resolution for the pupil or the lens is far better than the limit by the detector.

• The pupil opening is more like 1cm in diameter. – my2cts Apr 23 '19 at 19:20