When you go to the optometrist they test your reading by flicking you through many different lenses. Of course there are a finite number of lenses in their possession, so they can only correct your vision to some precision. if one could in principle make custom lenses precisely for a person’s eye, could one theoretically have perfect vision
? and how far would you be able to resolve images on a clear day?
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> if one could in principle make custom lenses precisely for a person’s eye
They already do. There’s a lot of parameters the optometrist is fiddling with and often it’s not just a matter of swapping in a different focus lens. For example my new glasses have the same value lenses as before but at a slightly different angle and it’s noticeably better.
> and how far would you be able to resolve images on a clear day?
At a clear *night*, couple million kilometers. You can see the moon pretty well, yes?
The limit isn’t distance, it’s angular resolution. Each receptor in your eye receives light from an expanding cone-ish shape that covers about 0.02 degrees vertically and horizontally. With 1x magnification (natural vision), that’s the limit of what you can see – if the object only covers one of those cones at the distance it is, you see a dot, if it fals into more of the cones you get to see a tiny blurry shape etc.
> if one could in principle make custom lenses precisely for a person’s eye
They already do. There’s a lot of parameters the optometrist is fiddling with and often it’s not just a matter of swapping in a different focus lens. For example my new glasses have the same value lenses as before but at a slightly different angle and it’s noticeably better.
> and how far would you be able to resolve images on a clear day?
At a clear *night*, couple million kilometers. You can see the moon pretty well, yes?
The limit isn’t distance, it’s angular resolution. Each receptor in your eye receives light from an expanding cone-ish shape that covers about 0.02 degrees vertically and horizontally. With 1x magnification (natural vision), that’s the limit of what you can see – if the object only covers one of those cones at the distance it is, you see a dot, if it fals into more of the cones you get to see a tiny blurry shape etc.
So light is a wave, right? And waves aren’t really *at* a single point: they’re kind of spread out. So it turns out that even with *perfect* lenses (or mirrors, but we don’t have those in our eyes usually) we can’t focus light emitted from a single point back into a single, perfect point. There will always be a fundamental blurriness due to the wave nature of light.
This limit is called the “diffraction limit” and it gets smaller (i.e., our vision would get sharper if everything in our eyes was perfect) if the wavelength of light is shorter (meaning bluer) and the aperture — how big the opening that lets light into our eye, with the lens width as an upper limit — is.
Surprisingly, our eyes can get pretty close to the theoretical maximum diffraction limit. Exceptional 20/10 vision corresponds to an angular resolution (how small an angle two points can be separated by and still be seen as two distinct points) of about 30 arcseconds. The diffraction limit for the human eye is no less than about 20 arcseconds (and some sources report it to be even worse), so 20/10 vision is pretty close to the theoretical limit for perfect optics!
So light is a wave, right? And waves aren’t really *at* a single point: they’re kind of spread out. So it turns out that even with *perfect* lenses (or mirrors, but we don’t have those in our eyes usually) we can’t focus light emitted from a single point back into a single, perfect point. There will always be a fundamental blurriness due to the wave nature of light.
This limit is called the “diffraction limit” and it gets smaller (i.e., our vision would get sharper if everything in our eyes was perfect) if the wavelength of light is shorter (meaning bluer) and the aperture — how big the opening that lets light into our eye, with the lens width as an upper limit — is.
Surprisingly, our eyes can get pretty close to the theoretical maximum diffraction limit. Exceptional 20/10 vision corresponds to an angular resolution (how small an angle two points can be separated by and still be seen as two distinct points) of about 30 arcseconds. The diffraction limit for the human eye is no less than about 20 arcseconds (and some sources report it to be even worse), so 20/10 vision is pretty close to the theoretical limit for perfect optics!
[deleted]
> if one could in principle make custom lenses precisely for a person’s eye
They already do. There’s a lot of parameters the optometrist is fiddling with and often it’s not just a matter of swapping in a different focus lens. For example my new glasses have the same value lenses as before but at a slightly different angle and it’s noticeably better.
> and how far would you be able to resolve images on a clear day?
At a clear *night*, couple million kilometers. You can see the moon pretty well, yes?
The limit isn’t distance, it’s angular resolution. Each receptor in your eye receives light from an expanding cone-ish shape that covers about 0.02 degrees vertically and horizontally. With 1x magnification (natural vision), that’s the limit of what you can see – if the object only covers one of those cones at the distance it is, you see a dot, if it fals into more of the cones you get to see a tiny blurry shape etc.
So light is a wave, right? And waves aren’t really *at* a single point: they’re kind of spread out. So it turns out that even with *perfect* lenses (or mirrors, but we don’t have those in our eyes usually) we can’t focus light emitted from a single point back into a single, perfect point. There will always be a fundamental blurriness due to the wave nature of light.
This limit is called the “diffraction limit” and it gets smaller (i.e., our vision would get sharper if everything in our eyes was perfect) if the wavelength of light is shorter (meaning bluer) and the aperture — how big the opening that lets light into our eye, with the lens width as an upper limit — is.
Surprisingly, our eyes can get pretty close to the theoretical maximum diffraction limit. Exceptional 20/10 vision corresponds to an angular resolution (how small an angle two points can be separated by and still be seen as two distinct points) of about 30 arcseconds. The diffraction limit for the human eye is no less than about 20 arcseconds (and some sources report it to be even worse), so 20/10 vision is pretty close to the theoretical limit for perfect optics!
Glasses just change the focal length of your vision through your cornea (which is like the lens on the camera that is your eye) behind that lens is your retina (which is like the image sensor inside your camera). Your eye is the equivalent of 12-15 megapixels in its fovea centralis (that’s the dense central cluster of light sensors in your retina, responsible for your centre of vision). A 15 megapixel camera given the best glass in the world still only shoots at 15 megapixels, imagine 15 million dots on a picture, perfect glass just means the locations of those pixels are perfectly exhibited in your picture.
>Of course there are a finite number of lenses in their possession, so they can only correct your vision to some precision.
There’s probably more than you think, standard lens are in +/- 0.25 diopter increments, and they also can impose a rotational correction for astigmatism. The real way of looking at it is they can correct your vision to at *worst* within 0.12 diopters (if increments are 0.25 and you land as far away from a perfect fit as possible on either increment that’s 0.12 diopters) that’s where the final touches of “which is better image 1 or image 2” come in. To gain an appreciation for a diopter a lens with 1 strength puts an object 1 meter away in focus. Going one way the focal point changes intervals by whole single meters 1,2,3 etc the other way by fractions of a meter 1, 1/2, 1/3, 1/4 etc. Imagine we did this with a camera and had the object 1 meter away from the camera at absolute worst lens fitment it would be like moving the obeject closer about 6cm or away about 12cm. If you do this experiment with a manual focus camera you’ll probably have a hard time noticing any significant difference cause I know I certainly do… “can I see number 1 again…number 2…number 1…hum maybe 2 one more time… … … let’s see number 1 again…”
If we had higher degrees of resolution in our retinas chances are we would just have more specific diopter increments.
If we had “perfect lenses” the big gain would be viewing angles out the corners of your glasses. Glasses are measured to correct through the centre of the lens and the fitment on your face and mounting in your frames can impact how you look through them and throw the corners off a little.
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