Image Formation Issue: Spherical Aberration & Fixing

[yas-say]

Hi guys
I've been trying to make a program that simulates image formation in the eye
so I simulated a spherical lens behavior in 3d coordinates
and I'm facing a strange results!
is it normal that the refracted rays don't intersect all at the same point
I began to think it's true because of the spherical aberration.
here's the problem:
can I continue with Image formation with this aberration or should I fix it
If I should how could I?

any help would be great
thanks in advance

 

[Rap]

Yes, its probably spherical aberration. The thinner the lens is, the less problem there should be. You could model a perfect lens, one that has no aberrations whatsoever. I forget what shape that is, it might be a parabola. Anyway, modelling the eye as a perfect lens will take care of the basic image formation, and then if you want to deal with lens aberrations in the eye, start introducing deviations from the perfect lens. Like if you want to model astigmatism or something.

A perfect lens would be one that was infinitely thin, and every ray parallel to the axis of the lens would pass through the focal point. Any ray (parallel or not) passing through the center of the lens will be undeflected. The equation for a perfect lens is - if a ray hits the lens at angle "a" to the normal, a distance z from the center of the lens, and the lens has focal length "f", then the ray will exit at angle a' where

Tan(a')=z/f - Tan(a)

 

[yas-say]

So if I want perfection I have to simulate a parabolic lens?
but can I simulate a spherical lens with the aberration and still image formation works
because all eye models are based on spherical lenses
if not, can I an equivalent parabolic lens from a spherical one
and what is the equation of a parabola in 3d space

 

[Rap]

So if I want perfection I have to simulate a parabolic lens?
but can I simulate a spherical lens with the aberration and still image formation works
because all eye models are based on spherical lenses
if not, can I an equivalent parabolic lens from a spherical one
and what is the equation of a parabola in 3d space

Im not sure a perfect lens is parabolic, but I gave the equations above. But these equations are for perfect image formation on a flat plane, not on the curved surface of the retina, so maybe these will not work well, I'm not sure.

If all eye models are based on spherical lenses, then perhaps you should stick with the spherical lens and realize that image formation will not be perfect. But If I model something, I like to start with a simple, perfect example, and then introduce the problems one at a time and note their effect on the result.

 

[yas-say]

Yes, its probably spherical aberration. The thinner the lens is, the less problem there should be. You could model a perfect lens, one that has no aberrations whatsoever. I forget what shape that is, it might be a parabola. Anyway, modelling the eye as a perfect lens will take care of the basic image formation, and then if you want to deal with lens aberrations in the eye, start introducing deviations from the perfect lens. Like if you want to model astigmatism or something.

A perfect lens would be one that was infinitely thin, and every ray parallel to the axis of the lens would pass through the focal point. Any ray (parallel or not) passing through the center of the lens will be undeflected. The equation for a perfect lens is - if a ray hits the lens at angle "a" to the normal, a distance z from the center of the lens, and the lens has focal length "f", then the ray will exit at angle a' where

Tan(a')=z/f - Tan(a)

I studied a little about lenses and I didn't come across this equation so could you tell me
where did it come from is it derived from snell's law, could you tell me about it
does it work for thick lenses.

and by the way I tried to refract rays on a spherical surface so it's basicly moving from one medium to another and the problem still exists.

I'm sorry for bothering you and I'll pay you later :shy: