General formula for lenses without spherical abberation

In summary, the publication "General formula for bi-aspheric singlet lens design free of spherical aberration" discusses a new analytic expression for designing the second surface of a lens to avoid spherical abberation. This formula simplifies the process and has been found to be more efficient than previous numerical approximations. The preprint does not include the formula, but notes that it is available in the full publication.
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Solution to a long-standing problem: How to make lenses without spherical abberation?
Publication: Rafael G. González-Acuña and Héctor A. Chaparro-Romo, "General formula for bi-aspheric singlet lens design free of spherical aberration," Appl. Opt. 57, 9341-9345 (2018)
Open access preprint: arXiv

Given one surface of a lens, how does the other surface has to look like to avoid spherical abberation? A question as old as the design of lenses. Computers found numerical approximations but an analytic expression is new. Just use this handy formula:

formula.png
 
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Wow this is quite cool. It’s funny how there are still physics problems hanging out there that have been pretty much forgotten except by those in the field.
 
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Very handy, indeed :D My hat's off to whomever typed that out, holy mother of ..
 
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If you look into the expression there are many repeated elements. Replace them by other symbols and the equation gets more handy already. The preprint doesn't have the formula and I don't have access to the full publication (not even the usual approaches work) so the image is all I have.
 
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1. What is the general formula for lenses without spherical aberration?

The general formula for lenses without spherical aberration is given by 1/f = (n-1) * (1/R1 - 1/R2), where f is the focal length of the lens, n is the refractive index of the lens material, and R1 and R2 are the radii of curvature of the two lens surfaces.

2. What is spherical aberration in lenses?

Spherical aberration is an optical phenomenon that occurs when light rays passing through a lens do not converge to a single point, causing blurred or distorted images. This is due to the spherical shape of the lens surface, which causes different parts of the lens to have different focal lengths.

3. How is spherical aberration minimized in lenses?

Spherical aberration can be minimized by using lenses with aspheric surfaces, which are designed to have a non-uniform curvature that compensates for the spherical aberration. Another method is to use multiple lenses in a lens system, with each lens correcting the spherical aberration of the previous lens.

4. What are the benefits of lenses without spherical aberration?

Lenses without spherical aberration can produce sharper and clearer images, making them ideal for use in optical instruments such as cameras, microscopes, and telescopes. They also allow for a wider field of view and better light gathering ability.

5. Are there any limitations to the general formula for lenses without spherical aberration?

Yes, the general formula for lenses without spherical aberration assumes that the lens is thin and has a small aperture. It also does not take into account other types of aberrations that may occur in a lens system. Therefore, it may not be accurate for all types of lenses and situations.

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