Lens shapes other than conic sections

AI Thread Summary
Lenses can be designed in various shapes beyond traditional conic sections, with specific geometries serving distinct applications. Aspheric lenses, defined by infinite geometric sums, enhance optical performance by reducing aberrations. Fresnel lenses, known for their compact design, are utilized in applications like lighting and projection. Additionally, some lenses, such as those used in missile guidance, prioritize aerodynamic shapes over optical considerations. Exploring non-conic lens shapes reveals innovative solutions in optics and engineering.
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This is just a curiosity question. Are there lens shapes different than just conic sections? Any research or any found applications?
 
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Lenses can be in any shape, but specific shapes are more useful for specific purposes than others.

For example, check out the aspheric lens, it's described by an infinite geometric sum.

Or also check out the Fresnel lens.
 
The front lens used in missile guidance applications have a shape dictated by aerodynamics, not optics. "Conformal optics" was trendy for a while.
 
I would like to use a pentaprism with some amount of magnification. The pentaprism will be used to reflect a real image at 90 degrees angle but I also want the reflected image to appear larger. The distance between the prism and the real image is about 70cm. The pentaprism has two reflecting sides (surfaces) with mirrored coating and two refracting sides. I understand that one of the four sides needs to be curved (spherical curvature) to achieve the magnification effect. But which of the...
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