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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?
There are three main types of lens shapes: spherical lenses, aspheric lenses, and cylindrical lenses.
A spherical lens has a constant curvature across its entire surface, whereas an aspheric lens has a continuously changing curvature. This allows for corrections of optical aberrations and improved image quality.
Cylindrical lenses have a curved surface in one direction and a flat surface in the other, while spherical lenses have a curved surface in both directions. This allows for correction of astigmatism and can be used in applications such as eyeglasses or camera lenses.
Aspheric lenses have a more complex shape that allows for corrections of spherical aberrations and other optical distortions, resulting in improved image quality and better control of light rays.
Cylindrical lenses can be more difficult to manufacture and align compared to spherical lenses. They are also more prone to scratches and other surface imperfections due to their asymmetrical shape.