Hyperbolic Lenses: Abberation-Free?

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Discussion Overview

The discussion revolves around the properties of hyperbolic lenses, specifically whether they are free of aberrations. Participants explore the types of aberrations present in various lens shapes and the theoretical possibilities of achieving aberration-free lenses.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions if hyperbolic lenses are free of aberration.
  • Another participant notes that while hyperbolic lenses have virtually no spherical aberrations, they still exhibit chromatic aberrations.
  • A theoretical inquiry is made about the existence of a lens shape that could focus rays onto a single point without any aberrations.
  • Discussion includes the identification of five third-order geometric aberrations: Spherical, Coma, Astigmatism, Distortion, and Curvature of Field, with a mention that parabolic lenses eliminate spherical aberration but not the others.
  • A participant explains that while diffraction-limited lenses can minimize imperfections, they are optimized for specific object distances and focal lengths, implying that no lens can be aberration-free for arbitrary conditions.
  • The concept of achromatic lenses is introduced, which are designed to be virtually free of chromatic aberration within a specific wavelength range.

Areas of Agreement / Disagreement

Participants express differing views on the capabilities of hyperbolic lenses regarding aberrations, with some agreeing on the presence of chromatic aberrations while others explore theoretical aspects of aberration-free lens shapes. The discussion remains unresolved regarding the existence of a completely aberration-free lens.

Contextual Notes

Limitations include the dependence on specific object distances and wavelength ranges for lens optimization, as well as the unresolved nature of theoretical lens shapes that could be free of aberrations.

bomba923
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Are hyperbolic lenses free of abberation?
 
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They still have chromatic abberations, but the spherical abberations are virtually non existant.
 
Theoretically speaking, what shape of a convergent lens (that focuses rays onto a single point) is free of abberation?

Does such shape/surface exist?
 
There are five 3rd order geometric aberrations; Spherical, Coma, Astigmatism, Distortion and Curvature of Field. A parabolic lens will eliminate spherical aberration, but not the others.

You can get lenses whose aberrations are less than the diffraction limited spot, in other words the lenses are so good that imperfections are washed out by diffraction. Such lenses are only optimised to a particular object distance and focal length, so you can't get lenses that are aberration free for an arbitrary object distance.

Chromatic aberrations are still present in the lens, you can get lenses called achromats (or achromatic lenses) that are virtually chromatic aberration free within a particular wavelength range.

To summarise, you can get diffraction-limited lenses, but only for a particular object distance and a particular wavelength range.

Claude.
 

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