Aspheric terms and Decartes' Perfect Lens , any association?

  • 21 August 2021
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Hello everyone,


While I have been searching on cartesian oval on the web, I have encountered that Descartes discovered the cross-section curve of the perfect lens, assumed to be a surface of revolution, is a fourth degree curve known today as the cartesian oval. The paper can be reached via the link below:

Here is my question; if  the perfect shape of a lens that will focus all rays from one radiant point source to one single image point, and that perfect shape is a surface of revolution with a fourth degree curve; why does ZOS aspheric terms are available more than a fourth degre?

Or otherwise, isn’t a fourth degree surface sufficient to make a perfect focus?


Best regards,



Best answer by Mark.Nicholson 21 August 2021, 19:40

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Well, if you could make a perfect point source, you would be able to image it with a Standard (conic asphere) surface with just R and k. BUT...

All real sources are extended, and indeed imaging systems are always a fairly wide field, which makes ‘perfect’ imaging of a single point irrelevant. You need the performance of the system averaged over all fields and wavelengths. That’s why we evolve ever more complex designs.

All this ‘perfect optics’ stuff is great on paper but it’s generally of little practical value. Plus, of course, diffraction limits the performance anyway so you could never resolve the ‘perfect’ image point. The image is always smeared over a Point Spread Function.

  • Mark