On 07/04/2013 23:33, Paul Ciszek wrote:

> In article <020420131053270165%(E-Mail Removed)>,

> Scott Schuckert <(E-Mail Removed)> wrote:

>> In article <(E-Mail Removed)>, Alfred

>> Molon <(E-Mail Removed)> wrote:

>>

>>> Just wondering, if money played no role how good could lenses be?

>>>

>>> No chromatic aberrations, no geometric distortions, huge sharpness from

>>> corner to corner even wide open, or are there some physical constraints

>>> which prevent from producing a perfect lens?

>>

>> Even shorter answer. No. Like almost anything in the physical universe,

>> you can get very close to a theoretical standard, but never achieve it.

>> In this case, you could get reasonably close, but...

>

> My understanding is that it is even worse--there is no mathematical algorithm that

> will focus the rays from each point in the object onto a corresponding point on the

> sensor. So you can't even theorize a perfect lens, other than to cheat and say

> "it gives me the picture I want, so there".
That is a rather odd way of thinking about it. The classical analytic

ray tracing methods worked well enough that the Victorians could design

telescopes and achromatic lenses without computers using geometric

raytracing matrix methods. These days there are programs like Zeemax

that can do it all for a huge bundle of rays and give you a very good

idea of what the image quality will look like for any optical design.

They even had matrix models for the geometrical aberrations back then

and rules of thumb for what was found to work experimentally.

Whilst the detail of the diffraction pattern is harder it can also be

done with modern computing once you have a basic solution.

That there is no closed form analytic solution to the problem is not an

issue in today's world of ubiquitous fast computers. The computational

power available is now so great that test jigs for some modern mirrors

are computed holograms designed to produce the required phases at a

particular laser test wavelength. See for example optics makers like

http://www.opcolab.com/page114.html
http://rayleighoptical.com/capabilities.html
Who will for a very large price make you any bespoke close approximation

to a perfect lens that you would care to specify.

A description of how aspheric surfaces may be computed for a given

optical element and material are online on Scribd.

http://www.scribd.com/doc/25043908/D...spherical-Lens
The hard part is specifying exactly what properties you want your lens

to have and what trade-offs you can live with. ISTR The first Vivitar

Series One lenses were specified with a decimal point error resulting in

insane pricing and close to diffraction limited performance.

--

Regards,

Martin Brown