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Re: Perfect lens

 
 
Paul Ciszek
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      04-07-2013

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".

--
"Remember when teachers, public employees, Planned Parenthood, NPR and PBS
crashed the stock market, wiped out half of our 401Ks, took trillions in
TARP money, spilled oil in the Gulf of Mexico, gave themselves billions in
bonuses, and paid no taxes? Yeah, me neither."

 
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Wolfgang Weisselberg
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      04-15-2013
Paul Ciszek <(E-Mail Removed)> wrote:
> Scott Schuckert <(E-Mail Removed)> wrote:


>>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".


Well, there's no known way to solve the three-body problem with
a mathematical algorithm. Yet such things exist, e.g. Sun +
Earth + Moon. The "we don't have a mathematical algorithm,
therfore ..." does not hold much water. You'd need to prove
mathematically that an X is impossible. (And that is valid
only as long as the assumptions stay true.)

-Wolfgang
 
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Martin Brown
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      04-18-2013
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
 
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J. Clarke
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      05-08-2013
In article <(E-Mail Removed)>, ozcvgtt02
@sneakemail.com says...
>
> Paul Ciszek <(E-Mail Removed)> wrote:
> > Scott Schuckert <(E-Mail Removed)> wrote:

>
> >>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".

>
> Well, there's no known way to solve the three-body problem with
> a mathematical algorithm.


Actually there is. If there was no algorithm for solving a 3 body
problem then NASA could not have successfully flown any of its lunar or
planetary missions.

The correct statement is that there is no closed-form solution to the
general case of the 3-body problem. There are closed form solutions to
particular cases and numerical solutions for just about any case.

> Yet such things exist, e.g. Sun +
> Earth + Moon. The "we don't have a mathematical algorithm,
> therfore ..." does not hold much water. You'd need to prove
> mathematically that an X is impossible. (And that is valid
> only as long as the assumptions stay true.)
>
> -Wolfgang



 
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