Re: Perfect lens

Discussion in 'Digital Photography' started by Paul Ciszek, Apr 7, 2013.

  1. Paul Ciszek

    Paul Ciszek Guest

    In article <020420131053270165%>,
    Scott Schuckert <> wrote:
    >In article <>, Alfred
    >Molon <> 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."
     
    Paul Ciszek, Apr 7, 2013
    #1
    1. Advertising

  2. Paul Ciszek <> wrote:
    > Scott Schuckert <> 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
     
    Wolfgang Weisselberg, Apr 15, 2013
    #2
    1. Advertising

  3. Paul Ciszek

    Martin Brown Guest

    On 07/04/2013 23:33, Paul Ciszek wrote:
    > In article <020420131053270165%>,
    > Scott Schuckert <> wrote:
    >> In article <>, Alfred
    >> Molon <> 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/Design-of-Spherical-Aberration-Free-Aspherical-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
     
    Martin Brown, Apr 18, 2013
    #3
  4. Paul Ciszek

    J. Clarke Guest

    In article <>, ozcvgtt02
    @sneakemail.com says...
    >
    > Paul Ciszek <> wrote:
    > > Scott Schuckert <> 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
     
    J. Clarke, May 8, 2013
    #4
    1. Advertising

Want to reply to this thread or ask your own question?

It takes just 2 minutes to sign up (and it's free!). Just click the sign up button to choose a username and then you can ask your own questions on the forum.
Similar Threads
  1. A Cowan

    FireFox would be perfect if....

    A Cowan, Mar 8, 2005, in forum: Firefox
    Replies:
    6
    Views:
    415
    A Cowan
    Mar 9, 2005
  2. James Silverton

    Re: Perfect lens

    James Silverton, Apr 2, 2013, in forum: Digital Photography
    Replies:
    6
    Views:
    183
    Helpful person
    Apr 16, 2013
  3. RichA

    Re: Perfect lens

    RichA, Apr 2, 2013, in forum: Digital Photography
    Replies:
    0
    Views:
    156
    RichA
    Apr 2, 2013
  4. Martin Brown

    Re: Perfect lens

    Martin Brown, Apr 2, 2013, in forum: Digital Photography
    Replies:
    13
    Views:
    312
    Wolfgang Weisselberg
    Apr 17, 2013
  5. Mark Sieving

    Re: Perfect lens

    Mark Sieving, Apr 10, 2013, in forum: Digital Photography
    Replies:
    3
    Views:
    173
    Doug McDonald
    Apr 18, 2013
Loading...

Share This Page