I've been designing a plastic lens and using POV's mesh2 object type to
raytrace and visualise the results.

The iterations are taking too long.

What I want to do is define a bounding area I want the light to shine into,
and a spot light or lite material, and have POV design the lens between and
output the results as a mesh.

Possible/Impossible ?
Comments?

--

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"Simon Dyer" <sim### [at] paradisenetnz> wrote:

>I've been designing a plastic lens and using POV's mesh2 object type to
>raytrace and visualise the results.
>
>The iterations are taking too long.
>
>What I want to do is define a bounding area I want the light to shine into,
>and a spot light or lite material, and have POV design the lens between and
>output the results as a mesh.

Have you already tried the intersection of two CSG-speres? That's just 
what real spheric optical lenses are.
And I guess, POV-Ray can handle it quite efficient.
And you wouldn't get aberration caused by the facets of your mesh-lenses.



Best regards,

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"=?ISO-8859-1?Q?G=FCnther?= Dietrich" <gue### [at] despammedcom>
wrote:
> "Simon Dyer" <sim### [at] paradisenetnz> wrote:
>
> >I've been designing a plastic lens and using POV's mesh2 object type to
> >raytrace and visualise the results.
> >
> >The iterations are taking too long.
> >
> >What I want to do is define a bounding area I want the light to shine into,
> >and a spot light or lite material, and have POV design the lens between and
> >output the results as a mesh.
>
> Have you already tried the intersection of two CSG-speres? That's just
> what real spheric optical lenses are.
> And I guess, POV-Ray can handle it quite efficient.
> And you wouldn't get aberration caused by the facets of your mesh-lenses.
>



http://news.povray.org/povray.binaries.images/thread/%3Cjkr0b19tiku4gcivd7ilrjdsiet3motjj0@4ax.com%3E/

Stephen

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G?nther Dietrich <gue### [at] despammedcom> wrote:
> Have you already tried the intersection of two CSG-speres? That's just 
> what real spheric optical lenses are.

  Are you sure? Can you give a reference?

  I have tried to find the exact mathematical function for a convex lens
geometry (ie. a lens which focuses perfectly and evenly) but I just can't
find it on the net.

  As far as I can tell, there are at least two possibilities: The surface
of the lens has to be parabolic, or it has to be spherical. It might also
be that it has to have some other shape. However, I can't find this info
anywhere!

-- 
                                                          - Warp

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Warp <war### [at] tagpovrayorg> wrote:
> G?nther Dietrich <gue### [at] despammedcom> wrote:
> > Have you already tried the intersection of two CSG-speres? That's just
> > what real spheric optical lenses are.
>
>   Are you sure? Can you give a reference?
>
>   I have tried to find the exact mathematical function for a convex lens
> geometry (ie. a lens which focuses perfectly and evenly) but I just can't
> find it on the net.
>
>   As far as I can tell, there are at least two possibilities: The surface
> of the lens has to be parabolic, or it has to be spherical. It might also
> be that it has to have some other shape. However, I can't find this info
> anywhere!
>
> --
>                                                           - Warp

Is this the sort of thing?
http://www.reference.com/browse/wiki/Lens_(optics)

Stephen

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"Stephen" <mcavoys_AT_aolDOT.com> wrote in message 
news:web.446da040d77f358ac6b359800@news.povray.org...

>> Warp <war### [at] tagpovrayorg> wrote:
>>   Are you sure? Can you give a reference?

> Is this the sort of thing?
> http://www.reference.com/browse/wiki/Lens_(optics)


Hecht is the more authoritative source, if you're looking for the more 
complete derivations:

Hecht, Eugene, Optics, 2nd Ed, Addison Wesley, 1987

(Although, IIRC, there's at least a 3rd edition out.  I'd check, but 
somebody around here seems to have borrowed my copy...)

- How

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Wasn't it Stephen who wrote:
>Warp <war### [at] tagpovrayorg> wrote:
>> G?nther Dietrich <gue### [at] despammedcom> wrote:
>> > Have you already tried the intersection of two CSG-speres? That's just
>> > what real spheric optical lenses are.
>>
>>   Are you sure? Can you give a reference?
>>
>>   I have tried to find the exact mathematical function for a convex lens
>> geometry (ie. a lens which focuses perfectly and evenly) but I just can't
>> find it on the net.
>>
>>   As far as I can tell, there are at least two possibilities: The surface
>> of the lens has to be parabolic, or it has to be spherical. It might also
>> be that it has to have some other shape. However, I can't find this info
>> anywhere!
>>
>> --
>>                                                           - Warp
>
>Is this the sort of thing?
>http://www.reference.com/browse/wiki/Lens_(optics)

The lenses in eyeglasses tend to be more complicated than that. Most
eyeglass prescriptions have a spherical and a cylindrical component, and
some (like those for my mother who has one eye that doesn't point in
quite the right direction due to a mild stroke) have a prism component.

Some info here:
http://en.wikipedia.org/wiki/Eyeglass_prescription

Eyeglass lenses never focus mathematically perfectly. In order to do
that they would have to be parabolic, but parabolic lenses are very much
more difficult to grind. The focussing error of spherical lenses
(spherical abberation) is not sufficient to be a problem for eyeglasses. 

I happen to use varifocal lenses, which have regions that warp and twist
the light in strange ways, but it doesn't cause a problem.

If you Google for "parabolic lens" you'll find that you get hits that
are generally for rather exotic applications, such as focussing X-rays
(plus a pile of hits for therapeutic lighting systems, I can't believe
they use optical quality parabolic lenses).

The spherical aberration effect is significant for telescopes: telescope
mirrors are often parabolic, but even for those the additional
complexity of creating a parabolic surface makes some constructors use
spherical mirrors together with other optical components that cancel out
the aberration.

-- 
Mike Williams
Gentleman of Leisure

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Stephen <mcavoys_AT_aolDOT.com> wrote:
> Is this the sort of thing?
> http://www.reference.com/browse/wiki/Lens_(optics)

  Why not give an url to the original article, which has the images etc.
intact and not raped like in that site?

http://en.wikipedia.org/wiki/Lens_(optics)

  The article says "the most common type of lenses are spherical lenses".
Then in the spherical aberration subsection it says that the spherical
shape is not the optimal for light focusing but it doesn't say what is.

  Why can't they simply give the mathematical function for the perfect
lens surface instead of just saying: "Lenses in which closer-to-ideal,
non-spherical surfaces are used are called aspheric lenses. These were
formerly complex to make and often extremely expensive, although
advances in technology have greatly reduced the cost of manufacture
for these lenses."

  What is the function for the perfect lens surface?

-- 
                                                          - Warp

Post a reply to this message

Wasn't it Warp who wrote:
>Stephen <mcavoys_AT_aolDOT.com> wrote:
>> Is this the sort of thing?
>> http://www.reference.com/browse/wiki/Lens_(optics)
>
>  Why not give an url to the original article, which has the images etc.
>intact and not raped like in that site?
>
>http://en.wikipedia.org/wiki/Lens_(optics)
>
>  The article says "the most common type of lenses are spherical lenses".
>Then in the spherical aberration subsection it says that the spherical
>shape is not the optimal for light focusing but it doesn't say what is.
>
>  Why can't they simply give the mathematical function for the perfect
>lens surface instead of just saying: "Lenses in which closer-to-ideal,
>non-spherical surfaces are used are called aspheric lenses. These were
>formerly complex to make and often extremely expensive, although
>advances in technology have greatly reduced the cost of manufacture
>for these lenses."
>
>  What is the function for the perfect lens surface?

I initially thought that parabolic lenses would have perfect optics,
like parabolic mirrors do, but it turns out that the light rays are not
at the correct angle when they reach the second surface.

Here's one solution that produces a lens with perfect optics, but you
wouldn't want one of these in your eyeglasses:

http://members.shaw.ca/quadibloc/science/opt0503.htm

I also came across this news article
http://www.azom.com/details.asp?newsID=2064
Which bears the title: "The Perfect Lens is Possible According to
Researchers at Purdue and MIT", but the text says "Researchers have now
shown, through rigorous mathematical analysis, that a perfect lens is
not possible, said Kevin J. Webb, a professor of electrical and computer
engineering at Purdue."

-- 
Mike Williams
Gentleman of Leisure

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Mike Williams <nos### [at] econymdemoncouk> wrote:
> "Researchers have now
> shown, through rigorous mathematical analysis, that a perfect lens is
> not possible, said Kevin J. Webb, a professor of electrical and computer
> engineering at Purdue."

  That's a rather surprising result (or not, after you study optics for
some time, I suppose).

  Seems that the best possible lenses available with current technology
are the so-called apochromats which try to minimize both spherical and
chromatic aberrations (but are not *perfect* either), and are really
expensive: http://en.wikipedia.org/wiki/Apochromat

-- 
                                                          - Warp

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