What are caustics as they apply to optics?

[W. eWatson]

I've searched the web for caustics and optics, but mostly see pictures
of them. They seem to have some positive use. In some fashion they seem
to magnify. They seem to be somehow related to critical curves, whatever
they are. Both seem to be helpful in gravitational lensing or in other
areas of optics. How?

[W. eWatson]

Post by W. eWatson
I've searched the web for caustics and optics, but mostly see pictures
of them. They seem to have some positive use. In some fashion they seem
to magnify. They seem to be somehow related to critical curves, whatever
they are. Both seem to be helpful in gravitational lensing or in other
areas of optics. How?

Let me simplify this. Of what value or interest are caustics and
critical curves?

[Phil Hobbs]

Post by W. eWatson
I've searched the web for caustics and optics, but mostly see pictures
of them. They seem to have some positive use. In some fashion they seem
to magnify. They seem to be somehow related to critical curves, whatever
they are. Both seem to be helpful in gravitational lensing or in other
areas of optics. How?

Caustics are curves defined by the crossing of rays. Back in the 1970s,
there was a fad for making cheesy sculptures by stretching string on
patterns of nails, so that curves and patterns emerged. Those curves
defined by straight strings crossing are effectively caustics. (A
particularly cheesy example is here: http://tinyurl.com/bppp2r4 .)

They aren't much use in imaging applications, since you have to have
gross amounts of aberration before you get any.

I think some folks use them as a shorthand method for non-imaging
concentrator design, but otherwise they're things to avoid.

Cheers

Phil Hobbs
--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510

hobbs at electrooptical dot net
http://electrooptical.net

[W. eWatson]

Post by Phil Hobbs

Post by W. eWatson
I've searched the web for caustics and optics, but mostly see pictures
of them. They seem to have some positive use. In some fashion they seem
to magnify. They seem to be somehow related to critical curves, whatever
they are. Both seem to be helpful in gravitational lensing or in other
areas of optics. How?

Caustics are curves defined by the crossing of rays. Back in the 1970s,
there was a fad for making cheesy sculptures by stretching string on
patterns of nails, so that curves and patterns emerged. Those curves
defined by straight strings crossing are effectively caustics. (A
particularly cheesy example is here: http://tinyurl.com/bppp2r4 .)
They aren't much use in imaging applications, since you have to have
gross amounts of aberration before you get any.
I think some folks use them as a shorthand method for non-imaging
concentrator design, but otherwise they're things to avoid.
Cheers
Phil Hobbs

Thanks. In my reading of gravitational lensing they both are mentioned
fairly often. They seem to have some value there. I've only recently
become interested in GL through a book that is quite good, and is not
mathematical. I'm not a physicist.

Caustics are mentioned here.

<http://en.wikipedia.org/wiki/Gravitational_microlensing>
<http://www.xray.mpe.mpg.de/theorie/cluster/SS10/07_SS10_Cosmology2_Hans.pdf>

[Helpful person]

On Mar 25, 2:29 pm, "W. eWatson" <wolftracks-

Post by W. eWatson
Thanks. In my reading of gravitational lensing they both are mentioned
fairly often. They seem to have some value there. I've only recently
become interested in GL through a book that is quite good, and is not
mathematical. I'm not a physicist.
Caustics are mentioned here.
<http://en.wikipedia.org/wiki/Gravitational_microlensing>
<http://www.xray.mpe.mpg.de/theorie/cluster/SS10/07_SS10_Cosmology2_Ha...>

I know nothing about gravitational lensing. However, if a caustic is
formed around the heavy mass causing the lensing, this could be
important. From what I remember (and please someone else confirm or
otherwise) obstructions at a caustic will not affect the far field.
In other words, any debris at a caustic will not affect the imagery.

As an aside, many years back I was going to study gravitational
lensing to answer the Lens Design Problem at one of the SPIE lens
design conferences. I have no doubt I would have at least received an
honorable mention for originality. Wish I'd done it.

http://www.richardfisher.com

[Salmon Egg]

Post by Phil Hobbs

Post by W. eWatson
I've searched the web for caustics and optics, but mostly see pictures
of them. They seem to have some positive use. In some fashion they seem
to magnify. They seem to be somehow related to critical curves, whatever
they are. Both seem to be helpful in gravitational lensing or in other
areas of optics. How?

Caustics are curves defined by the crossing of rays. Back in the 1970s,
there was a fad for making cheesy sculptures by stretching string on
patterns of nails, so that curves and patterns emerged. Those curves
defined by straight strings crossing are effectively caustics. (A
particularly cheesy example is here: http://tinyurl.com/bppp2r4 .)
They aren't much use in imaging applications, since you have to have
gross amounts of aberration before you get any.
I think some folks use them as a shorthand method for non-imaging
concentrator design, but otherwise they're things to avoid.
Cheers
Phil Hobbs

There are optical applications that do not require very good imaging.
For example, designers of optics for solar collectors used to heat
fluids in tubes may find knowledge of caustics useful. Even without
accurate imaging, there may be tradeoffs between size of tubes and
tracking of the sun.

A caustic is nothing more than the envelope formed for a family of
curves. For light, that envelope is most likely to of a familly of rays.

[Skywise]

Post by Phil Hobbs
They aren't much use in imaging applications, since you have to have
gross amounts of aberration before you get any.

Would not even the focal point from a lens system be considered
a caustic? To qualify, isn't it a special case?

I am familiar with the concept of caustics from the other kind
of ray-tracing - CGI. In that field, any form of light pattern
rendered onto another object/surface after a refracting or
reflecting surface is termed a caustic. It may be that it's
not considered such in the 'real world' of optical design, but
I've not encountered any different usage.

As for gravitational lensing (I'm also an amateur astronomer)
those are much like the ripples of light on the bottom of a
swimming pool caused by the non-flat surface of the pool. In
this case, though, they are caused by the curvature of space-
time resulting from large gravitational fields. Unlike in the
example of a swimming pool, the lensing action takes place in
a 3D volume rather than being confined to a 2D surface.

From our perspective on Earth looking out into space, it's
kind of like freezing the pool surface so the pattern doesn't
keep changing, and then placing your eye in the bright area
at the bottom of the pool. When you look up, you'd see the
Sun distorted out into an extended shape coming from multiple
directions, much like the image of gravitationally lensed
galaxy arcs, or in special cases, an Einstein cross or ring.

http://en.wikipedia.org/wiki/Gravitational_lens
http://en.wikipedia.org/wiki/Einstein_cross
http://en.wikipedia.org/wiki/Einstein_ring

http://en.wikipedia.org/wiki/Caustic_%28optics%29

Brian

[W. eWatson]

Post by Skywise

Post by Phil Hobbs
They aren't much use in imaging applications, since you have to have
gross amounts of aberration before you get any.

Would not even the focal point from a lens system be considered
a caustic? To qualify, isn't it a special case?
I am familiar with the concept of caustics from the other kind
of ray-tracing - CGI. In that field, any form of light pattern
rendered onto another object/surface after a refracting or
reflecting surface is termed a caustic. It may be that it's
not considered such in the 'real world' of optical design, but
I've not encountered any different usage.
As for gravitational lensing (I'm also an amateur astronomer)
those are much like the ripples of light on the bottom of a
swimming pool caused by the non-flat surface of the pool. In
this case, though, they are caused by the curvature of space-
time resulting from large gravitational fields. Unlike in the
example of a swimming pool, the lensing action takes place in
a 3D volume rather than being confined to a 2D surface.
From our perspective on Earth looking out into space, it's
kind of like freezing the pool surface so the pattern doesn't
keep changing, and then placing your eye in the bright area
at the bottom of the pool. When you look up, you'd see the
Sun distorted out into an extended shape coming from multiple
directions, much like the image of gravitationally lensed
galaxy arcs, or in special cases, an Einstein cross or ring.
http://en.wikipedia.org/wiki/Gravitational_lens
http://en.wikipedia.org/wiki/Einstein_cross
http://en.wikipedia.org/wiki/Einstein_ring
http://en.wikipedia.org/wiki/Caustic_%28optics%29
Brian

I'm an amateur astronomer too. I happened onto GL in a 30 min lecture
from a Great Courses. At one point the lecturer talked a bit about GL
being useful in detecting and weighing dark maker. That came as a big
surprise.

After scouring the web, I found a book titled Einstein's Telescope. No
math, but very descriptive. Caustic came up a number of times, but was
not described. If you search for the book on Amazon, you can "Look" at a
lot of the book. Just search for caustic. Pages 133 and 134 bring up the
topic.

I did recently briefly had access to a book on optics, that showed the
math of a caustic. Best I could figure out is that forms around a ray
through the center of the lens. Other rays not focused build a surface
from those rays (beyond the focal point?). I get impression these
surfaces somehow define sub-lenses in the irregular gravitational lens.

This pdf talks quite a bit about caustics. It's chapter 7 of some larger
tome. Too bad I can find 1-6.
<http://www.xray.mpe.mpg.de/theorie/cluster/SS10/07_SS10_Cosmology2_Hans.pdf>

[Skywise]

Post by W. eWatson

Post by Skywise
http://en.wikipedia.org/wiki/Gravitational_lens
http://en.wikipedia.org/wiki/Einstein_cross
http://en.wikipedia.org/wiki/Einstein_ring
http://en.wikipedia.org/wiki/Caustic_%28optics%29
Brian

I'm an amateur astronomer too. I happened onto GL in a 30 min lecture
from a Great Courses. At one point the lecturer talked a bit about GL
being useful in detecting and weighing dark maker. That came as a big
surprise.

In the wikipedia article on GL linked above, half way down, is a
picture of the reconstructed distribution of dark matter derived
from gravitational lensing.

Brian

[W. eWatson]

Post by Skywise

Post by W. eWatson

Post by Skywise
http://en.wikipedia.org/wiki/Gravitational_lens
http://en.wikipedia.org/wiki/Einstein_cross
http://en.wikipedia.org/wiki/Einstein_ring
http://en.wikipedia.org/wiki/Caustic_%28optics%29
Brian

I'm an amateur astronomer too. I happened onto GL in a 30 min lecture
from a Great Courses. At one point the lecturer talked a bit about GL
being useful in detecting and weighing dark maker. That came as a big
surprise.

In the wikipedia article on GL linked above, half way down, is a
picture of the reconstructed distribution of dark matter derived
from gravitational lensing.
Brian

Yes, the Einstein Telescope book I mentioned has some of these. It's all
very clever.

[Phil Hobbs]

Post by Skywise

Post by Phil Hobbs
They aren't much use in imaging applications, since you have to have
gross amounts of aberration before you get any.

Would not even the focal point from a lens system be considered
a caustic? To qualify, isn't it a special case?

Sort of. In a stigmatic optical system, the rays all cross at one
point, so the caustic curve consists of just that one point. I think
the distinction is useful enough that I'd say no--a caustic has to be
larger than the diffraction limited spot, at a minimum.

Post by Skywise
I am familiar with the concept of caustics from the other kind
of ray-tracing - CGI. In that field, any form of light pattern
rendered onto another object/surface after a refracting or
reflecting surface is termed a caustic. It may be that it's
not considered such in the 'real world' of optical design, but
I've not encountered any different usage.

"Any form of light pattern" is pretty general. Would that include the
face of the guy you shave with? ;)


Cheers

Phil Hobbs
--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510 USA
[phone]

hobbs at electrooptical dot net
http://electrooptical.net

[Skywise]

Post by Phil Hobbs

Post by Skywise
Would not even the focal point from a lens system be considered
a caustic? To qualify, isn't it a special case?

Sort of. In a stigmatic optical system, the rays all cross at one
point, so the caustic curve consists of just that one point. I think
the distinction is useful enough that I'd say no--a caustic has to be
larger than the diffraction limited spot, at a minimum.

Not being an optics pro I'm not 100% sure what "stigmatic" means
in this context, but I get the gist. I agree it's not what is
generally meant by a caustic. However, in the context of CGI, it
is technically a caustic as those settings are what control the
rendering of the image, even if it's just a picture of a lens
focusing a light source to a spot.

Post by Phil Hobbs

Post by Skywise
I am familiar with the concept of caustics from the other kind
of ray-tracing - CGI. In that field, any form of light pattern
rendered onto another object/surface after a refracting or
reflecting surface is termed a caustic. It may be that it's
not considered such in the 'real world' of optical design, but
I've not encountered any different usage.

"Any form of light pattern" is pretty general. Would that include the
face of the guy you shave with? ;)

Yeah, I'm being too generalized. For example, a glass object
sitting on a table, and light is refracted through it. The light
pattern on the table is the caustic.

Your whimsical example I don't think would be considered a
caustic even in CGI. Diffuse reflections would be called
radiosity, and that can be modeled as well. The mirror would
certainly reflect those radiosity rays, however.

Rendering these effects realistically is CPU intensive, both
caustics and radiosity. But, they go a LOOOOONG way towards
making a scene look realistic. The subconscious eye-brain expects
to see these things and when they are absent, the image will
look 'wrong' even if you can't say why. (I like trying to find
CGI errors in movies and other imagery)

I don't do a lot of rendering, but when I work on something, my
goal is photorealism. The most recent example of my work which I
did about a year ago is here:

http://www.luxrender.net/forum/gallery2.php?g2_itemId=22240

Dang, I need to get back to doing this. Too many hobbies, not
enough CPU time.

Brian

[Daniel Pitts]

Post by Skywise

Post by Phil Hobbs

Post by Skywise
Would not even the focal point from a lens system be considered
a caustic? To qualify, isn't it a special case?

Sort of. In a stigmatic optical system, the rays all cross at one
point, so the caustic curve consists of just that one point. I think
the distinction is useful enough that I'd say no--a caustic has to be
larger than the diffraction limited spot, at a minimum.

Not being an optics pro I'm not 100% sure what "stigmatic" means
in this context, but I get the gist. I agree it's not what is
generally meant by a caustic. However, in the context of CGI, it
is technically a caustic as those settings are what control the
rendering of the image, even if it's just a picture of a lens
focusing a light source to a spot.

Post by Phil Hobbs

Post by Skywise
I am familiar with the concept of caustics from the other kind
of ray-tracing - CGI. In that field, any form of light pattern
rendered onto another object/surface after a refracting or
reflecting surface is termed a caustic. It may be that it's
not considered such in the 'real world' of optical design, but
I've not encountered any different usage.

"Any form of light pattern" is pretty general. Would that include the
face of the guy you shave with? ;)

Yeah, I'm being too generalized. For example, a glass object
sitting on a table, and light is refracted through it. The light
pattern on the table is the caustic.
Your whimsical example I don't think would be considered a
caustic even in CGI. Diffuse reflections would be called
radiosity, and that can be modeled as well. The mirror would
certainly reflect those radiosity rays, however.
Rendering these effects realistically is CPU intensive, both
caustics and radiosity. But, they go a LOOOOONG way towards
making a scene look realistic. The subconscious eye-brain expects
to see these things and when they are absent, the image will
look 'wrong' even if you can't say why. (I like trying to find
CGI errors in movies and other imagery)
I don't do a lot of rendering, but when I work on something, my
goal is photorealism. The most recent example of my work which I
http://www.luxrender.net/forum/gallery2.php?g2_itemId=22240

Nice picture.

I happened into this newsgroup because of a cross-post to another
newsgroup which is also a hobby of mine (electronics). I actually came
here to see if people were talking about raytracing and the like. I've
actually built my own (naive) raytracers, and adding "caustics" was one
of my todo's, along with kd-trees and other optimizations.

Post by Skywise
Dang, I need to get back to doing this. Too many hobbies, not
enough CPU time.

It's even harder when you've got CBU constraints (Central Brain Unit). I
just don't have enough time in the day to work on all my hobbies, pay
the bills, and spend time with my family.

Also, I'm just not talented enough in aesthetics to create pretty
pictures with my ray tracer.

[Skywise]

Post by Skywise
http://www.luxrender.net/forum/gallery2.php?g2_itemId=22240

Nice picture.

Thanks!

...also a hobby of mine (electronics).

Same here. But I don't peruse any related groups.

Post by Skywise
Dang, I need to get back to doing this. Too many hobbies, not
enough CPU time.

It's even harder when you've got CBU constraints (Central Brain Unit). I
just don't have enough time in the day to work on all my hobbies, pay
the bills, and spend time with my family.

Agreed....

Also, I'm just not talented enough in aesthetics to create pretty
pictures with my ray tracer.

That's a big struggle I have. I find it hard to do more than
just render primitives, beautiful though they may be when I
add in dispersion and IOR. I came up with that scene simply
because I had been reading about absinthe at the time and
decided to use it as a subject.

Brian

[Phil Hobbs]

Post by Skywise

Post by Phil Hobbs

Post by Skywise
Would not even the focal point from a lens system be considered
a caustic? To qualify, isn't it a special case?

Sort of. In a stigmatic optical system, the rays all cross at one
point, so the caustic curve consists of just that one point. I think
the distinction is useful enough that I'd say no--a caustic has to be
larger than the diffraction limited spot, at a minimum.

Not being an optics pro I'm not 100% sure what "stigmatic" means
in this context, but I get the gist. I agree it's not what is
generally meant by a caustic. However, in the context of CGI, it
is technically a caustic as those settings are what control the
rendering of the image, even if it's just a picture of a lens
focusing a light source to a spot.

Jargon differs between optics and CGI, then. No huge surprise.

Post by Skywise

Post by Phil Hobbs

Post by Skywise
I am familiar with the concept of caustics from the other kind
of ray-tracing - CGI. In that field, any form of light pattern
rendered onto another object/surface after a refracting or
reflecting surface is termed a caustic. It may be that it's
not considered such in the 'real world' of optical design, but
I've not encountered any different usage.

"Any form of light pattern" is pretty general. Would that include the
face of the guy you shave with? ;)

Yeah, I'm being too generalized. For example, a glass object
sitting on a table, and light is refracted through it. The light
pattern on the table is the caustic.

That's _really_ not what it means in optics. Such a pattern might have
caustics, or it might not.

Post by Skywise
Your whimsical example I don't think would be considered a
caustic even in CGI. Diffuse reflections would be called
radiosity, and that can be modeled as well. The mirror would
certainly reflect those radiosity rays, however.

The guy I shave with is usually grumpy rather than whimsical, because
it's usually too early in the morning. ;)

Cheers

Phil Hobbs
--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510 USA
[phone]

hobbs at electrooptical dot net
http://electrooptical.net

[Skywise]

Post by Phil Hobbs
Jargon differs between optics and CGI, then. No huge surprise.

I've discovered that the wikipedia article titled "Caustic (optics)"
is more in line with my description and "Caustic (mathematics)" is
more in line with yours.

http://en.wikipedia.org/wiki/Caustic_%28optics%29
http://en.wikipedia.org/wiki/Caustic_%28mathematics%29

The mathematical article does state that it's used in "geometric
optics", which is what you do, so I think that's why we differed in
our descriptions.

You deal with the rays themselves (and the associated math) whereas
I deal with the patterns generated when those rays hit a surface
(pretty pictures), even though both are generated the same way and
governed by the same equations. For me the math is hidden in the
software.

So maybe it's not really that the jargon differs, but that we are
looking at the same thing from different perspectives (pardon all
the puns). Our goals are different.

Now if only the render engine I use could handle diffraction. It
does most everything else - IOR, dispersion, scattering, even
thin film effects; and works with full spectra and not just RGB.
It's truly physics based rather than just mimicking the effect
with shortcuts. (At the cost of rendering time, but well worth
the results IMO.)

Brian

[boxman]

Post by W. eWatson
I've searched the web for caustics and optics, but mostly see pictures
of them. They seem to have some positive use. In some fashion they seem
to magnify. They seem to be somehow related to critical curves, whatever
they are. Both seem to be helpful in gravitational lensing or in other
areas of optics. How?

In non-imaging optics (those that deal with concentration and
illumination rather then image forming) the caustic is defined as the
envelope of a one-parameter family of light rays. By definition that
envelope is a curve that is tangent to every curve in the one parameter
family.

A simple example would be a set of parallel rays reflecting off a
parabolic reflector at some angle to the parabolic axis. In this case
the family of rays are straight lines. The caustic curve in this case
would be the optimal receiver shape to provide maximum collection.

[W. eWatson]

Post by W. eWatson
I've searched the web for caustics and optics, but mostly see pictures
of them. They seem to have some positive use. In some fashion they seem
to magnify. They seem to be somehow related to critical curves, whatever
they are. Both seem to be helpful in gravitational lensing or in other
areas of optics. How?

Well, this pretty well nails it for me, since my original interest is
how it is used in gravitational lensing.

"Caustic and critical lines have important properties regarding the
number and parity of the images. For instance, if we consider a source
far away from the line of sight to the lensing distribution, there will
be just one image of the source if the lens are non-singular. However,
if were to displace the background source towards the center of the
lensing distribution, additional images will appear in pairs whenever
the source crosses a caustic.

This goes on for a 1/2 page. It's from the book Grav Lensing and
Microlensing by Silvia Mollerach"

Look at it on Amazon. You can Look at pages or search for words. This
material is on page 43f.

[J-C]

I've searched the web for caustics and optics, but mostly see pictures of
them. They seem to have some positive use. In some fashion they seem to
magnify. They seem to be somehow related to critical curves, whatever they
are. Both seem to be helpful in gravitational lensing or in other areas of
optics. How?

I don't know about gravitational lensing, the experiment is too hard to
perform in the lab and I do not have the brains for the theory, barely.

Caustics are the envelopes of the reflected or refracted rays.

Examples of caustics are the nice curves (nephroids) that you see in your
coffee cup (add a little milk or cream to make it more visible) and
rainbows.

Many examples with Google Images.

The shape and classification of caustics is a fairly important part of
"catastrophe theory" (a ridiculous name for a very serious and useful
mathematical discipline).

Just look at the pictures in these references:

http://www.theeshadow.com/h/caustic/

http://wigner.elte.hu/science/images/iwepnm10_caustics.pdf

http://ntur.lib.ntu.edu.tw/bitstream/246246/163522/1/20.pdf

http://www.phy.bristol.ac.uk/people/berry_mv/the_papers/BERRY089.pdf

Caustics are also important in lighting applications and realistic rendering
in computer graphics.

[TempGuy]

Post by W. eWatson
I've searched the web for caustics and optics, but mostly see pictures
of them. They seem to have some positive use. In some fashion they seem
to magnify. They seem to be somehow related to critical curves, whatever
they are. Both seem to be helpful in gravitational lensing or in other
areas of optics. How?

have you heard about the 'citizen scientist' mass project SPACEWARPS?