Prev: ¬ What does this symbol mean and how is it used?
Next: variance of product of uncorrelated variables
From: David Bernier on 9 Jun 2005 19:51
Suppose we take the parabola y = x^2 and rotate it around the
y axis, outside the x-y plane or "page". The result is
a paraboloid surface. If the correct side of the
surface is reflective, rays of light parallel to the
y axis, oriented in the negative-y direction, will
reflect off the surface and all pass through a common
point, the focus.

(source: Greek geometers)

What happens with parallel rays that are not
parallel to the y axis? Do they pass through
a common point after being reflected off the
surface?

Wikipedia has an entry about "Coma" here:

< http://en.wikipedia.org/wiki/Coma_%28optics%29 >

I'm inclined to believe that parallel off-axis
rays will not pass through a common point
after being reflected off the paraboloid surface...


David Bernier
From: Minus XVII on 9 Jun 2005 20:56
they don't; probably some sort of caustic surface.

it can just be considered as one end of am ellipse and
one of its foci.

David Bernier wrote:

> What happens with parallel rays that are not
> parallel to the y axis? Do they pass through
> a common point after being reflected off the
> surface?

--ils ducs d'Enron!
http://tarplet.net/bush12.htm

From: NG, Sing on 9 Jun 2005 22:03

"David Bernier" <david250(a)videotron.ca> wrote in message
news:LB4qe.63486$tf4.218439(a)wagner.videotron.net...
> Suppose we take the parabola y = x^2 and rotate it around the
> y axis, outside the x-y plane or "page". The result is
> a paraboloid surface. If the correct side of the
> surface is reflective, rays of light parallel to the
> y axis, oriented in the negative-y direction, will
> reflect off the surface and all pass through a common
> point, the focus.
>
> (source: Greek geometers)
>
> What happens with parallel rays that are not
> parallel to the y axis? Do they pass through
> a common point after being reflected off the
> surface?
>
> Wikipedia has an entry about "Coma" here:
>
> < http://en.wikipedia.org/wiki/Coma_%28optics%29 >
>
> I'm inclined to believe that parallel off-axis
> rays will not pass through a common point
> after being reflected off the paraboloid surface...
>


It depends upon the f/d ratio. If fast (4 to 6) then it goes out of focus
quickly off axis. If the mirror is slow (10 to 14) then it does not. there
is a crossover at the larger f/d ratios (over 10) where the mirror can be
spherical and not parabolic. Therefore the rays as you ask above would be in
focus, the same focus.
(f,d =>focal length, diameter)


From: Joerg Glissmann on 10 Jun 2005 05:01
David Bernier wrote:
> <description of parabolic surfaces>
> (source: Greek geometers)
>
> What happens with parallel rays that are not
> parallel to the y axis? Do they pass through
> a common point after being reflected off the
> surface?
>
> Wikipedia has an entry about "Coma" here:
> < http://en.wikipedia.org/wiki/Coma_%28optics%29 >
>
> I'm inclined to believe that parallel off-axis
> rays will not pass through a common point
> after being reflected off the paraboloid surface...
>
> David Bernier

Hi David,

one click from the wikipedia website is
http://www.opticalmechanics.com/about_coma.htm
which decribes the effect of coma for newtonian telescopes, which IMHO
is what you're looking for.

Best Regards,

Joerg

--

Joerg Glissmann - Guending - Germany
remove PANTS to reply ;-)

From: Steve Willner on 20 Jun 2005 19:18
In article <LB4qe.63486$tf4.218439(a)wagner.videotron.net>,
David Bernier <david250(a)videotron.ca> writes:
> ...a paraboloid surface. If the correct side of the
> surface is reflective, rays of light parallel to the
> y axis, oriented in the negative-y direction, will
> reflect off the surface and all pass through a common
> point, the focus.

> What happens with parallel rays that are not
> parallel to the y axis? Do they pass through
> a common point after being reflected off the
> surface?

No, but rays nearly parallel to the axis pass near a common point.
The result is that a simple paraboloid produces acceptable images
over a finite angular field of view, the size being determined by the
focal ratio of the paraboloid and by how bad an image can be
tolerated. As you indicate, coma is usually the biggest aberration,
but astigmatism and spherical aberration (and higher order
aberrations) are present too.

Just for fun, I tried ray-tracing a 100 mm diameter f/10 paraboloid.
As expected, rays parallel to the axis focus (ignoring diffraction)
to a perfect point at a distance of 500 mm from the mirror vertex.
Rays coming in 1 degree off-axis produce an image with an rms radius
of 28 microns.

You may want to try web searches for "optical ray tracing" or for
"third-order aberrations" or similar.

--
Steve Willner Phone 617-495-7123 swillner(a)cfa.harvard.edu
Cambridge, MA 02138 USA
(Please email your reply if you want to be sure I see it; include a
valid Reply-To address to receive an acknowledgement. Commercial
email may be sent to your ISP.)
 |  Next  |  Last
Pages: 1 2
Prev: ¬ What does this symbol mean and how is it used?
Next: variance of product of uncorrelated variables