Gaussian Mirror...

Next
 From:  futagoza (STEFAN)
8768.1 
Hi all,

i'm following a tutorial and i like to model a (small circular concave) gaussian mirror.

Quote from Tutorial:

What do you mean by a Gaussian Mirror?
A mirror that has a curvature angle lower than 10 degrees,
and has the incident rays the closest to it's central axis.

End Quote.

Since i don't deal with curvature stuff etc., when doodling
with MoI, how do you do that? Do i only have to draw
an arc ,lower than 10 degrees and then revolve it at one
end?

Regards
Stefan

EDITED: 6 Jan by STEFAN

  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  Frenchy Pilou (PILOU)
8768.2 
Like this ?



  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  futagoza (STEFAN)
8768.3 
No Pilou,

much simpler. Simply do something like revolving an arc segment so that you have a more flat looking bowl shape.

Regards
Stefan
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  bemfarmer
8768.4 In reply to 8768.1 
Hi STEFAN,

A bit of web searching brings up (at least) TWO different interpretations of the term Gaussian Mirror.

I. From https://en.wikipedia.org/wiki/Curved_mirror#Mirror_equation_and_magnification
The Gaussian mirror equation, also known as the mirror and lens equation, relates the object distance, d0, and image distance, di, to the focal length f.


II. Something to do with Laser mirrors, and/or Apodization (whatever that means), "The degree of reflection slopes from the center of the optic in a Gaussian distribution. Used in unstable resonators"
This ring resonator contains a hyperbolic-cosine-Gaussian apodized aperture. ... “Graded-phase mirror resonators with a super-Gaussian output in a cw CO2 laser ...

- Brian
(No I do not understand...:-)

Car headlights?

This link seems to have relevant terms:
https://en.wikipedia.org/wiki/Gaussian_optics

EDITED: 6 Jan by BEMFARMER

  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  bemfarmer
8768.5 In reply to 8768.1 
After finding the right cross section equation, (whatever it is,) revolving it seems appropriate.
No, I disagree with myself. Variable Reflectivity may be expressed as an equation???

- Brian

https://physics.stackexchange.com/questions/309378/what-is-a-gaussian-mirror
"A Gaussian mirror is a mirror whose surface profile is in the shape of a gaussian function..."
"To first order, a gaussian is a parabola (exp(±r²) ≈ 1 ± r²) and ..."

EDITED: 6 Jan by BEMFARMER

  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  futagoza (STEFAN)
8768.6 
Hi Brian,

thanks for your reply! I like to do a laser experiment with Thea Render. For the laser i
would like to use a spot light aiming at the center of the mirror. The goal should be
that the reflecting light beam from the mirror is then parallel and only the parallel
beam will be seen in the image.

I guess i will have also to adjust the light parameters, from the spotlight several
times to get the desired look.

But first i must know how to draw that simple surface mirror with it's correct
curvature angle in order to do the test. :-)

P.S. according to this Thea tutorial this for getting thicker parallel light beams.
And the author shows a picture as proof that this works. He describes also other
techniques, but i like to try out this one. I could ask also on the Thea forum,
but i don't know if there are many MoI users or if the author modeled this
in another NURBS or poly package...

Regards
Stefan
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  futagoza (STEFAN)
8768.7 In reply to 8768.6 
Thanks for the edit Brian,

but how would i do that in simple terms with MoI? :-)

Best regards
Stefan
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  bemfarmer
8768.8 In reply to 8768.7 
Well I am totally confused.
Can you post a link to the Thea author article?

Gassian mirrors are also called Variable Reflectivity Mirrors
The link here shows an equation and a "bellish" curve, for describing the reflectivity, which seems to be done by optical coatings, with minimal or zero
physical curvature of the mirror.
http://www.standaphotonics.com/variable-reflectivity-mirrors/
http://www.altechna.com/product_details.php?id=927
https://www.lasercomponents.com/us/product/gaussian-mirrors/

- Brian

EDITED: 6 Jan by BEMFARMER

  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  futagoza (STEFAN)
8768.9 
Well, i would like to post this tutorial, but i'm not sure if this
is allowed, because non-registered users can't see this tutorial
and then i have to contact the author for permission, i guess. :-(

But let's forget for a moment all this laser optics stuff, how do
i have to measure or construct properly "a flat fruit bowl surface" with
a curvature angle less than 10 degrees, let's say for example 9.5 :-)

If i can do this properly i "only" must play with the light settings,
i assume, in order to get the desired result.

Regards
Stefan
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  futagoza (STEFAN)
8768.10 
O,k the shape should look something like this:

I used an arc with 9.5 as settings and then revolved it.

Is this now the right approach to get the curvature settings
lower than 10 degrees?



Regards
Stefan

  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  bemfarmer
8768.11 In reply to 8768.10 
From the geometry of the spherical mirror, note that the focal length is half the radius of curvature:
The angle of curvature is show in the link, as ...???

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/mireq.html

- Brian
I'll have to study the math and drawing for a while... :-)

EDITED: 6 Jan by BEMFARMER

  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  futagoza (STEFAN)
8768.12 
Thanks for looking into it, much appreciated! :-)

Regards
Stefan
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  bemfarmer
8768.13 In reply to 8768.12 
I have not been able to find the definition of the "curvature angle of the mirror"
Assuming the curvature angle = angle of incidence of the parallel ray, then the 9.5 degree arc of a circle,
resulting from the rotation of a radius curve by 9.5 degrees,
would be the curve to be revolved to form the mirror.

- Brian
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  futagoza (STEFAN)
8768.14 
Thanks very much for your explanation.

I tried it now and i must fiddle a bit with the light settings distance etc..

Would had been cool if the tutorial had some some sample files to study...

Regards
Stefan
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  futagoza (STEFAN)
8768.15 
Hi Brian,

after googling a bit i think i found an easier solution, instead of using a gaussian mirror.

I will check this out tomorrow and if all goes well, i post my findings.

Best regards
Stefan
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
Next
 From:  futagoza (STEFAN)
8768.16 
Hi Brian,

i went by this explanation, for a normal concave mirror, which is also easy to understand.

http://physics.tutorpace.com/mirror-formula-online-tutoring







Best regards
Stefan

  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged

Previous
 From:  bemfarmer
8768.17 In reply to 8768.16 
Thanks Stefan.
That is a good tutorial.
- Brian
  Reply Reply More Options
Post Options
Reply as PM Reply as PM
Print Print
Mark as unread Mark as unread
Relationship Relationship
IP Logged
 

Reply to All Reply to All