<p>If you're asking in regards to testing methods, as indicated in the comments, the simplest setup for interferometrically testing convex conic mirrors is with a Hindle Test, shown below in a figure from the University of Arizona College of Optical Sciences.  This setup can achieve a perfect null after adjusting the reference sphere to be focused at the focus of the test optic - the catch is that the sphere needs to be larger than your test optic, with a hole through it as shown.  </p>

<p><a href="https://i.sstatic.net/U5jbv.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/U5jbv.png" alt="Hindle Test"></a></p>

<p>In industry, it is much more common to use an aperture-stitching interferometer for small quantities of non-research-level optics.  Larger, more precise, and higher quantity aspheres may use a set of nulling optics, or a diffractive/holographic element to create a null wavefront, as covered in better detail in the link below, which is a slideset from U of Arizona's optical fabrication and testing course.</p>

<p><a href="http://fp.optics.arizona.edu/jcwyant/Short_Courses/SIRA/7-TestingAsphericSurfaces.pdf" rel="nofollow noreferrer">http://fp.optics.arizona.edu/jcwyant/Short_Courses/SIRA/7-TestingAsphericSurfaces.pdf</a></p>

<p>If you're feeling especially ambitious, there is a concept for measuring surface form of a mirror by displaying points on a monitor and using an HD camera to see where the reflections come from, thus telling you the angle of the optical surface at that location.  The data is then integrated to form a full surface map.  In theory, this system could be developed at low cost, with relatively high performance.</p>

<p><a href="https://www.osapublishing.org/ao/abstract.cfm?uri=ao-13-11-2693" rel="nofollow noreferrer">https://www.osapublishing.org/ao/abstract.cfm?uri=ao-13-11-2693</a></p>

<p>Hope this (or at least some of it) helps!</p>

<p>-J</p>

CC BY-SA 3.0
2016-03-02T17:57:38.793Z
How much would it degrade things to use an offset spherical mirror and rotate the test item? (I'm curious in general but, as it happens, my application wouldn't include the center of the fabricated mirror anyway.) For that matter, how well does that system work for measuring the central portion of the mirror?
BCS
CC BY-SA 3.0
2016-03-03T18:12:18.113Z
Regarding rotating the mirror, if you approach it with the mindset of a stitching interferometer, it should be able to give a fairly reliable result if you keep part of the previous aperture in your succeeding aperture to verify your alignment.
nflemming2004
CC BY-SA 3.0
2016-03-03T18:33:37.770Z
Regarding the center of the optic, it's true that the Hindle test doesn't allow you to measure the very center of the aperture (and the portion you can measure depends on the radius of curvature of your sphere).

The only way I can think to measure the center of the aperture would be to use on of the other approaches discussed in the slideset attached to my original answer; back-side measurement or image-stitching.  I don't think the nulling optics would work very well unless they're significantly larger than your test piece.
nflemming2004
CC BY-SA 3.0
2017-03-08T14:02:29.233Z
Texereau "how to make a telescope" **parabolizing**: https://www.google.com/search?q=texerou+how+to+make+a+telescope&ie=utf-8&oe=utf-8#q=texereau+%22how+to+make+a+telescope%22+parabolizing&*
Wayfaring Stranger
CC BY-SA 3.0
2016-03-02T05:15:27.307Z
2016-03-02T05:15:27.307Z
nflemming2004
<p>Apparently there is a way of testing a convex mirror by making it from optical grade glass and testing it through the back. The refractive part of the light path creates a situation that if you test it as a sphere or paraboloid in that way (I forget which) the actual curve you get is a hyperboloid.  </p>

CC BY-SA 3.0
2017-03-08T13:23:37.570Z
2017-03-08T13:23:37.570Z
Rufus Doofer
<p>I know it's practical to hand grind a convex spherical mirror and that it's practical to make a <em>concave</em> parabolic mirror from a spherical one. But as I understand it, the procedure for doing so depend on tracking progress by using interference patters generated by focusing light off the mirror, and that procedure clearly can't be used (unmodified) with a convex mirror.</p>

<p>Short of floating the blank in a bath of index of refraction matched optical fluid and apply the concave procedure to the back side, does anyone know of a way to do that sort of grinding?</p>

<p>Also, I've never actually run across a procedure for finishing a hyperbolic mirror for either convex or concave, though I haven't spent much time searching on that one. </p>

CC BY-SA 3.0
2016-03-01T16:29:10.140Z
To clarify - are you asking about testing the surface to check it's of the required shape, or about the actual grinding and polishing of the shape? (I'm sure the grinding is possible but don't know about the testing.)
Andy
CC BY-SA 3.0
2016-03-01T16:35:46.547Z
Also: you might be able to find something relevant here: (lots of mirror grinders, including a few Cass/Mak/Dall-Kirkham etc.) http://www.cloudynights.com/forum/70-atm-optics-and-diy-forum/
Andy
CC BY-SA 3.0
2016-03-01T17:32:13.997Z
I guess primarily the testing. I'm assuming that if there is a way to measure deficiencies, that they can be corrected.
BCS
CC BY-SA 3.0
2016-03-01T17:41:09.527Z
I suspect there might be a trick to measure the convex surface against a reference (i.e. accurately known) concave sphere, possibly counting fringes... but not sure. That might turn up some ideas though.
Andy
CC BY-SA 3.0
2016-03-02T15:57:22.060Z
Lens making procedures might include description of the device you seek.
Wayfaring Stranger
<optics>
Is it practical to hand grind a convex parabolic or hyperbolic mirror?
BCS
# Is it practical to hand grind a convex parabolic or hyperbolic mirror?

(Asked by: username_0 on 2016-03-01)

I know it's practical to hand grind a convex spherical mirror and that it's practical to make a *concave* parabolic mirror from a spherical one. But as I understand it, the procedure for doing so depend on tracking progress by using interference patters generated by focusing light off the mirror, and that procedure clearly can't be used (unmodified) with a convex mirror.

Short of floating the blank in a bath of index of refraction matched optical fluid and apply the concave procedure to the back side, does anyone know of a way to do that sort of grinding?

Also, I've never actually run across a procedure for finishing a hyperbolic mirror for either convex or concave, though I haven't spent much time searching on that one.

**Tags:** optics
> **Comments:**
> **username_1**: To clarify - are you asking about testing the surface to check it's of the required shape, or about the actual grinding and polishing of the shape? (I'm sure the grinding is possible but don't know about the testing.)  
> **username_1**: Also: you might be able to find something relevant here: (lots of mirror grinders, including a few Cass/Mak/Dall-Kirkham etc.) http://www.cloudynights.com/forum/70-atm-optics-and-diy-forum/  
> **username_0**: I guess primarily the testing. I'm assuming that if there is a way to measure deficiencies, that they can be corrected.  
> **username_1**: I suspect there might be a trick to measure the convex surface against a reference (i.e. accurately known) concave sphere, possibly counting fringes... but not sure. That might turn up some ideas though.  
> **username_2**: Lens making procedures might include description of the device you seek.  

---

## 2 answers

### Answer by username_3 on 2016-03-02. Score: 3

If you're asking in regards to testing methods, as indicated in the comments, the simplest setup for interferometrically testing convex conic mirrors is with a Hindle Test, shown below in a figure from the University of Arizona College of Optical Sciences. This setup can achieve a perfect null after adjusting the reference sphere to be focused at the focus of the test optic - the catch is that the sphere needs to be larger than your test optic, with a hole through it as shown.

[![Hindle Test](https://i.sstatic.net/U5jbv.png)](https://i.sstatic.net/U5jbv.png)

In industry, it is much more common to use an aperture-stitching interferometer for small quantities of non-research-level optics. Larger, more precise, and higher quantity aspheres may use a set of nulling optics, or a diffractive/holographic element to create a null wavefront, as covered in better detail in the link below, which is a slideset from U of Arizona's optical fabrication and testing course.

<http://fp.optics.arizona.edu/jcwyant/Short_Courses/SIRA/7-TestingAsphericSurfaces.pdf>

If you're feeling especially ambitious, there is a concept for measuring surface form of a mirror by displaying points on a monitor and using an HD camera to see where the reflections come from, thus telling you the angle of the optical surface at that location. The data is then integrated to form a full surface map. In theory, this system could be developed at low cost, with relatively high performance.

<https://www.osapublishing.org/ao/abstract.cfm?uri=ao-13-11-2693>

Hope this (or at least some of it) helps!

-J

> **Comments:**
> **username_0**: How much would it degrade things to use an offset spherical mirror and rotate the test item? (I'm curious in general but, as it happens, my application wouldn't include the center of the fabricated mirror anyway.) For that matter, how well does that system work for measuring the central portion of the mirror?  
> **username_3**: Regarding rotating the mirror, if you approach it with the mindset of a stitching interferometer, it should be able to give a fairly reliable result if you keep part of the previous aperture in your succeeding aperture to verify your alignment.  
> **username_3**: Regarding the center of the optic, it's true that the Hindle test doesn't allow you to measure the very center of the aperture (and the portion you can measure depends on the radius of curvature of your sphere).  The only way I can think to measure the center of the aperture would be to use on of the other approaches discussed in the slideset attached to my original answer; back-side measurement or image-stitching.  I don't think the nulling optics would work very well unless they're significantly larger than your test piece.  
> **username_2**: Texereau "how to make a telescope" **parabolizing**: https://www.google.com/search?q=texerou+how+to+make+a+telescope&ie=utf-8&oe=utf-8#q=texereau+%22how+to+make+a+telescope%22+parabolizing&*  

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### Answer by username_4 on 2017-03-08. Score: 0

Apparently there is a way of testing a convex mirror by making it from optical grade glass and testing it through the back. The refractive part of the light path creates a situation that if you test it as a sphere or paraboloid in that way (I forget which) the actual curve you get is a hyperboloid.


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