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Calculate conic constant of a hyperbolic mirror

ATM Optics Reflector Mirror Making
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#1 Kanishka827

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Posted 25 September 2021 - 01:29 AM

I have fabricated a 10-inch f/2 hyperbolic concave mirror and I want to calculate the conic constant (K). I would be grateful if anyone could recommend me a method to calculate the conic constant of the mirror with some literature.

 

Thank you.



#2 MKV

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Posted 25 September 2021 - 01:49 AM

1) How do you know it's hyperbolic?

2) How hyperbolic it's supposed to be?


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#3 Kanishka827

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Posted 25 September 2021 - 02:27 AM

1) How do you know it's hyperbolic?

2) How hyperbolic it's supposed to be?

By observing  Ronchi patterns



#4 MKV

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Posted 25 September 2021 - 02:37 AM

Okay. Do you have any ronchigrams? State if the images are inside or outside of ROC and what's the screen frecuncy (i.e. how many lines per inch or mm).

 

Also, what's the conic you're trying to achieve?

 

What are you going to use your f/2 mirror for?



#5 Mike I. Jones

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Posted 25 September 2021 - 03:26 AM

Ronchi patterns are good for qualitative assessment of figure shape and smoothness, and aren't so great at quantitative measurement of figure.  Direct testing using Foucault and/or wire testing gives you actual numbers.  At f/2, the Foucault knife-edge test isn't suitable. Replace the knife edge with a thin (~125-150um) diameter wire, and you have a good test method.  If the wire moves with the source, the zonal shifts are -kr²/2R, where k is the conic constant, r is the radial distance from the mirror center, and R is the vertex radius of curvature.  If the mirror is a paraboloid, k=-1, and if hyperboloidal, k<-1.  Read up on the caustic test as well, it gives slightly better and more repeatable test data.


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#6 Pinbout

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Posted 25 September 2021 - 09:28 PM

If you take the ronchi images, inside / outside radius of curvature, you can down load a program called “Diffract” to match what your seeing and you can get a rough idea of what kind of conic your working with. I would not use it it to call a mirror finished but it gives you a rough idea where you are.

 

https://youtu.be/FnEs7vyPArE


Edited by Pinbout, 25 September 2021 - 09:29 PM.

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#7 Pinbout

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Posted 25 September 2021 - 10:04 PM

Cool animation

 

https://fb.watch/8fDadLX_zF/


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#8 Kanishka827

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Posted 06 October 2021 - 11:41 PM

Ronchi patterns are good for qualitative assessment of figure shape and smoothness, and aren't so great at quantitative measurement of figure.  Direct testing using Foucault and/or wire testing gives you actual numbers.  At f/2, the Foucault knife-edge test isn't suitable. Replace the knife edge with a thin (~125-150um) diameter wire, and you have a good test method.  If the wire moves with the source, the zonal shifts are -kr²/2R, where k is the conic constant, r is the radial distance from the mirror center, and R is the vertex radius of curvature.  If the mirror is a paraboloid, k=-1, and if hyperboloidal, k<-1.  Read up on the caustic test as well, it gives slightly better and more repeatable test data.

 

 

If you take the ronchi images, inside / outside radius of curvature, you can down load a program called “Diffract” to match what your seeing and you can get a rough idea of what kind of conic your working with. I would not use it it to call a mirror finished but it gives you a rough idea where you are.

 

https://youtu.be/FnEs7vyPArE

Thank you for sharing the knowladge



#9 Kanishka827

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Posted 06 October 2021 - 11:43 PM

Ronchi patterns are good for qualitative assessment of figure shape and smoothness, and aren't so great at quantitative measurement of figure.  Direct testing using Foucault and/or wire testing gives you actual numbers.  At f/2, the Foucault knife-edge test isn't suitable. Replace the knife edge with a thin (~125-150um) diameter wire, and you have a good test method.  If the wire moves with the source, the zonal shifts are -kr²/2R, where k is the conic constant, r is the radial distance from the mirror center, and R is the vertex radius of curvature.  If the mirror is a paraboloid, k=-1, and if hyperboloidal, k<-1.  Read up on the caustic test as well, it gives slightly better and more repeatable test data.

Thank you for your kind reply. I will try this method. Could you please suggest me any literature for that? Still I couldn't find any literature on calculating conic constant. Thank you.


Edited by Kanishka827, 06 October 2021 - 11:47 PM.


#10 MKV

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Posted 07 October 2021 - 04:19 AM

If your mirror is a Cassegrain primary, it will have a central perforation. This will make it impossible to determine the exact paraxial focus and null the paraxial zone for zero reading. 

 

Rather, you should set your wire tester so that the wire shadow just bisects the very edge (margin) of the mirror and set the reading to zero.

 

Now, translate along the optical axis until the wire shadow bisects the 71% zonal radius (rz), and take a reading, dz. Calculate the conic K = -2dzR/rz2.

 

wire test_3.jpg

___________

 

Example:

 

Your mirror is 200 mm f/2, and has a large central perforation. The mirror's clear aperture radius is 100, and its radius of curvature is 800.

You zero the tester at the very edge (margin) of the mirror's clear aperture.

 

Now move the tester until your wire shadow bisects the the zone at the radius of 71 mm, and read the distance traveled, d= 3.2 mm.

 

It will look something like this

 

d 0.4.JPG

(Use a suspended ruler in front of the mirror to see where the zones are)

 

Now you have everything needed to calculate the conic constant (K).

 

dz = 3.2

R = 800

(rz)2 = (71)2 = 5000

 

K = -2dzR/rz2 = -2*3.2*800/5000 = -1.024 (a weak hyperboloid)

____________

 

A wire tester consists of a bright point source and a taught wire/hair close to the light source.

 

For the wire tester measurements along the axis you'll need a micrometric X-Y stage

 

wire tester.jpg

_________________

 

Incidentally, you can use a single human hair as a wire. A human hair is anywhere from 17 to 180 microns. Look for thin ones. :o)

 

Mladen

 

edit: typos 


Edited by MKV, 07 October 2021 - 05:36 PM.

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#11 davidc135

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Posted 07 October 2021 - 04:54 AM

Thank you for your kind reply. I will try this method. Could you please suggest me any literature for that? Still I couldn't find any literature on calculating conic constant. Thank you.

You use the word calculate rather than measure the conic constant suggesting that you want to know what it should be. I might be reading too much into that but there is an online Cassegrain calculator which will give conics and other details once you feed in the basic parameters- including the type of Cassegrain eg Ritchey Chretien.

Enter in Tomas Maruska Cassegrain calculator and it should come up.

 

David




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