
Re: Fourier transforms of Zernike polynomials
Bruce, Where you using DFTFringe for that experiment? It does not sound logical too me that that should happen. So I tried it myself and at least for the test case I chose it was not the case.
Bruce, Where you using DFTFringe for that experiment? It does not sound logical too me that that should happen. So I tried it myself and at least for the test case I chose it was not the case.

By
Dale Eason
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#31016
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Re: Fourier transforms of Zernike polynomials
I had noticed that using a Gaussian blur adds a non existent hollow to the centre of the computed surface when analysing an interferogram that only has defocus. The amplitude/depth of the hole
I had noticed that using a Gaussian blur adds a non existent hollow to the centre of the computed surface when analysing an interferogram that only has defocus. The amplitude/depth of the hole

By
Bruce Griffiths
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#31015
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Edited


Fourier transforms of Zernike polynomials
This has nothing to do directly with DFTFringe, so feel free to ignore this post. Fourier transforms of Zernike polynomials have some interesting properties and important applications  the famous
This has nothing to do directly with DFTFringe, so feel free to ignore this post. Fourier transforms of Zernike polynomials have some interesting properties and important applications  the famous

By
Michael Peck
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#31014
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Edited


Re: Zernike term calculation ?
Nice! Now maybe watch the part of this video where I talk about Spherical Aberration and the DFTFringe null feature:
https://youtu.be/T5DNzVPwrzc?t=455
Nice! Now maybe watch the part of this video where I talk about Spherical Aberration and the DFTFringe null feature:
https://youtu.be/T5DNzVPwrzc?t=455

By
George Roberts (Boston)
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#31013
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Re: Zernike term calculation ?
I used a pure sinus coma as an example.
With DFTFringe and its Zernike wavefront simulation tool I created a front with the value 0.771.
Then I saved that wavefront and turned it into an image.
I used a pure sinus coma as an example.
With DFTFringe and its Zernike wavefront simulation tool I created a front with the value 0.771.
Then I saved that wavefront and turned it into an image.

By
jeanpierre_chiappini@...
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#31012
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Edited


Re: Zernike term calculation ?
Michael's explanation uses orthonomal Zernike polynomials which are weighted so that the integral of the square of each Zernike polynomial over the unit circle is 1. The Wyant Zernike polynomials
Michael's explanation uses orthonomal Zernike polynomials which are weighted so that the integral of the square of each Zernike polynomial over the unit circle is 1. The Wyant Zernike polynomials

By
Bruce Griffiths
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#31011
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Re: Zernike term calculation ?
Yes! Very close. I think instead of "h / Z7" it's "h * Z7". Instead of the "mean", it's the "integral". Basically the same idea (for each pixel value h, find h*Z7 then divide by the surface area
Yes! Very close. I think instead of "h / Z7" it's "h * Z7". Instead of the "mean", it's the "integral". Basically the same idea (for each pixel value h, find h*Z7 then divide by the surface area

By
George Roberts (Boston)
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#31010
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Re: Zernike term calculation ?
Here's a brief outline of the algorithm for working with actual data sampled at a discrete grid of points:
1) Given the previously determined size and location parameters of the interferogram(s)
Here's a brief outline of the algorithm for working with actual data sampled at a discrete grid of points:
1) Given the previously determined size and location parameters of the interferogram(s)

By
Michael Peck
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#31009
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Re: Zernike term calculation ?
C7 = (Integral of product of h*Z7 over the surface)/(Integral of Z7*Z7 over the surface)
Where Z7 is the Zernike polynomial and C7 its amplitude
The Integral of Z7*Z7 over the surface = 1/8.
The
C7 = (Integral of product of h*Z7 over the surface)/(Integral of Z7*Z7 over the surface)
Where Z7 is the Zernike polynomial and C7 its amplitude
The Integral of Z7*Z7 over the surface = 1/8.
The

By
Bruce Griffiths
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#31008
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Re: Zernike term calculation ?
Much like fitting a line to a group of points.
You can use a "least squares fit" of each point to the polynomial. It is complex but straight forward if you know the math. You can find it in the
Much like fitting a line to a group of points.
You can use a "least squares fit" of each point to the polynomial. It is complex but straight forward if you know the math. You can find it in the

By
Dale Eason
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#31007
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Edited


Zernike term calculation ?
Good morning all,
If we know the wave front (W) or in other words we know the height of the deformation (h) at each point expressed in wave value, how are the zernike terms calculated?
For example how
Good morning all,
If we know the wave front (W) or in other words we know the height of the deformation (h) at each point expressed in wave value, how are the zernike terms calculated?
For example how

By
jeanpierre_chiappini@...
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#31006
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Re: Testing old mirrors
Paul, thanks for your letter.
About Gregorian telescopes on the mid. of 18 century  they could be left all spherical and be diffraction limited.
Attached please find a design sample of 2.25"
Paul, thanks for your letter.
About Gregorian telescopes on the mid. of 18 century  they could be left all spherical and be diffraction limited.
Attached please find a design sample of 2.25"

By
Yuri
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#31005
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Edited


Re: Updated Wiki Page: Diverger lens Residual Spherical aberration
#wikinotice
Thanks for that!!
Lost me at "Thin lens"
Kind regards,
John
Thanks for that!!
Lost me at "Thin lens"
Kind regards,
John

By
jkmetrology
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#31004
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Updated Wiki Page: Diverger lens Residual Spherical aberration
#wikinotice
The wiki page Diverger lens Residual Spherical aberrationhas been updatedby Bruce Griffiths <bruce.griffiths@...>.
Compare Revisions
The wiki page Diverger lens Residual Spherical aberrationhas been updatedby Bruce Griffiths <bruce.griffiths@...>.
Compare Revisions

By
Interferometry@groups.io Notification <noreply@...>
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#31003
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Re: Testing old mirrors
Yuri,
Remember that James Short was making Gregorian Telescopes of a crude nature before there
was a full understanding of the properties of the Gregorian Configuration.
If he was matching secondary
Yuri,
Remember that James Short was making Gregorian Telescopes of a crude nature before there
was a full understanding of the properties of the Gregorian Configuration.
If he was matching secondary

By
paul valleli
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#31002
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Re: Testing old mirrors
Dale and All,
I have to put this project on hold. Just need to study more about testing of a nonspherical mirrors.
Yuri
Dale and All,
I have to put this project on hold. Just need to study more about testing of a nonspherical mirrors.
Yuri

By
Yuri
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#31001
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Re: Testing old mirrors
Another way to find focus point is almost identical to how you do it with Foucault tester:
First remove all tilt  in other words try to get a "bulls eye" pattern visible. Then push gently on the
Another way to find focus point is almost identical to how you do it with Foucault tester:
First remove all tilt  in other words try to get a "bulls eye" pattern visible. Then push gently on the

By
George Roberts (Boston)
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#31000
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Re: Testing old mirrors
Dale,
I will play with a defocus on the weekend. Moving 1mm from the ROC point will make too many fringes, I will try a smaller amount (up to 10 micron level). So far I have checked the result by
Dale,
I will play with a defocus on the weekend. Moving 1mm from the ROC point will make too many fringes, I will try a smaller amount (up to 10 micron level). So far I have checked the result by

By
Yuri
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#30999
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Re: Testing old mirrors
George, thanks for videos, I watch the first one at lunch and got some info I missed, thanks a lot!
As per the Bath, I am not familiar with it, doing all test with a very compact TG for APOs testing.
George, thanks for videos, I watch the first one at lunch and got some info I missed, thanks a lot!
As per the Bath, I am not familiar with it, doing all test with a very compact TG for APOs testing.

By
Yuri
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#30997
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Re: Testing old mirrors
Yuri,
When using a Bath interferometer how far you set it from the ROC of the Mirror determines the defocus value. I assume that will be the same for the interferometer you are using. So move the
Yuri,
When using a Bath interferometer how far you set it from the ROC of the Mirror determines the defocus value. I assume that will be the same for the interferometer you are using. So move the

By
Dale Eason
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#30996
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