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Inexpensive interferometers for measurement of fast spherical surfaces

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#1 BGRE

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Posted 07 June 2019 - 09:22 PM

Measurement of a 75mm diameter F/1.2 sphere is impractical with a Bath due to excessive field astigmatism and other (calibration) issues.
A relatively inexpensive interferometer the residual errors of which can be calibrated inexpensively is desirable.
The uncalibrated interferometer errors should be somewhat less than a wave ptv to ensure accurate measurement.

The random ball test can be used to calibrate any fast spherical wave interferometer with an accessible real test beam focus and sufficient working distance so that the center of the ball can be made to coincide with the test beam focus.
Suitable Grade 5 Silicon nitride balls are readily available.

A Twyman-Green interferometer using a "microscope" objective to produce a suitably located external focus is one possibility.
Another is to use a PDI plate located at the long conjugate of a finite conjugate (or equivalent) microscope objective together with a beamsplitter located in the slow beam to allow coaxial illumination of the test surface from a near diffraction limited point source.

The PDI version is a common path interferometer allowing short coherence length sources to be used.

One option for the "microscope" objective is an aspheric singlet typically used as a fiber collimator plus a long focal length PCX singlet lens (or equivalent).
The "microscope" objective forms a real image of the test surface which in turn is imaged onto the image sensor by the camera optics.
The distortion in the imaging of the test surface onto the image sensor has to be corrected when calculating the surface error.
However achieving a sufficient working distance to permit calibraion via the random ball test is an issue when an NA of 0.2 is required unless a 12mm diameter ball is used with an 11mm efl lens.
https://wp.optics.ar...m-Ball-Test.pdf

Edited by BGRE, 07 June 2019 - 11:07 PM.


#2 BGRE

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Posted 07 June 2019 - 09:44 PM

Further Random ball test papers:

http://www.loft.opti..._Randomball.pdf
https://www.spiedigi...503.short?SSO=1

Sources of grade 5 Silicon Nitride balls:

https://www.ebay.com...hrqcZQ2CEiDNycw

https://www.henderso...r-1mm-10mm.html

Edited by BGRE, 07 June 2019 - 09:45 PM.


#3 TOMDEY

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Posted 07 June 2019 - 10:29 PM

TWG would work well. Also, if you have access, ZYGOs (old and new) have available transmission spheres that are plenty fast enough. That would violate he cheap benchmark.   Tom



#4 BGRE

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Posted 07 June 2019 - 11:08 PM

The original question posed in the Bath/Zygo comparison thread was essentially "can such a surface be measured by a Bath or by other low cost means?"
Whilst an on axis Bath could be adapted to do this with the aid of an auxiliary lens, calibrating the errors due to the external lens is an issue without an inexpensive solution..

Edited by BGRE, 07 June 2019 - 11:09 PM.

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#5 BGRE

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Posted 07 June 2019 - 11:28 PM

It would be practical to match or at least reduce the difference test and reference optical path lengths when using a Twyman-Green so that a short coherence length source could be used.
The test surface RoC is only 180mm. This would allow a spatially incoherent ring or disk source to be used to reduce the effects of dust diffraction and other coherent artifacts.
If the budget allowed a long working distance microscope objective could be used so that a larger calibration ball could be employed reducing some of the associated calibration errors incurred.
The classical absolute calibration method could also be used but its not cheap due to the relatively large number of tilt/tip rotation and translation stage needed.

#6 gr5org

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Posted 08 June 2019 - 07:33 AM

>Measurement of a 75mm diameter F/1.2 sphere is impractical with a Bath

 

A convex mirror sphere?  Or a concave mirror sphere?

 

Are you talking about the beam separation issue?  That's not a big deal since the astig is consistent so you can just rotate the mirror under test 90 degrees, measure again and average the two results.  This will cancel any astig caused by beam separation, right?



#7 BGRE

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Posted 08 June 2019 - 07:57 AM

That's true if and only if you can maintain the astigmatism constant to within a tolerance smaller than the target wavefront error (i.e.to better than 1% or so of the field astigmatism).
The return reference beam comes to a focus at a distance of about 90mm in front of the diverger lens whereas the reference beam starts with one infinite conjugate. The resultant difference in the SA imparted to the test and reference beams is likely significant.
Then there are issues with the acceptance angle of the beamsplitter cube with a a 22 degree included angle test beam cone angle.
Any SA common to both beams results in tilt dependent aberrations that need to be accounted for.

#8 gregj888

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Posted 08 June 2019 - 02:40 PM

If you pull the collimation lens off of a laser pointer it makes a pretty good point source but might not spread enough.  Run it non-lazing.

 

Twyman Green but you still need a reference sphere.



#9 BGRE

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Posted 08 June 2019 - 05:45 PM

If you pull the collimation lens off of a laser pointer it makes a pretty good point source but might not spread enough.  Run it non-lazing.
 
Twyman Green but you still need a reference sphere.


Why?
You don't need one (if the test beam has an accessible real focus with sufficient room to allow a calibration ball to be used) for calibration with an F/2 test beam (a Grade 5 Silicon Nitride ball suffices).
A flat reference surface can be used or a virtual reference interferometer with no physical reference surface could be used.

If you are considering a "Williams" interferometer one indeed has to resort to calibration with an accurate, expensive reference surface to calibrate it.
If you have a diffraction limited point source then a PDI plate could be used to measure the aberrations in the beam reflected by the test surface.
"Pretty good" isn't an adequate specification you actually have to measure the source aberrations.

Edited by BGRE, 08 June 2019 - 05:59 PM.


#10 gregj888

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Posted 09 June 2019 - 10:54 AM

Why?
 

 

Leaning on inexpensive.  In my limited experience an f/1.2 beam is difficult to reach and still be inexpensive.  Just a thought.  Would not help with the calibration ball requirement (?).

 

Would also be curious about the optic and it's  use: 75mm., f/1.3, mirror or lens?  Whatcha building now?

 

Thx


Edited by gregj888, 09 June 2019 - 11:01 AM.


#11 BGRE

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Posted 09 June 2019 - 05:12 PM

See posts #2, #4, #6, #12 in
https://www.cloudyni...ath-comparison/

#12 Ed Jones

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Posted 10 June 2019 - 12:17 PM

I'm curious why you need to test an F/1.2 sphere?  Few ATMs even make lenses and when they do they would likely need a lot slower F number.  I made a 6 inch f/3.2 transmission sphere when I had access to optical equipment but it was not an easy project or cheap.  A F/1.2 optic would best be tested with a test plate viewed through the optic, at least for lowest cost.


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#13 MKV

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Posted 10 June 2019 - 03:35 PM

Benach, is this a lens for the corrector of the "Super Houghton" Mike Jones designed for you ├Žons ago? I don't have the design handy, and my memory may not be accurate, but such a surface would certainly stand out and I don't recall anything even close. I agree with Ed. Make a test plate and use contact interference method. I can't imagine testing this lens with a Bath. Otherwise, use a Twyman-Green or a Williams type IF.

 

twyman_Green_IF_2.jpg



#14 BGRE

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Posted 10 June 2019 - 04:58 PM

So how exactly does one inexpensively certify a convex test plate?

#15 Ed Jones

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Posted 11 June 2019 - 06:48 AM

I'm sure test plate manufacturers use a Zygo but that's sort of a catch 22.



#16 BGRE

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Posted 11 June 2019 - 07:29 AM

One could purchase test plates but they are exactly inexpensive. Kreischer Optics used to have price info for these on their website.

https://www.spiedigi...2.2029324.short
is an interesting paper on retrace error and how to design transmission spheres with reduced sensitivity to small amounts of defocus etc..

#17 Ed Jones

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Posted 11 June 2019 - 09:29 AM

Using a test plate on a steep curve like this has its own problems of viewing correctly.  Still a test plate is probably the best option for an ATM making a convex curve.


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#18 MKV

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Posted 11 June 2019 - 10:33 AM

So how exactly does one inexpensively certify a convex test plate?

I think making a relatively small spherical test plate to about 1/20 wave with a knife-edge null is within experienced ATM's ability. 



#19 gr5org

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Posted 11 June 2019 - 11:21 AM

I'm not sure what you mean - I know how to do that with a concave spherical mirror.  How does the setup change for a convex spherical mirror?



#20 MKV

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Posted 11 June 2019 - 11:38 AM

I'm not sure what you mean - I know how to do that with a concave spherical mirror.  How does the setup change for a convex spherical mirror?

Let's say that you buy a plano-convex lens on e-Bay that you wish to use for the Ross null test. Naturally, you wish to make sure the lens is of sufficiently high quality for that purpose. You can test the flat side with a known flat (or with two more unknown flats),  but testing the figure of the convex surface is a problem. You can measure its radius of curvature, and that's about it. To check the figure with contact fringes you need to make a concave test surface of the same ROC as the convex one and figured to a precise sphere.



#21 BGRE

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Posted 11 June 2019 - 04:50 PM

I think making a relatively small spherical test plate to about 1/20 wave with a knife-edge null is within experienced ATM's ability.

Proving the mirror is actually 1/20 wave or better without a lot of unverified assumptions isn't that simple..

#22 MKV

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Posted 12 June 2019 - 03:14 AM

Proving the mirror is actually 1/20 wave or better without a lot of unverified assumptions isn't that simple..

I would say it isn't easy, as it requires good skill and patience, but a "clean" (i.e. zone-free and without any observable features wavefront), uniform graying k-e null of the pupil is going to be much better than 1/20 wave.

 

For the 75 mm f/1.2 spheroid lens in question, a 1/20 wave error would be clearly observable (and measurable) if  the lens surface were 99.87% sphere (i.e. a conic constant of -0.00128).

 

Below are two traces of the lens with that conic constant at ROC in OSLO and SYNOPSYS showing 1/20 wave interferometric results, as well as the results of a knife-edge test.

 

It's worth noting that if "featureless" and "flat" knife-edge optical null were observed, the wavefront error would be around 1/50 wave, or better.

 

75 f1_2.jpg



#23 Venetia2004

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Posted 20 June 2019 - 11:07 AM

I have a nice Bath interferometer that I built a few years back but I've never used it for real analysis , only  for experiments since I've never been able to get over "the proper fringe igrams contrast";either they were "over exposed" or "underexposed" so I found it subjective once you do not know the right contrast level...It's been sitting aside but it would be a very nice tool if these igram contrast related pitfalls had been resolved. I mostly rely on DPAC and star tests...Once you have the correct set up and be "critical" with what you see, you cannot go wrong with those...


Edited by Venetia2004, 20 June 2019 - 11:13 AM.


#24 gr5org

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Posted 20 June 2019 - 12:27 PM

You can be a few stops over or under exposed and get good results with DFTFringe.  Getting the exposure right is probably crazy difficult with an iphone but with a cheap used DSLR it should be very easy.  Basically you need a camera with a manual mode.

 

I have some videos on how to setup a bath and get good photos and another on how to use DFTFringe.  Here:

https://www.youtube....jouHwmS-qAjp8Tw

 

I spent a ton of time on these videos and I hope it helps someone :)


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#25 Venetia2004

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Posted 21 June 2019 - 12:06 AM

You can be a few stops over or under exposed and get good results with DFTFringe.  Getting the exposure right is probably crazy difficult with an iphone but with a cheap used DSLR it should be very easy.  Basically you need a camera with a manual mode.

 

I have some videos on how to setup a bath and get good photos and another on how to use DFTFringe.  Here:

https://www.youtube....jouHwmS-qAjp8Tw

 

I spent a ton of time on these videos and I hope it helps someone smile.gif

Thank you for your reply .I''ll surely check the link... I've tried with all kinds of cameras including the DSLR in manual mode. I've never, ever could get the "right exposure" to have an igram like some people post,nice, clean pictures...When tolerances are so tight ,depending on some digital picture exposure I doubt that the test results would be accurate...

I was able to get excellent 2017 sun eclipse pictures in RAW mode with my DSLR but with  these Igrams seem to be  different ...


Edited by Venetia2004, 21 June 2019 - 12:21 AM.



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