Testing old mirrors


Dale and All,
I am trying to test antique mirrors made in the 17-18 Century.
They are mostly the metal primary mirrors from Gregorian type telescopes.
Diameters are in range from 1" to 4", all have a central perforation. Some have a good reflectivity, some - not. All made from metal.
I am using a TG i-meter @543nm. Tests are done from the center of curvature. Shape of the mirror is usually unknown, quality is far from modern standards.
The goal of test is to find appr. figure of the mirrors and quality.
Have a  problem with setting the Center filter size.
Going from 0 to 15 makes quite different results.
Attached is a sample of i-gram.
James Short's mirror circa ~1762

Filter size        Best fit conic
0                      -3.49
3                      -2.25
6                      -1.32
9                      -1.30  (max Strehl)
12                     -1.38
15                     -2.02
Strehl goes from   0.00 to 0.09 max
Any suggestions are welcome.
Thanks, Yuri

Dale Eason

Yuri,   Thank you for the igram.   I'm working on it.  I get what I think is a reasonable analysis with a blue circle of 8 to 9.  At that point I get a strehl of about .7 using a gaussian filter of 5% and a conic of -1.2.      However I think I have found a couple bugs in DFTfringe using that igram.   The profile seems to double the size of the inside outline.  It also does not save the inside outline parameters in the .wft file as it should.   

I will look into my bugs.  But like you say changing the radius of the blue circle makes a big difference which is usually not the case.  It may help to use a more positive defocus value so that we get a better defined side lobe.  This igram has a defocus of -2.3 which makes for a very indistinct edge of the side lobe  something I try to avoid.


Dale Eason

My bugs turned out to be operator errors by me.   Here is my analysis using a blue circle center filter value of 9.   Not too bad of a mirror for it's time.   Rolled outer edge and a raised ring around the center hole.


- thanks a lot, Dale. Your results are quite different (one magnitude order) than mine... It is almost a diffraction limited mirror (!). I hope it is close to reality. I have a few more mirrors of the same master to test.
What would be the best route to such results when testing mirrors of unknown shape?
1. I am usually setting Desired conic to 0.0, you set it to -1.
2. The Center filter size: should I pass from 0 to 15, etc. and then to choose the best results and keep the center filter size for next i-gramms. Any algorithms here?
3. How to set up the defocus value  or it is done automatically, are any tips here?
Attached are couple of analysis: Before reading your post with Des. Conic 0.0 (lower image) and after reading it and Des. conic = -1   - this result is close to yours!(-1)
Thanks in advance,

George Roberts (Boston)

The defocus value is calculated from your igram.  If you have the bath setup exactly at focus - the nominal distance form the mirror - you will get a defocus of 0 waves.  You can tell when the Bath is at defocus of zero (or near zero) as things flip around and also there are minimum number of fringes if you haven't added any tilt.

If defocus is positive in dftfringe then it means you were outside of focus - meaning your bath was farther from the mirror.  If defocus is negative then your bath is closer to the mirror than at perfect focus.

In the last photo in your previous post you can see the mirror looks horrible with a strehl value of 0.089.  Most good mirrors are over 0.5.  A strehl value of 0.9 would mean 90% of the light is within the airy disk - meaning you see sharp focused bright stars.  A value of 0.089 would mean only 10% of the light is in the star - really horrible.

But this isn't a horrible mirror - you just haven't setup the null feature properly in DFTFringe.  I recommend watching these two videos that explain about the defocus and also setting up the mirror configuration and how/why it all works.  I spent a ton of time making these videos as understandable and informative as possible.  Both have foreign language closed captions.


- George

George Roberts (Boston)

Wait - I just realized I'm replying to Yuri.  I think Yuri knows just as much about Bath Interferometers as I do and probably doesn't need to watch my videos.  Hmm.  So why disable the null?

Dale Eason


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 your interferometer back from the ROC a very small amount  (a mm or so) with your fine motions stage if that is what you have.   Then take a few igrams and analyze them to see what their defocus value is.   Do that until you get a defocus value of 1 or larger.

We have several issues to work through.   The first is I assumed the desired surface was a parabola with a conic of -1.   That might not be the case for that mirror.   I just don't know.   You will have to figure that out from the telescope optical equations needed for that style of scope.

The next issue is that DFTFringe does not use annular Zernike polynomials.   That is ok if the central hole is less than 25%.   But that hole is 28%.   How much of an error does that make I do not know.

I have found that the center blue filter diameter does not change the best fit conic much.   Mostly a large value causes the edge of the mirror to get an upward fringe where the filter overlaps the side lobe.  I don't know why one time the best fit conic changed a lot with the filter but it does not now.  Attached is an image comparing a filter value of 1 and 12.   The profile shows both but the other plots and data are for the filter values of 12.  From that you can see where the lower right quadrant edge gets raised using the value of 12.


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.
Regards, Yuri


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 averaging 2÷3 shots + rotation + final averaging. The result is similar to yesterday's data from a single shot.
As per theory, the Gregorian type of telescope asks for a parabolic shape for the primary and elliptical for secondary. But in the mid. of the 18-th century there were no control methods. Primary mirrors were tested from ROC, secondaries had spherical shape at the best.

George Roberts (Boston)

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 bath left or right.  Watch which way the "bulls eye" moves when you push left or right.  If the bulls eye moves the same direction as you are pushing then I call this "same".  If they move opposite directions I call this "different".  When you pass through the focus point it will switch to the other .  

Now I need to know if you are looking at the igram through a camera or on paper and how your bath is setup.

If your bath is like the left picture where the laser points towards the mirror under test then
a) if you are projecting onto paper then "same" means inside focus and "different" means outside focus
b) if you are looking at the igram directly with your eye or with a camera then "same" means outside focus

If your bath is like the right picture where the laser points 90 degrees from the mirror then
c) if you are projecting onto paper then "same" means outside focus and "different" means inside focus
d) if you are looking at the igram directly with your eye or with a camera then "same" means inside focus

"inside" means the bath is closer to the mirror than "at focus".  "outside" means the bath is farther from the mirror.
For me, "d" is most common and the one I memorized.  I memorized this "for me, 'same' is inside".

Note also that if you are setup like the left photo you need to check the box in the dftfringe mirror configuration that says "flip interferogram left to right on loading".  If you don't do that you may be rotating the images the wrong way or polishing your mirror in the wrong spot.


Dale and All,
I have to put this project on hold. Just need to study more about testing of a non-spherical mirrors.

paul valleli

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 mirrors to the primary, then your interferograms will have limited value.
The best you could do is relate the Primary surface figure to the desired prolate spheroid and then 
either make a Null Test setup for Conjugate foci or just report the shape of the Primary as related 
to a spherical reference at the Center of Curvature. Diameter and Radius of Curvature could be reported
but results of star imaging could be very poor if the mirrors are mis-spaced compared to a nominal design.
A missing secondary could mess up the imaging performance or introduce erroneous Spherical Aberration.
Personally, I would record a set of interferograms for each Primary and RoC, Best Fitting Conic, and 
amount of Astigmatism if it is a property of the test setup.
What to do, if the mirrors are flexing as mounted? That is where the stand-alone interferograms provide
a reference point, depending on gravity caused distortion, vs. mounting problems. 
To keep this analysis as practical evidence of Short's work would require amassing a large, but 
incomplete, database for each mirror. 
It might be reasonable just to provide the serialized interferograms with a manual profile reduction. Same for
the secondary mirrors. 
Is a convex test plate available ?
Interferograms of Secondary surfaces, made to avoid making erroneous measurements at incorrect 
spacings could simplify the analysis.
For the cases where the complete telescope is available, a qualitative evaluation of image quality at 
intended range and at infinity could help define relative quality.
In my opinion, the surface profiles obtained as topographic surface maps would be most meaningful.
Paul V. 

On Fri, May 7, 2021 at 10:36 PM Yuri via groups.io <tec=idcomm.com@groups.io> wrote:
Dale and All,
I have to put this project on hold. Just need to study more about testing of a non-spherical 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" diameter Gregorian telescope by the same master. The data are from Smith's Optics,1738 and it is related to Short's earlier telescopes.
 The second image is a sketch of telescope construction - just for a reference, I have this unit (278/1325 = 9 1/2").
Most of the scopes I have in collection are completed and in working condition. Testing of primary mirrors had a goal to check the shape and appr. quality.
I may consider testing whole telescopes, but it would not be as easy task.
Regards, Yuri


Dale and All,
since May 4-th and until yesterday I had a problem with unpredictable results with DFTF when testing old mirrors. The results were different compared to other people's tests and depended on the "blue filter" size as I mentioned in the first post.
With the help of Alex I realized that I am not outlining the Central Hole (!) counting that I have already set it up in the "mirror configuration" ....
Why? - a good question, I usually do many tests per day, but all of the objectives with no obstructions.
Well, now all problems are solved and I am back to tests.
BTW. While having issues with DFTF, I returned to working with the AtmosFringe again, which was helpful since results were repeatable.

Attached are tests of the primary mirror of the Gregorian telescope by Amici. the Atmos test in the middle, DFTF on the right (via Alex).
Tests were done before and after focus - BF, AF.
Thank you all for trying to help me, special thanks to Alex!

                                                    AtmosFringe                     DFTF
1 Before focus Strehl / Conic       0.774 / -0.733                   0.791/ -0.649
2 After focus  Strehl / Conic         0.785 / -0.736                  0.783 / -0.548