Statistische Angaben über RMS, Strehl- und PV-Werte

[suessenberger]

... bei Torus Mirrors.

Grüße: Uwe

[Rohr]

Hallo Uwe,

at first I've looked for the different fringes pattern and was astonished about that:
In all the examples the astigmatism is deactivated . The coma value, this is
OK, but the astigmatism? Is there any explanation one can do so?
Look here:
http://www.opticalmechanics.com/Test_Data_Intro.htm
and here:
http://www.opticalmechanics.com/25-19-060305.htm

Torus New 635/2540 (5080) Serial# 25-19-060305
Peak to valley .230 wave, RMS .038 wave, Strehl ratio .940
Tested on the wavefront at 550 nm Focal length 101.0"

Results with FringeXP with the artificial fringes pattern

incl. astigmatism PV 2.032*Lambda Strehl = 0.000
astigm. deactivated PV 0.188*Lambda Strehl = 0.963

I calculated several examples with fringeXP. The Torus results would be correct
if you substract the astigmatism. Could you give me a short comment for
doing this?

If you have questions about your test results contact me, James Mulherin via E-mail jcmulherin@opticalmechanics.com or telephone (319) 351-3960

one more example: http://www.opticalmechanics.com/Test_Data_Intro.htm





http://www.opticalmechanics.com/20-74-082504.htm

The same situation:
FringeXP + astigmatism PV 0.657*Lambda Strehl 0.514
FringeXP - astigmatism PV 0.174*Lambda Strehl 0.972
----------------------------------------------------
Torus . . (- astigmatism PV 0.171*Lambda Strehl 0.977

[James Mulherin]

Hello Wolfgang:

It’s nice to hear from you. I visit Astro-foren occasionally and find the topics of discussion interesting.

I’m attaching an article written by Steve Koehler that presents some information on an 18” mirror that Steve and I analyzed using different test techniques. I hope that you will find the article interesting in general because it treats the topic of test stand errors (astigmatism and trefoil).

With regard to astigmatism and turning it off in our test results: we test all of our mirrors in autocollimation with an optical flat. Almost all of our mirrors are made from 2” thick Pyrex. The 25” in question is also made from 2” Pyrex. In the test the mirrors are held in a cable sling. This is the most practical method for us to hold the mirror in the test. As you probably know, this is not the best way to hold a mirror in general because the mirror will exhibit the maximum amount of test stand errors. In other words, the mirror is showing the maximum amount of bending in this position. This bending error is comprised mostly of astigmatism and trefoil. In order to obtain a reasonable result with respect to spherical aberration and the other residual errors of figure that are rotationally symmetric we subtract astigmatism and trefoil out of our test results. In other words, we are assuming that the astigmatism is all test stand error.

Of course, this results in an approximation of the mirrors true P-V, RMS and Strehl values but for practical reasons this is the best estimate that we can provide. When measuring a mirror with the zonal Foucault test you are making a similar assumption because you can only measure across one mirror diameter at a time. The resulting P-V, RMS and Strehl values automatically assume that the mirror has perfect rotational symmetry.

The question you will likely as is “Is it valid to assume that the mirror has reasonable rotational symmetry and hence is it valid to subtract out astigmatism?” In over 500 mirrors in the 12.5” to 25” aperture we have never had a complaint of real mirror astigmatism when the mirror is tested on the sky. That said, of course there is risk that the mirror may have real astigmatism. Avoiding real mirror astigmatism is a matter of good glass and good process. We take the following steps to avoid real astigmatism:

We use only precision anneal Pyrex or Sital, Zerodur or ULE.

The back of the mirror blank is fine ground flat

We grind mirror face down on oversize tools (6/5 of mirror diameter)

We polish mirrors face up using only full size laps

We stop the polisher every 30 minutes and rotate the mirror ~1/4 turn

Our machine turn tables are accurately ground (Blanchard) flat and we use adequate padding between the table and mirror

We do check mirrors for astigmatism using the visual Ronchi and Foucault tests during figuring. As you may know, test stand astigmatism is always in the vertical plane (plane of gravity). Testing the mirror with a vertical Ronchi grating or knife edge you will see no astigmatism because the fringes and shadows are in the plane of the astigmatism. If you do detect astigmatism in the test it means that you have astigmatism that is out of the plane of gravity. This is an indication that the mirror has astigmatism that is not due to bending in the test stand. We rarely see this but when we do we put the mirror back on the machine for full size lap polishing to remove the astigmatism.

I hope this answers your questions. I’ll be happy to continue the discussion in more detail.

Best regards,

James

James Mulherin
Optical Mechanics, Inc.
jcmulherin@opticalmechanics.com
www.opticalmechanics.com

Tel: (319) 351-3960

Fax: (319) 351-3943

[Rohr]

Dear James,

my warm and hearty wellcome on our forum, it's very nice of you giving us
some informations about the problem with the astigmatism of large mirrors.



Some days before I had that problem with this 25" f/4.5 mirror. All the qualitativ
tests were excellent but there was a small astigmatism with star testing and
the fringes pattern in CoC and a bigger one in compensation test and we had
the problem, how much you can subtract of these values. The next problem is
what kind of error is the trefoil and are we allowed to subtract that error?

There are different discriptions what the Zernike Coeffitients are and
what trefoil is. Look at the different tables.

http://rohr.aiax.de/zernike_1.jpg
http://rohr.aiax.de/zernike_3.gif
http://rohr.aiax.de/zernike_bar1.jpg

I just got this Link:
http://www.opticalmechanics.com/inte...ic_testing.htm

[James Mulherin]

Hello Wolfgang:

Thanks for the warm welcome.

In a 24" F/4 you should expect to see some astigmatism in the star test when your mirror is hanging in the sling. I find that astigmatism becomes detectible in the artificail star test when it is about 1/2 wave or larger. Less than 1/2 wave and it's really not objectionable. If you do see astigmatism in your star test, you mentioned that you rotate the mirror. If the astigmatism rotates with the mirror, then it belongs to the mirror. If it stays in the same orientation then it is test stand error. This same mirror rotation test works for testing on a real star. I live in Iowa and much of the time we have the Jet Stream overhead. So, I raraly have seeing that allows me to do accurate star testing.

You asked about trefoil: this is a higher order astigmatism (I think 5th order) with three sided symmetry. After subtracting out astigmatism, trefoil is the dominant asymmetric test stand error in a sling support. There are some studies that show that trefoil is an expected test stand error. A paper by Daniel Vukobtatovich is one where finite element analysis shows that a sling induces trefoil. I've never had a report of trefoil being visible in a star test so I think it's safe to subtract it out. Incidentally, I think it would be difficult to polish real trefoil into an mirror, even if you wanted to.

James

James Mulherin
Optical Mechanics, Inc.
jcmulherin@opticalmechanics.com
www.opticalmechanics.com
Tel: (319) 351-3960
Fax: (319) 351-3943

[Rohr]

Some more information from James:

http://rohr.aiax.de/Steve K analysis of 18-64.pdf

Analysis of Torus Mirror 18-64

Stephen C. Koehler

steve koehler@securecomputing.com

January 2004

1 Introduction
This report documents my ongoing efforts to understand the optical quality of my 18” f/4.5 Torus
mirror, based on a variety of optical tests. My general approach is to use the tests to cross check
each other, and to use the unique strengths of each test for maximum effect. The end result is a
rather complete picture of the optical characteristics of this mirror from different viewpoints, not
all of them in agreement. I hope eventually to resolve the discrepancies. Until then, I will refrain
from drawing final conclusions.
The report is organized by test method. Each quantitative method is compared against interferometry,
which provides the most detailed model of the mirror’s surface. I begin with a summary
of results, which provides a road map to the rest of the paper. The individual sections explain
my methodology and justify my conclusions. Some of the sections (especially Interferometry) are
rather detailed. If the analysis goes beyond your patience or interest you may skip ahead to sections
that are of more interest.
I have tried to make the figures in this report readable both on the screen and in a printed copy.
However, there are some graphics that will always appear better on the screen. This includes a few
graphs where I use color to make subtle distinctions and some gray images where the contrast is
better when viewed on the screen. If you are having trouble understanding a graphic in a printed
copy, I recommend looking at that graphic on the screen, instead.
1.1 Background
In the summer of 2003 I took delivery of Torus mirror 18-64. This mirror replaced my original
Torus mirror (18-27), which unfortunately was misplaced by the coater after I had sent it in for
some rework. As a favor to me, because of my interest in optics, James Mulherin (President/Master
Optician at Torus/OMI) supplied me with an unusually large amount of documentation on 18-64,
including seven Ronchi images, six Foucault (knife test) images, and twenty interferograms and
associated analysis. Table 1 shows the overall specifications reported by OMI. These specifications . . . .

This link gives anybody an overview to the system of the Zernike Coeffitients.

http://wyant.opt-sci.arizona.edu/zernikes/zernikes.htm

[Rohr]

Eine interessante Untersuchung, die sehr gut zum Thema paßt, veröffentlichte
Alois hier: http://www.astrotreff.de/topic.asp?T...81&whichpage=2
Mit seiner Einwilligung darf ich sie hier ebenfalls veröffentlichen:



Die Aussage von Alois ist sehr interessant:
Bei einem 451/2040 Newton ergibt das Airy-Scheibchen einen Durchmesser
von 0.00607 mm bei 0.307 arcsec. Der von ihm gemessene Astigmatismus
von 0.75 * Lambda PV der Wellenfront ist ein erheblicher Wert. Trotzdem
ist das Kreuz des Astigmatismus exakt im Fokus gerade einmal 0.007 mm
und erreicht in etwa die Pixelgröße heutiger CCD-Kameras.

Auch visuell ist die tatsächliche Coma bei einem Achsabstand von nur 3 mm
bereits um den Faktor 3-4 größer als das astigmatische Zerstreuungs-Scheib-
chen. Natürlich reduziert sich der Strehl-Wert gerade über den Astigmatismus
äußerst stark, also unter Strehl = 0.50, was den Foucault-Testern gar nicht
gefallen wird, die bei der Quantifizierung von Astigmatismus erheblich ein-
brechen.

Die wohl wichtigste Frage aber bleibt: Wie gewichtet man den Astigmatismus
bei großen Spiegeln,
a) die Zuordnung bei der Messung selbst
b) die Auswirkung am Himmel bei kleiner werdendem Airy-Scheibchen

Kurt im gleichen Link: dazu kann ich eigene Erfahrungen mit meinem 16" f/4,7 Dobson
beisteuern. Es hat ca. 0,6 lambda wave Asti. Das hab ich auch erst ein Jahr
später bei Interferometermessungen recht gut reproduzierbar festgestellt und
zwar ganz schlicht in COC, ohne Kompensation und bei normaler Streifenlage.
Das Teleskop wird fast ausschließlich für DS- Beobachtungen mit niedriger bis
mittlerer Vergrößerung eingesetzt. Nachdem ich von dem Asti wusste, war der
bei gutem seeing, einwandfreier Kollimation und hoher Vergrößerung beim
Startest am Polaris auch erkennbar. Ich würde mir aber nicht zutrauen danach
den Grad des Asti ermitteln zu können.

Das klang aus der Feder von Kurt vor einiger Zeit noch ganz anderes,
ist aber ein deutlicher Lernzuwachs auf seiner Seite. Gratulation !
Ob his "masters voice" ebenfalls dazugelernt hat?

[Barry]

Hello Wolfgang and James,

I have been reading with great interest this thread. To begin with I would like to pass a few comments if I may based on pure logic rather than specific ones to interferometry.

I am considering just one mirror size here for clarity.

1. All the mirrors of one size are the same diameter, obviously.
2. They are of the same thickness
3. They are all placed on the same stand with the same strap support
4. They are all tested under the same conditions.
5. All mirrors show astigmatism on test, currently attributed to flexure of the mirror on the test stand.

From James’s posting the above seems to be the case. OK, a couple of things which are giving me problems following the logic behind the total removal of astigmatism in every test case.

1. From the data on http://www.opticalmechanics.com/Test_Data_Intro.htm web site why do all the mirrors have differing amounts of astigmatism, some have enormous differences of a factor of around four fold.
2. It must be assumed that if the test adds the same amount of astigmatism to the mirror in question, and I can’t see why it shouldn’t, that some of the mirrors which show only a small amount of astigmatism, have in effect, much more than is visible.

When testing any optical surface which is designed to be a figure of revolution, it is totally incorrect to remove astigmatism from the calculation to reach an overall PV wavefront error value. Piston, tilt, power, coma, yes, no problem because these are not part of the image forming wavefront of the optic. Astigmatism and trefoil are surface errors and as such are essential to be included in the calculation.

I would be pleased to consider removing astigmatism in any test provided the amount in the testing equipment was known, the exact amount and axis being introduced during flexure was known. These two could be removed but, in a manual system other than a Zygo for example, it is impossible to do.

To remove astigmatism completely from all tested mirrors and quote that its PV is an ‘estimate’ to 3 decimal places seems a little bit irregular.

Regards to all

Barry

[James Mulherin]

Hello Barry:

When testing large thin mirrors we all see test stand errors that are much larger than the diffraction limit. Unfortunately, this is the physical reality of making large thin mirrors. Many amateur astronomers aren't aware of this practical problem that we all face in testing mirrors. This is because the most common test used in the amateur community, the zonal Foucault test, ignores test stand errors. I'm very pleased to see that this topic is now being discussed on many of the astronomy forums these days because for many, it's an introduction to the reality of the practical problems of mirror testing.

Regarding the variation in the amount of astigmatism from one mirror to the next, there are several factors that affect your astigmatism results. The largest factor is support placement. We use a cable sling. Ideally, the sling should be in the plane of the mirror's center of gravity. This will minimiz test stand astigmatism. A small displacement of the sling out of the plane of the mirror's center of gravity cause a significant change in the amount of test stand astigmatism. This topic has been discussed at length in other astronomy forums and several analyses have been done using PLOP. I have also done tests on a 20" mirror where I intentionally displaced the cable sling and tested the mirror with the interferometer. The bottom line is, the amount of test stand astigmatism is very sensitive to sling placement. I'll dig up the article on the 20" mirror astigmatism vs. sling placement tests and post it later today.

Air currents and stratification of the air in the test chamber are also contributors to your astigmatism results. If you look at the Steve Koehler article you will see that the astigmatism term varies from one interferogram to the next, even for the same mirror in the same test session. Averaging a number of interferograms helps to reduce these random errors.

Regarding turning off astigmatism in the tests: We choose not to use a test that ignores test stand errors because you lose other important errors at the same time. Given the practical reality that test stand errors exist we first take steps in the production process to avoid real mirror astigmatism, then subtract out what we assume is primarily test stand error. Like I said, this results in an approximation of the mirror's wavefront, but knowing what I know, and based on practical investigations by myself and others I beleive that it is a reasonable approximation. It's certainly better than the approximation that the the zonal Foucault test will produce. How much better, I can't say. You can certainly make an excellent mirror with the Foucault test.

Any way, the real test is in the mirror's performance on the sky. We've not had any reports of astigmatism in our mirror's on the sky.

Best regards,

James

[James Mulherin]

Barry:

I forgot to mention: In the auto-collimation test, astigmatism is in part an alignment error. In other words, misalignment of the mirror to the flat introduces both coma and astigmatism. So there is a misalignment induced component in your overall astigmatism term.

James