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Y. Herstein

These days, interferometers become cheaper and therefore more common every day. This is an asset for amateur astronomy because this allows far better optics than in the days of only Foucault testing. In this short article, based on actual measurements of a secondary mirror, I will very briefly explain how to interpret this data.

In my daily life I work as a optomechanical engineer. Since this topic does not review any equipment, it is needless to declare any bias since this is irrelevant for the article.

Below one can find the reflectance data from a secondary mirror measured.

On the horizontal axis one can see the wavelength, the color of the light measured. 400nm is violet and 700nm is red light. 550nm is green light. On the vertical axis one can see the reflectance. For aluminium the reflectance is high for all wavelengths, preferably above 90% at an angle of incidence (AOI) of 0⁰. However, this mirror has been measured at 45⁰ thus values are slightly different. Above 85% for the entire visual spectrum which is enough. If you get this report, check the following:

• AOI, angle of incidence. Should be the AOI which the mirror is used.
• %R, percentage of reflectance. Should be the about 90% for normal aluminium and about 93% for enhanced aluminium.

This is a report from MetroPro, the standard datasheet that comes out of a Zygo interferometer.

1. The surface wavefront error map. This is a height map of all the wavefront errors of the mirror. Compare this to a normal map: these highest values are the mountains whereas the loweast values are the valleys. The colors in itself mean nothing apart that it gives an indication of the roughness and zones.
2. This is the same mirror, now in helicopter view. Nothing can be seen from this apart from that it gives a better idea of the surface shape.
3. This is an interferogram of the mirror. For a flat mirror the lines should be straight, parallel to eachother and on equal distances. If the surface is spherical or parabolical, either extra optics are needed to correct for this, or one should do special techniques to get the surface data from this. Often a combination is done for optical surfaces.
4. This is a crossection of the surface at the black line you see in (1). The PV and rms values are measured the same way as explained in 5 but measured only over the cross section.
5. This is the personal data from the supplier. This should be correct.
6. The PV value is the “depth of the valley” + “height of the mountain”. According to the Rayleigh criterion, this value should not be more than 0.25 waves or lambda/4. However, these days an optical  is often made much better than this, less than 0.125 waves or lambda/8 is more common.

The RMS value is the average height difference. For a good mirror, this should be lambda/14=0.071 or less. (Marechal criterion)

The surface power is the inverse of the radius of curvature of the surface. This is zero for a flat mirror but for other mirrors, the curvature can be measured this way very accurately.

All the other data on the data sheets is irrelevant. Most other outputs from other programs work roughly similar.

• buckeyestargazer, Alfredo Beltran, artem2 and 3 others like this

CarlDD

Thanks Benach

I've had these reports for primary and secondary mirrors and had always wondered how to read it and what it was telling me, now I know.

Best Regards

Carl

• rogeriomagellan likes this
KLWalsh

Locator [3] is missing from the figure, but clearly it should be indicating the image at lower right.

One other bit of discussion I would like to see is a comparison of the relative importance of the Peak-to-Valley value vs the Root Mean Squared value. PV, I assume, describes the overall flatness of the mirror, whereas RMS describes the surface texture. So, a lower PV number means a relatively sharper final image. On the other hand, a higher RMS number means more scattered light and reduced contrast. --But these are just my assumptions. Some discussion of the relative merit of the PV and RMS values would be appreciated.

Good article!

Thanks.

• wrvond likes this
Benach

Funny to see that it has finally been published. Anyway, the image on the lower right is an interferogram of what one should expect if a reference surface is place on top of the tested surface. Straight and equidistant bands point out that the surface is smooth and there is no difference in the curvature between the surfaces.

About the merits of PV vs. RMS: one can do lengthy discussions on this but these days usually the RMS value is appreciated more because this gives the most reliable data on smoothness/flatness. The PV value can be measured but in a Foucault test it is usually not enough data to get proper asses the quality of the optics (undersampled). Apart from that: it is problematic when the mirror is slightly scratched. Does one also has to take the scratches into account when the PV value is measured? Stricktly speaking one should do this, but practically this gives misleading information. Same applies for central humps that fall in the shadow of the secondary mirror. So this is misleading again. These are some of the reasons why the PV value alone is considered very misleading.

But the Strehl ratio alone is also misleading. Although it is derived from the RMS value, it is not giving all the information one needs. I remember talking to a friend and he asked me the (theoretical) Strehl ratio of my special Houghton telescope "0.8 it is." I replied. Those who read Harold Suiter's well written book know that this is on the brink of satisfaction. So my friend laughed at me. However, what I used were the weighted average of the Strehls over the entire full frame field and for all colors from Near IR to Near UV. If I would make the same calculation for his simple Newtonian telescope, it would be probably much closer to 0.1. See, these numbers don't say everything. One needs to wonder what has and was has not been taken into account.

TOMDEY

Nice! I did optical metrology (among other optics stuff) my whole life. Couple comments: The set-up for interferometry is crucial, if the report is to mean anything. That is, the "cavity" should be certified as near-perfect or accurately-characterized, and backed-out. That's oft the weak link once we get down to tenth-wave PV or better. Ummm... the optic under test (especially if a mirror!) should be unstressed, or, even better... in its in-use mount and orientation. There are user-selectables in the software that must be set correctly: single vs double pass, surface or wavefront, test vs use wavelength, raw vs power/coma/astig models, etc. Your throughput e.g., where the fold mirror is characterized at the USE angle, wonderful! But the wavefront... best-practice there is to set up the test cavity so it is also at the use angle! I did that on about 20 ea "star diagonals" and reported them that way. Thanks!  Tom

TOMDEY

Oh, I peeked some more. I see that, in this interferometric test, only piston and tilt were removed (of course) good! If tested at 45-deg, power may also be removed! And, importantly, that the scaling factor of 0.5 was used, so that, in this face-on test, what is being reported is surface (not wavefront). A low-pass spatial filter was used, probably fine, for a smooth mirror like this one. The test was, undoubtedly, HeNe, with default use wavelength HeNe? If so, the vis wavefront will be about 15% worse. (The sub-menu, to define different test and use wavelengths, is hard to find.)  Only other one that I can think of, it's often nice to also include a "most-fluffed" image of the fringes. That will, very overtly, reveal even the slightest hint of astig. Otherwise, straight, parallel, evenly-spaced fringes may not catch astig, if "parallel to either focal line". This re' the pictures only, the phase-sensing gizmo, of course catches everything! Well, I'm probably coming across as a blowhard...  Nice column on an important topic!  Tom

pastorgalactico

Hello;
I am lately updating myself on all this of the quality of the mirrors and special of the GSO mirrors of 16 "F4.5.
And from what I have understood it is better to look at the data and if they tell you that a mirror is at 1/6 PV (Valley Peak) and a Radio strehl from 0.93-0.94 you can already be happy to have that GSO optics.
By the way, how about GSO optics in 16 "f 4.5 optics?
Are acceptable or good optics for those € 1400 worth?

Greetings.

Benach

Hello;
I am lately updating myself on all this of the quality of the mirrors and special of the GSO mirrors of 16 "F4.5.
And from what I have understood it is better to look at the data and if they tell you that a mirror is at 1/6 PV (Valley Peak) and a Radio strehl from 0.93-0.94 you can already be happy to have that GSO optics.
By the way, how about GSO optics in 16 "f 4.5 optics?
Are acceptable or good optics for those € 1400 worth?

Greetings.

Hi,

1/6 lambda PV and a Strehl ratio of 0.93 is good enough for most if not all telescope applications. I do not know if this is applicable to the GSO optics you referred to but if so, you have my answer. Is this worth \$1400.- is an entirely subjective question I cannot answer for you. If you'd buy a car that speeds to 200kmh, worth \$14.000.- or is it worth \$20.000.- or \$6.000.-? I don't know...

pastorgalactico

Hello;

I asked him if the GSO optics that have passed through his hands or analyzed have at least the minimum quality of limited diffraction, or are somewhat superior to that.
Regards;

J.Tapioles

Benach

Hello;

I asked him if the GSO optics that have passed through his hands or analyzed have at least the minimum quality of limited diffraction, or are somewhat superior to that.
Regards;

J.Tapioles

Diffraction limited is 1/4 lambda PV. This is better so somewhat more superior. But note that this requirement is the minimum requirement and often considered an outdated minimum requirement.

pastorgalactico

Hello;

But from your experience, I would say that it is advisable to buy a GSO if you guarantee at least the limited diffraction.
Or that they guarantee me at least a limited diffraction with a previous analysis of the optics.
Regards;

J.Tapioles

Benach

A guarantee is worthless unless you have a qualified test report and/or an independant test report. I have seen mirrors that were sold as 1/10 lambda PV that came out as 3 lambda PV when I tested them. I have also seen mirrors that were as spec'ed. This is independent of the brand, nor the price. So the best way to solve this: buy a mirror and ask someone independent to test the optics.

pastorgalactico

Hello;
http: //r2.astro-fore...m/index.php/de/
I do not know if it will be independent, because it analyzes mirrors and TS telescopes in Germany.
I can also ask a friend of mine, who understands a lot of telescope optics that he will analyze in the mounted telescope and if the optics are not good, I can return the optics to TS.
Regards;
J.Tapioles

Benach

My Spanish is not as good as it used to be. Can you please post in English and English only?

pastorgalactico

Hello;

Sorry, but I'm Spanish.

TOMDEY

Good stuff. The most common, and most devastating aberration is Astigmatism... because it's RMS/PV ratio is the highest, aka a little of it degrades things a lot. Daniel Malacara and I did a joint paper "Telescope Quality - How Good is Good Enough?" about 25 years ago. I examined Spherical (sic over or under correction) and he looked at high-freq stuff. Our conclusion was that a smooth wavefront that is well-corrected, Will perform well. Also found that for ground-based astronomy, large (especially Very Large) scopes, can be less perfect, and STILL blow the socks off of smaller scopes. If one has the luxury of a good AC interferometer... any scope that can fluff onto one single fringe (that is, the light or dark part of one fringe fills the pupil)... that scope will perform magnificently and test well. BY FAR, the most common failure is axial astigmatism, next most common is spherical. The ONLY commercial scopes that we tested as Very Good, back then... were Questars (both 3.5 and 7)! They had a blush of Trefoil, and nothing else significant. The other ~Big Two~ SCTs... were pretty terrible. I believe that was the era of iffy SCTs, and trust modern ones are decent.  Tom

pastorgalactico

Hello;
I have reserved this mirror and have if the experts see this decent mirror with these data.

TOMDEY

That computer output: Notice that he has removed all the astigmatisms and comas and applied a conic target of -1 and normalized to surface (not wavefront) by applying the half-wave per fringe. (I'm assuming the test is COC single-pass, not AC, which would have targeted a conic K = 0.) The low order coma IS valid to remove, because that is corrected when the telescope is aligned in-use... but removing the low and high-order astigs and high order comas... is NOT valid, because these WILL be seen in use. I might be missing something regarding the test set-up being different than what I am imagining. Notice that the "3-D" graphic is completely symmetric. That is BECAUSE the comas and astigs have been removed... all that's left are the spherical aberrations. Other stuff (that could be in there) has been filtered out of the analysis. The best tests (AKA what you see is what you will get in use) would be autocollimation, with only tilt, focus and primary coma removed, reporting wavefront at the use wavelength (typically around 550nm) . The central obstruction makes me suspect this might be an AC test, but then the targeted K = -1 would have been zero.  Is a sketch of the test configuration provided? Tom

pastorgalactico

Hello;

I do not understand what he means.
I could explain it without so much technicality.
Thank you very much.

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