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# P-V, RMS, Strehl #s

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### #1 PKDfan

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Posted 26 January 2021 - 11:00 PM

Hi all, I have seen some numbers recently that have me scratching my head in confusion.
The examples that I have seen in one instance are .13 p-v,.012 rms and a Strehl of 99.2. The other was .183, .024 and a 98 Strehl. It was my understanding that for a very high Strehl # you had to have a correspondingly high peak to valley number also. The first examples p-v # was less than 1/7.5 lambda yet a 99.2 Strehl. The second was less than 1/5.5 lambda and yet a 98 Strehl. Also, if the rms # was so low then why was the p-v # not also low(high lambda)?
So confused, so anyone willing to help explain this discrepancy would be very grateful indeed!

Clear skies & Good seeing

### #2 ngc7319_20

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Posted 26 January 2021 - 11:20 PM

p-v tells you about the worst spot on the optic, whereas rms and Strehl tell you about the average errors.

So you can have a very bad p-v -- assuming a very small area is bad -- and still have a good rms and Strehl.

rms and Strehl are directly related, but p-v is not necessarily related to the other two.

If the worst errors cover a large area of the optic -- like spherical aberration -- you tend to get rms is about 1/4 or 1/3 of the p-v.  But if the bad area is very small, the p-v could be almost any big error.

Sometimes if the interferometer is not set up very well, you can get a few crazy high error numbers near the edge -- and hence a large p-v -- even if the optic is good.

Edited by ngc7319_20, 26 January 2021 - 11:31 PM.

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### #3 luxo II

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Posted 27 January 2021 - 01:07 AM

You might find this interesting, from test results of 128 catadioptric scopes 7"-12" aperture. The curves are least-squares fits in MS Excel and not surprisingly there's a direct correlation between RMS and strehl. Separate graphs for ALL, Celestron, Meade, Russian and Chinese.

The Russian examples are all Rumaks, the Chinese mostly Gregory Maksutovs and a couple of Mak-Newtonians, while the Celestrons and Meades are SCTs.

Apart from a couple of outliers below strehl 0.6, the Chinese appear to be getting close to the Intes glass for both quality and consistency.

Read what Lord Rayleigh actually wrote (https://www.cloudyni...d-rayleigh-say/)

"...we may consider that aberration begins to be decidedly prejudicial when the wave surface deviates from its proper place by about a quarter of a wave-length….” and "…In the case of perpendicular reflection from mirrors, ... no considerable area of the surface should deviate from truth by more than one eighth of the wave-length…”

This is unfortunately mis-interpreted by many to imply that optics with a wavefront error around a quarter-wavelength are "diffraction limited". He never stated that, as such.

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Edited by luxo II, 27 January 2021 - 03:21 AM.

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### #4 Pinbout

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Posted 27 January 2021 - 10:53 AM

Dick Parker has a couple of great vid's on his website you have to download...

but someone recorded his presentation and posted it on youtube

PV meauses the conic and how well it fits within the shell of tolerance of the conic... +/- whatever fraction of a wavelength of light.

### #5 ngc7319_20

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Posted 27 January 2021 - 11:44 AM

You might find this interesting, from test results of 128 catadioptric scopes 7"-12" aperture. The curves are least-squares fits in MS Excel and not surprisingly there's a direct correlation between RMS and strehl. Separate graphs for ALL, Celestron, Meade, Russian and Chinese.

These are very interesting tests!  Are they written up somewhere?

### #6 PKDfan

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Posted 27 January 2021 - 07:55 PM

Thank you very much NGC7319_20, luxo II, Pinbout for your informative posts! I will check out thoroughly the links to fill in my gaps in knowledge.
I did realize that it was an average error vrs worst error thing, it just seems fishy that you could have such a perfect optic and have such a mediocre p-v #?!?
I am also curious that such a low rms # could be derived without some regard to the error of the interferometry setup being mentioned. .012 rms is 1/83.3 lambda and the average error in a Zygo without a custom calibration is what..1/50 lambda? Its difficult to reconcile these #'s to real world realities.
I will slog through some more optical theory and peer deeper into W. Rohrs information heavy reviews at astro-foren.de.
Many thanks again folks!!

Clear skies & Good seeing

### #7 ngc7319_20

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Posted 27 January 2021 - 08:20 PM

Yes Wolfgang Rohr has excellent info...

### #8 Pinbout

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Posted 27 January 2021 - 08:44 PM

just seems fishy that you could have such a perfect optic and have such a mediocre p-v #?!?

You can’t

### #9 ngc7319_20

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Posted 27 January 2021 - 09:08 PM

Your two scopes are shown by the star symbols at the lower left.  The p-v are a little higher than the overall trend, but they are not crazy high.

The other fact to note is that there are almost no other scopes on the chart with Strehl ~>0.98 for comparison, so it is a little hard to know what happens in that corner of the graph.

Edited by ngc7319_20, 27 January 2021 - 10:53 PM.

### #10 luxo II

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Posted 27 January 2021 - 09:56 PM

I know of 2 Intes Rumaks above 0.98, and I have the DPAC test certificates. One being my 10”, with strehl 0.984 and P-V at 0.09 wave another being an 11” with P-V at 0.10 wave.

With P-V close to 0.2 strehl is likely somewhat overstated.

Edited by luxo II, 27 January 2021 - 11:49 PM.

### #11 hamishbarker

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Posted 28 January 2021 - 03:24 PM

I highly recommend that the OP read Star Testing Astronomical Telescopes by Suiter (if he can find a copy now that Willman Bell is no longer trading). A great and approachable treatment of the subject.

### #12 PKDfan

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Posted 28 January 2021 - 05:02 PM

Hi hamishbarker! Yes I would love to get my hands on a copy and went to Willman-Bell to order a copy and discovered(here!) that they went under. Then went to amazon and found that some clowns wanted over 500\$ for a copy!! Hahaha

So pinbout, do you agree then a 99.2 Strehl number is not consistent with a less than 1/8 wavelength?

These are real world numbers that I distilled from recent posts and I found it odd that the numbers did not seem to add up and its frustrating because its what everyone wants, a reliable test with solid numbers and with one of the best, a Zygo, it seems to be possible to manipulate the data, that any number is possible. That is a crying shame! Everyone then, even if you have a 'report card' it behooves you to do a startest and find out for sure. It very well could be true but in my honest opinion it could very well NOT be.

Trust but VERIFY!

CS & GS
Edit: fixed quote

Edited by PKDfan, 28 January 2021 - 06:11 PM.

### #13 ngc7319_20

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Posted 28 January 2021 - 05:43 PM

...do you agree then a 99.2 Strehl number is not consistent with a less than 1/8 wavelength?

I don't believe one can decide whether a given test result is "consistent" without testing the lens.  There is some distribution of p-v.  A few scopes with high p-v and high Strehl are possible and perhaps expected.  Of course, those are the ones that stick out.

I absolutely agree the owner should verify the test by as many methods as possible.  That is the ideal situation -- high Strehl interferogram and perfect star test in the field.

"TRUST but verify" or in the Russian from which it came "Doveryai, no proveryai."  Yes thats exactly how to handle test results.  Verify!

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