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Wavefront error of optical system?


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I am tying to look for advice from someone who is well versed in telesope optics, particularly when it comes to newtonian reflectors. I have a keen eye set on OO uk for a VX range OTA. I have skoen to Barry about several issus and he was very helpful with answering most of my questions, but I felt that he was somewhat bussy, and the line at times was not too clear. So I thought it might be worth a shot to shoot my questions here as well.

Barry uses a zygo interferometer that works at 632.8 nm. He measures the wavefront error at the centre of radius of only the primary mirror.

Here is the thing, from the optical texts I have read up on, I have noticed that the minimum figures one wants to aim for when it comes to optical quality is 1/4th P-V wavefront and 0.08 RMS wavefront, as measured at the focal plane. Barry does not measure at the focal plane but the centre of radius. I do not think there is a difference between the measurements whether taken from the centre of radius or the focal plane, but would like to know what you the readers know. Would there be a difference in the results?

Secondly, I have also read that the wavefront errors of the secondary mirror, can sometimes cancel out or add up with those of the primary, and that is why it is paramount to take the measurements at the focal plane of the system (I presume the complete optical system, including both the primary and secondary mirrors). Examples are given in the text, where in one of the worst case scenarios, if the P-V wavefront at the secondary surface is 1/5 wave, and that of the primary was 1/5 wave, then the two would add (not cancel out in this instance) 1/5 +1/5 = 1/2.5

This is not good, as a primary mirror quoted to have 1/6 (for instance) wavefront may not at all have this (when coupled with the secondary mirror), and could be way worser or better off at the focal plane of the optical system. From my correspondance with Barry, I was under the impression, that the RMS wavefront measurments cannot be combined from the two mirrors in this way, but the surface P-V wavefront measurments can. Would this be correct?

Thus, would it also be correct in assuming that when the RMS wavefront measurment is taken (of the primary mirror) at the centre of curvature, this can be taken as the RMS wavefront measurment at the focal plane regardless of the surface smoothness of the secondary mirror?

Last but not least. A question about wavelengths. The zygo interferometer uses 632.8 nm red laser, whereas the human eye is sensitive at 550 nm (green to yellow). So a 1/6 P-V wavefront at 632.8 nm would be equivalent to a maximum error difference of (1/6) X (632.8 nm) = 105.5 nm

Thus, at 550 nm, the P-V ratio would be (105.5 nm)/(550 nm) = 1/5. Note that 1/5 > 1/6. So the error quoted at 632.8 nm is actually only about 90% of the error that would be seen at 550 nm (the wavelength that matters most to the eye, when it comes to sensistivity). Barry had informed me that the wavefront measurments could not be scaled like this, but did say that the comparison would be about 90% at 632.8 nm from the wavefront readings at 550 nm. Interestigly though (maybe by coincidence) when I divide 1/6 by 1/5, I get 0.83 which could easily be rounded to 90%. I am not sure whether he was reffering to the RMS wavefront that could not be scaled in this way, or the P-V wavefront, or possibly both. Could someone shed some light on this please?

I have a booked titled "Advanced Amateur Astonomy" by Gerald North (2nd edition 1997). In it, I qoute;

For a two-mirror reflecting telescope a 1/4 wavelength error at the focal plane means that the error at each reflection is limited to no more than 1/8 wave (we are assuming that the errors add, it is possible that the errors could cancel out). Worse, the wavefront error produced at each reflection is twice the innacuracy in its surface. In other words, for a 1/4 wave error at the focal plane each reflecting surface should be accurate to better than 1/16 wavelength (about 30 nm). Even then, the performance of the telescope is still much less than perfect.

Telescopes are commonly advertised with '1/8 wave' or '1/16 wave' optics. It is rarely stated whether this figure refers to the wavefront error at the focal plane or the accuracy of the surfaces of the optics (it is usually the latter, though the focal plane error is the one that really counts). Even then, there are a number of ways this figure can be calculated (maximum deviation from perfection, average deviation from perfection, r.m.s. error, etc). The r.m.s. value ought to be no more than 0.08 wavelength as measured at the focal plane to ensure reasonable optical quality.

Also, manufacturers are sometimes coy about revealing the wavelength of light against which these accuracies are measured. After all, the wavelength of red light is 50% greater than that of violet light! The 1/4 wave peak-peak (I think the author here, meant peak-valley) or the 1/12 wave r.m.s. values that are desired are for a wavelength of 5X10-7 m (500nm) which is in the yellow-green part of the spectrum.

So there you go folks. Pretty self explanatory. Barry's secondary mirrors are at 1/5 P-V wavefront (I presume taken at the surface, as thir focal length would be infinity, if I am not mistaken). Thus, if I chose a 1/10 P-V wavefront 'Ultra' Grade primary mirror (taken from the centre of curvature which I am told is the same as taking it at the focal plane (the focal plane being half that distance)) and a 1/5 P-V wavefront secondary, then according to the above text and logical reasoning, the P-V wavefront error at the focal plane calculates to (1/10)+(1/5)=3/10. This is assuming that the errors are being added, being unlucky in the exact placement of the mirrors in the tube. (3/10)>(1/4). So for paying for the 'ultra' upgrade, a '1/10 wave' primary mirror, I could end up with a P-V wavefront error (calculated at the focal plane) possibly being worse than the accepted minimum optical quality (1/4 wave)! Based on all that info, am I missing anything? Is what I have just done, correct?

Barry mentioned that the standard grade of the VX6 OTA had a primary mirror of no more than 0.03 - 0.04 RMS wavefront, as measured at the centre of curvature, using the 632.8 nm wavelength. Should I scale this figure down to 550 nm as I did with the P-V wavefront above, and should I also add the RMS wavefront error of the sencondary mirror (adding in the unlucky case of mirror placement) to the primary as I did for the P-V wavefront errors above?

And what did the author mean in the quote (noted above) when he said?

Worse, the wavefront error produced at each reflection is twice the innacuracy in its surface. In other words, for a 1/4 wave error at the focal plane each reflecting surface should be accurate to better than 1/16 wavelength (about 30 nm).

Anyway, I know that was a bit long, and wish I could have shortened it, but as many of you know, telescope optics is not always a quick topic, especially when it comes down to finding and buying a really reputable, high qualtiy instrument. And I really want it to be a newtonian reflector this time round, as they are real easy to collimate and easy to repair, and simple to adapt. Plus the optics can be recoated at a reasonable cost. A NR is excellent when it comes to low maintinance.

I really am interested in hearing anyones' thoughts and insights into this annoyingly complex and controversial subject, as these grey areas in marketting really needs to be ironed out and safegaurded for the keen amateur astronomer in my opinon. To say this is confusing for some, is an understatement!

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Some comments, but not a complete reply.

First, Orion Optics quote wavefront errors, not surface errors (so do not double), They are quoted for red light so you can scale up by about 20% for green. Their mirrors are good and the certificate they supply will give you the strehl (the only figure you need worry about) for the main mirror, which is usually well in excess of 0.9 (0.8 generally considered to be diffraction limited). I know of no issues with Orion secondaries. The mechanics have been improved over the years and are definitely repairable and upgradeable (though Orion parts are not cheap). There are many happy owners of Orion Newtonians and I think you would not be disappointed if you were to buy one.

If I was buying new again, I would buy one of their longer focal length models.

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My understanding was that P-V difference was the old fashioned way of measuring surface deviation (as in when I was a boy), now people tend to prefer Strehl ratio with 80% being considered accurate

The problem as i understand it is that while P-V gives the maximum deviation peak to valley from desired curve it doesn't give you information about the average roughness - your 1/4 wave mirror may have one bump of that P-V but your 1/5 wave may have a surface like a waffle with many peaks and vally's. So it could be said that there is a bit of ambiguity creeping into the definition of P-V, whereas the Strehl ratio gives an overall picture

Further if you consider modulation transfer function (MTF) then the total MTF of a system inc mirrors, lenses, collimation,eyepieces, seeing, bad weather is given by

MTFtotal = MTFperfect(MTF1/MTFperfect)x(MTF2/MTFperfect)...x(MTFn/MTFperfect) so the total MTF is the product of all degradations (ref : Harold Suiter 'Star Testing Astronomical Telescopes)

(if you look at any of the digital camera technical forums you will see that the discussion always revolves around MTF of the system inc lens and sensor)

There are some telescopes that are designed specifically that one mirror corrects for another (but by design not by accident)

eg Stevick-Paul which is close to perfect http://bhs.broo.k12.wv.us/homepage/alumni/dstevick/stevpaul.htm (I started building one years ago but haven't got past the primary :embarrassed: )

and the Yolo which even has a mirror warping harness http://bhs.broo.k12.wv.us/homepage/alumni/dstevick/yolo.htm

see http://bhs.broo.k12.wv.us/homepage/alumni/dstevick/weird.htm for many weird designs

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I have had several mirror from OO and all have been excellent. In a Newtonian the primary mirror has the most impact on the image quality. The combined errors of the primary and secondary are not simply addative as the secondary is much closer to the focal plance and has less imapct. Unless you are after high resolution planetary/lunar imaging then there is no need for the very best optics as seeing will dominate the image resolution.

Regards Andrew

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I have had several mirror from OO and all have been excellent. In a Newtonian the primary mirror has the most impact on the image quality. The combined errors of the primary and secondary are not simply addative as the secondary is much closer to the focal plance and has less imapct. Unless you are after high resolution planetary/lunar imaging then there is no need for the very best optics as seeing will dominate the image resolution.

Regards Andrew

It's nice to have great optics, but the final part of Andrews post is so very relevant.

The state of the atmosphere is usually the limiting factor. Most nights a bog standard skywatcher or similar will give results that are as good as a premium scope.

Only on excellent nights with a steady atmosphere will the premium optics perform at their best.

Not putting down top notch optics at all, if astronomy is your passion, then it's very nice to know you have the best, and on great nights it will perform.

Regards, Ed.

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Thanks for the feedback people. It feels like I might still be living in the old days. So I started looking deeper now into the newer techniques of rating mirrors, and I think I am starting to understand this now, particularly how the RMS and the consequent theoretical strehl figure is derived. It also made the interferometry-example-report on the OO webpage easier to understand, coupled with the short explanantion provided. The four best link pages I have found on this topic concerning rating telescope optics and ways of testing the performance of such optics, I have included below. I find them very self explanatory if you go through them slowly, and hope they can benefit anyone else who wants to understand more about how their telescope optics are rated.

http://www.nicholoptical.co.uk/The%20Testing%20of%20Astronomical%20Telescope%20Optics.pdf

http://www.rfroyce.com/standards.htm

http://www.rfroyce.com/testmethod.htm

http://www.bbastrodesigns.com/ratemirrors.html

The third article also answers my question about accounting for the wavelength difference between the He Ne laser of the zygo to a more meaningful wavelength of 587 nm of the d line in He. You simply multiply the difference factor (here being 1.078) to the RMS wavefront taken at the 632.8 nm wavelength. Some have said in my investigations that the values can not be scaled like this, and some others have mentioned you can only scale the surface P-V value. It is interesting to note that the author of the article is using an interferometer that is measuring the RMS wavefront, that would be based on the P-V values at the centre of radius.

As I feel I should say again, these four articles listed above have been incredibly helpful to me in my investigations, not to mention the great explanatory reports on the OO uk website about P-V errors, coatings, testing, e.g. interferometer reports (that are explained, etc.).

So I hope this post saves some people time and a headache when they choose to delve deeper into this maze.

Again, thanks for the input everyone, and to OO uk for their helful explanations on their website.

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The other thing to remember is that it's not just about wavefront figures like p-v and rms strell etc Other optical issues can have a big impact on the telescopes performance .Defects like a turned edge and primary and micro ripple can be present on a mirror with good rms and strell figures and ruin it's performance ,so you need a smooth surface figure as well.

Also i'm not a fan of computer generated interferograms ,especially single ones ,i like to see several and peferably some photographic ones as well as zygo, to measure the fringes for yourself .But each mirror maker has their own methods .

Like previous posters have pointed out here in the uk the telescope is alway's likely to be seeing limited which means anything over 10 inches apeture is likely to be seeing limited.

However better accuracy will still be desirable even in less than ideal conditions ,up to a point ,as it can become the law of diminishing returns ,and merly bragging rights .

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The state of the atmosphere is usually the limiting factor. Most nights a bog standard skywatcher or similar will give results that are as good as a premium scope.

Only on excellent nights with a steady atmosphere will the premium optics perform at their best.

Regards, Ed.

Very true- and easily proved. Just look at any bright star at high magnification, if it's 'dancing around' a bit then that dictactes the size of your image circle for the session- and not necessarly the quality of the optics. Nights of good seeing and high transparency are very few and far between in the in the UK I can't remember that many good nights last year (maybe two?). Given that is the case the money spent on a premium mirror might be better invested in more apperture? Although, as has also been said said it's nice to have the best kit too!

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RayGood, what scope have you got at present ?

I have a number of scopes aquired /assembled over the years an astrophysics 180 EDT a 10 inch f8 newtonian with zerodur optics and an optical window made by the sinden optical company

and a 16 inch f6 f 15 naysmyth cassegrain /newtonian optics by sinden optical company on an equatorial fork the 16 inch primary is 1/30th wave measured by null testing /interferometry sindens mirrors are some of the best worldwide and expensive with the reflector projects i started out with the optical specs and layout i wanted then got the best optics i could afford first as the mounting and tube assemblies can always be upgraded /improved as time /money allows ,as russell porter said ( the mirrors the thing)

But i started out with a topic 3 inch refractor which i still have.

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To White Dwarf.

I have none at the moment. Last year, I had sold my SV90T Apo Raptor (630mm fl at f/7). I am wanting a top end reflector (newtonian) now. I used to have one yonks ago. I love the design and easy maintanance of the bog standard reflector.

I also understand why many are not so fussy when it comes to near-perfect optics because of seeing conditions. That's fine. But I, like some others like perfection, and when there is a rare, steady clear night, I want my optics to perform as top dancer, especially when wanting to do spectroscopy, high res. imaging, etc. But of course, everything within a budget. And plus, it feels great to have top-end optics! Hence the triplet APO I used to have.

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Ray - If you want perfection then you need to go for a zero expansion ceramic mirror e.g.Zerodur as even pyrex and the like can't hold a "perfect" figure as the temperature changes. You will also need to ensure you can remove the boundary layer of air just above the mirror surface as well as all intrusive tube currents.

Andrew

PS I had OO make me a 300mm Zerodur mirror. I think it was the first they ever did.

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Ray - If you want perfection then you need to go for a zero expansion ceramic mirror e.g.Zerodur as even pyrex and the like can't hold a "perfect" figure as the temperature changes. You will also need to ensure you can remove the boundary layer of air just above the mirror surface as well as all intrusive tube currents.

Andrew

PS I had OO make me a 300mm Zerodur mirror. I think it was the first they ever did.

Even a zero expension mirror needs to be kept very close to ambient temperature, with fans for larger mirrors, otherwise air currents will disturb the image.

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I just googled Sinden Optical, have to say their website isn't particularly useful.

http://web.onyxnet.c...et.co.uk/M1.htm

Ufortunatly the sinden optical company dosen't deal with the amatuer astronomical community any more .The website is old and not updated they only deal with professional observatories nasa and specialised optical companies these days , since the death of the companies founders david and helen sinden .two of the nicest people i have been lucky to know.

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To White Dwarf.

I have none at the moment. Last year, I had sold my SV90T Apo Raptor (630mm fl at f/7). I am wanting a top end reflector (newtonian) now. I used to have one yonks ago. I love the design and easy maintanance of the bog standard reflector.

I also understand why many are not so fussy when it comes to near-perfect optics because of seeing conditions. That's fine. But I, like some others like perfection, and when there is a rare, steady clear night, I want my optics to perform as top dancer, especially when wanting to do spectroscopy, high res. imaging, etc. But of course, everything within a budget. And plus, it feels great to have top-end optics! Hence the triplet APO I used to have.

Hello ray

Having previously posted on this thread i understand where you are coming from so to speak . The problem is who do you source your high end optics from in the uk ?

The best maker of high end optics was the sinden optical company recommended to me by jim hysom formerly of A E optics another maker of superb optics . jon owen another good optician former employee of AE OPTICS AND E S REID also former employee of A E optics .

Jon nichol, of nichol optical may be able to produce optics of the calibre you wish have a chat with him !

Orion optics uk can produce a good but not great mirror caveat emptor ask them to produce you a mirror on zerodur or quartz substrates beyond 1/10th wave as this accuracy on any other substrate is possible but suspect .Give them a specification of surface /waveront accuracy , then say you will have it verified by the national physics laboratory loser pays the fee's .

That is to say their optical quality is variable and inconsistant so both good and bad . But you do tend to get what you pay for As an example my 16 inch zerodur primary mirror in 2002 the mirror blank cost £2000 the finished mirror to 1/30th wave £8000 the cost of accuracy !! will a quarter wave mirror out perform it ? no i doubt it even in the worst seeing conditions . if yes then why do expert opticians even bother to try ? look through a telescope with high accuracy optics and their is a difference ! is it worth it ? only you can say.

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Orion optics uk can produce a good but not great mirror caveat emptor ask them to produce you a mirror on zerodur or quartz substrates beyond 1/10th wave as this accuracy on any other substrate is possible but suspect .Give them a specification of surface /waveront accuracy , then say you will have it verified by the national physics laboratory loser pays the fee's .

That is to say their optical quality is variable and inconsistant so both good and bad .

What evidence do you have for these claims about OO optics? Have you measured any of there mirrors and if so how?

Regards Andrew

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Theres quite a lot there to answer folks. I can not answer all though as I do not have all the answers.

Going for low expansion pyrex bases and/or using quartz, is going to push the costs beyond my budget. This is why, within my budget I am trying to establish, by reputation and admittance by each manufacturer, measured numbers for their produced mirrors. I had originally set my sights on SW optics, but to my dismay and frustration, syntec would not relay the technical performance minimums for their mirrors. That is what OVL had told me. Naturally this raises alarm bells for me. This is also what optical texts warn of. OOuk seem after all, not afraid to divulge their typical performance results of their mirrors, and are happy to produce higher minimums for their mirror performance if the customer is willing to pay for the upgrades. I naturally wanted to look into the modern techniques then, of how OOuk manufacture and rate their mirrors, like using the zygo interferometer, etc. After my research, as summarised above, I was happy with what I had found out. Their minimums was also in accordance to what modern texts recomend, such as the wavefront errors, rms, strehl, etc. These minimums OOuk gaurentee. If the text books state these minimums and I am givern the option to upgrade to even better standards, such as "research" and "ultra" grade, then I am happy with that. So when the seeing conditions permit and in dark sky locations (to which I am located near to) I can get the best out of my instrument.

So, I guess what I am trying to say here, is I am trying to find the best optics that my budget will allow for. This is the same aproach I used with SV optics in the US when I purchased my original triplet APO.

I have never owned or tested the performance of any OOuk mirrors. This is why I have conducted the research that I have, as well, direct communication with OOuk. I liked the conversations that I had with them (time permitting of course) as numbers and figures were not held back or techniques. I was a bit clued at first with a lot of these modern techniques now being employed in the manufacture of mirrors, but after looking into these very techniques, I very quickly gained an understanding as to what was meant by them. When it comes to reflectors, I was an old buff, going on the old rating techniques and the common method of rating mirrors was, such as surface P-V, as well as the still used rms ratings. Strehl, was not so much talked of back then, as the techincal ability to measure the wavefront areas in a "integral sum" fashion was very new, and the equipment very expensive to do so. I also like very much the interferometer reports that are issued with each mirror for OOuk. And they are not just derived from a few measurments, but are taken hundreds of times and averaged out, to minimise any measurment errors. This is in a way, a proof or a gaurentee report of sorts, where, if I am not happy with the optical performance, I can have the mirror independently tested on a optics bench and can then try to confirm the report if I feel the optics are suspect. Most lower end OTAs, you can not do this with, as you do not have any base refference report by which to measure by (i.e. the manufacturers claims of the optics when dispatched).

Going soely on first light reports and comparison reports by differeing persons, is not such a sure method when it comes to demanding high standards. Such reports are very helpful though to an extent, but they all ultimately come down to time permitting, seeing conditions, age of optics being compared to, condition of one's eyes, etc. etc. If one needs more accuracy in a report, then I think it has to ultimately come down to mounting the mirrors or lenses on the optics bench!

This accuracy is what I am looking for in a medium priced OTA. OOuk is the best out there when it comes to producing these standards that I have found so far for not just the amateur, but also for serval proffessional bodies that they supply their "research" and "ultra" grade optics to. I do not see syntek publishing such figures or mentioning univerities, labatories, etc. purchasing their optics. I want everyone here to know, I am not putting down syntek optics or mechanical equipment. I am just saying that for my requirments, within my budget, I am trying to find the best I can.

Any suggestions of companies coming out with similar claims to OOuk similar to their price range, I welcome. But I also would prefer to purchase otpics and OTAs manufactured in the UK (as OOuk do) to help support our economy and the private sector to. And thats just a personal prefference. Sometimes it is not always possible, but I like to do my best. So I was pretty chuffed when I looked at OOuk and enquiring about their manufacturing techniques and standards by which they claim to work by.

At least I know that if and when I settle on an OTA from OOuk, and feel through multiple testing sessions and employing a ronchi grating test (say like the one OOuk supply having 250 lines/inch), testing the theoretical resolution through AP electronic imaging, etc., that the optics are suspect, I can have an independant report done, and if the report is worse than that issued buy OOuk, I can then have it sent back with that report for OOuk to check out, re-test and make any corrections or faults that are there. I think that would be somewhat more difficult to do with a low-end budget OTA that also does not issue detailed test reports for the optics, especially if you are seeking higher than standard minimum performance from an optical set, that the manufacturer can claim whatever figures is an "acceptable minimum" (figures that they refuse to publish for what ever reason!).

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What evidence do you have for these claims about OO optics? Have you measured any of there mirrors and if so how?

Regards Andrew

Hi andrew yes i have tested two orion mirrors a 10 inch and a 12 inch. by the only test method availiable to me namely star testing and a star test using a ronchi grating eyepiece , and although the test is a bit subjective they were good mirrors never said they were not They appeared to be as claimed in the test reports ,but they did exibit faults typically found in mass produced commercial mirrors that of a narrow turned edge .The other problem is that of some roughness which i have not seen directly myself because you can't (but see the surface plots) but has been reported by independant tests using lyot phase testing . Would i buy one yes i would .

All i said that if i were buying an ultra grade mirror i'd like a bit more than a single computer generated test report . a simple focugram shows you a lot namly the turned edge and surface roughness which could be confirmed by lyot phase testing but optical metrology is expensive to set up and would probably increase the cost of the mirror.The other thing i would say is that their test reports on some mirrors again independantly tested have tested out to a higher figure than orion claimed ,which is a good thing .

I also think that they are to be applauded for trying to give their customers and prospective customers confidence in their product by producing a report rather than just saying all our mirrors are guarranteed diffraction limited which is what we had in the past .

You seem to get what you pay for from them maybe better , it;s easy to get hung up on the numbers what counts is what you see at the eyepiece Thier are no perfect mirrors in this world. Testing aside the lunar and planetary views were very good .

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I would just like to say thankyou very much for the links to those test reports Star Forming. They will be very useful in helping me to decide. And to Nebula, thankyou for your personal experience and input to the OOuk OTAs you own. They sound as if they meet your expectations.

May I ask Nebula, have you written any first light reports or reviews of the OOuk OTA reflectors that you own? If so, could you please direct me to those pages, as I would be very interested to read up on what you had to say about them?

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