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Ajohn
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Baker Reflector Corrector help
      #5661743 - 02/04/13 01:06 PM

It sounds like this could correct an F3 parabolic mirror over a much wider field than I need. The design is in ATM III but uses old glasses. Modelling them is too inaccurate and leaves far too much for me anyway to correct.

It seems that some one called ?? Gregory sorted this out for modern glasses but I can't find any info on the web. Maybe some one has details?

Failing that full 6fig 3 colour RI's for these glasses would help.

Rolled ophthalmic crown C-1 523586
Dense flint DF-2 617366
Crown BSC-2 517645

It seems that the extreme blue with these glasses is not too good so visual wavelengths would be best.

With these figures I may be able to work out modern glasses for one element at a time.

The field angle seems to be huge - a plate covering a 50% obstruction.

John
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DAVIDG
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5661773 - 02/04/13 01:22 PM

The glass is Bausch and Lomb material. You can find the data at Bob May's website http://www.webring.org/l/rd?ring=telescopemaking;id=16;url=http%3A%2F%2Fbobma...
By the way we have one of these correctors for use on 24" Tinsley Cass. The Cassegrain front end assembly is removed and the Baker Corrector swapped into place.

- Dave


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Ajohn
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Re: Baker Reflector Corrector help new [Re: DAVIDG]
      #5662953 - 02/05/13 06:27 AM

Thanks for the link.
I missed a comment in the article - optimised for blue light - but he also implies that it's ok for white. So far either r g or b can be diffraction limited over a 5x4in plate film on a 20in mirrored scope with a 17in corrector. It covers a semi angle of 2 degrees. I thought that this was rather spectacular for 3 pieces of glass and a mirror.

Going to play some more though as the focal length doesn't come out correctly so may have made a mistake working out the spacings. Also I suspect that the corrector needs more orders than olso's sliders can give. Unfortunately he only give a sag for the base curve rather than a direct radius. That's +0.00174in and variations in the other digits may have an effect.

John
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DAVIDG
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5663163 - 02/05/13 09:39 AM

We used the Baker Corrector with 7" x 7" Kodak 103 glass plates.The last time it was used was for a NASA project for Halley's comet back '85-'86 The images were sharp because the sensitivity of the glass plate matched that of the color correction of the Baker design so the unfocused light wasn't being recorded. With modern day CCD's one would have to image thru a filter since the chromatic aberration would be recorded and the star images would be bloated badly.

- Dave


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MKV
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5663377 - 02/05/13 11:09 AM

Quote:

Also I suspect that the corrector needs more orders than olso's sliders can give.



Please post the design. I don't have time to look for my ATM books.


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Ajohn
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Re: Baker Reflector Corrector help new [Re: MKV]
      #5663779 - 02/05/13 03:28 PM Attachment (48 downloads)

This is the design as near as I can get it to the aricle. Oslo doesn't come up with the correct focal length without the rad on the 1st surface. Only problem there is if I play around after setting that rad and then reset everything back to how it was the focal length sometimes doesn't go back to what it was.

Somehow I think that there is something amiss with the numbers in the article but I have managed to get distinct r g b focuses that can be bought onto the focal plain one at a time via the corrector. There seems to be a colour focal length problem with it - spots can be ok but can't all come together.

He mentions the nearest curve to the aspheric having a 0.00174in sag and hand figured from a sag of 0.002in. The aspheric should be on surface 1. I've had similar results with it on 2.

If anyone can get it fine in white same or ordinary cheap glasses please post the len file.

I'm switching to a windows laptop as I'm bothered by things not resetting as they should.

John
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Ajohn
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5665510 - 02/06/13 03:26 PM Attachment (19 downloads)

There seems to be errors in the rad's he gives for the achromat. Having a better idea now of using the sliders on the schmidt type plate I managed this. Who has a ccd camera with a 5in diagonal chip?

One problem though. The vacpan spread sheet runs perfectly on my libreoffice spreadsheet program but it uses a different type of aspheric constants to olso edu. How do I convert from one type to the other?
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MKV
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5666360 - 02/07/13 01:24 AM Attachment (15 downloads)

John, you got as close as possible I believe with the original design. I simply departed form it, split the lens, changed some spacing and the second radius of curvature and optimized the aspheric surface. You can remove the small residual of coma by refiguring the primay to a conic = -1.019, reducing the corrector to mirror distance to 80.2 instead of 81 inches, and refocusing by -0.0017 inches.

Mladen

Edited by MKV (02/07/13 01:40 AM)


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MKV
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Re: Baker Reflector Corrector help new [Re: MKV]
      #5666380 - 02/07/13 01:43 AM Attachment (16 downloads)

and here is the configuration adjusted for coma as described above.

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Ajohn
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Re: Baker Reflector Corrector help new [Re: MKV]
      #5666659 - 02/07/13 08:56 AM Attachment (24 downloads)

The trick to balancing it seems to be the basic curve of the corrector and the achromat. The achromat must have some positive power to flatten the field. It's all a lot to play with.

I stuck with the cemented achromat as 2 less glass surfaces. If I have done my sums correctly 0.001in on the focal plane is just under 0.05 seconds. Pretty impressive at 1.75 degrees.

He points out it's most suitable for 12in plus primary mirrors. I quickly looked at 220mm using BK7 and F4 but the back focal length is too short to get it to the outside of the tube for a dslr. I'm going to try reducing the back focal length from the lens and using a diagonal.

If it works out even more encouragement to try and make an F3 to F15 cassegrainian.

The oslo file is attached.

John
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MKV
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5666778 - 02/07/13 10:20 AM Attachment (16 downloads)

With the glass Baker used you can't really get much improvement in the polyshcormatic spectrum, save for cosmetic touch-ups. Lateral chromatic aberration is huge, which is why Baker intended the scope to work in the blue and violet end fo the spectrum only, using 103 F film (which was the standard astronomical emulsion).

As DavidG mentioned, that emulsion recorded only a narrow spectral range of colors and was "blind" to all others. It was essentially monochromatic photography. With slight readjustment in the aperture stop to mirror distance to 82.4 inches, practically all residual coma at 0.4863 m wavelength disappears, and you have an essentially perfect photographic telescope covering 3.5 in the Baker's original configuration. So, there's no need to change anything as long as oyu stay in the intended blue-violet spectrum.

The real problem is not in the design but in recording such a huge field with today's technology. As you already observed, who's got a 5 inch CCD sensor to cover this field? Even a 12-inch version would required a 3-inch sensor. Baker's reflector Corrector was designed to work with large professional astronomical glass plate emulsions of yore on systems that are simply not feasible anymore. Today's most expensive 2x2 inch processors will cover only 16% of the FOV area. Is that "progress"?


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Ajohn
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Re: Baker Reflector Corrector help new [Re: MKV]
      #5667222 - 02/07/13 02:46 PM

Playing around I had it so that any of the 3 colours could bought onto the focal plain while playing with the corrector plate constants the wrong way. Setting for sa seems easier than trying to use the ray intercepts. I need to find a tutorial on the meaning of the intercepts. There was one on the web but it seems to have gone.

One thing I would like to know MKV is your view on the ideal base rad for the corrector. I notice you have used one that doesn't have the sag mentioned in the article. He describes the lens as a weak plano convex with a focal length of about a mile that doesn't have much effect. Me well I find it does and it's best to get that right before attempting to do anything with the achromat.

People can still buy film for plate cameras. Roll film too.

John
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MKV
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5667693 - 02/07/13 07:14 PM

John, the lens as you have it has a focal length of about 1/2 mile. I assumed the NZ to be at the 86.6% of the radius and he actually wants his to be at 70%. That would certainly flatten the first radius quite a bit.

But if you want a pcx lens of 1 mile focal length (1 mile = 63,360 inches) you'll need a radius of approximately 39,000 inches.

I don't do slides, John. I let OSLO optimize the design for me. I just pick parameters. You need to review some of the optimization videos and articles. It will save you a lot of time. I let the program optimize the vertex radius and the deformation coefficients, and that's how I ended up with a much shorter radius on the corrector.


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Ajohn
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Re: Baker Reflector Corrector help new [Re: MKV]
      #5668355 - 02/08/13 05:40 AM

I've used opic a lot MKV. Not GENII though. I'm presented with a box of options with that one and no info so far on what each one does.

Sliders have there place for seeing trends but are very cumbersome to use as oslo comes. I recently read a comment by Ross ( I think ) "Missed because of the extensive use of computerised optimisation which just wouldn't do this".

I would love some links to good videos and web pages on this general subject but if they are there then they are rather hard to find. Oslo optimisation for instance brings up a page on the atmsite on edu and others on LT and premium. I have 1/2 hr every now and again looking. I'm surprised there isn't a list of links somewhere on the web. The atmsite has some but I have looked at those. One I found recently on there points out that the author lacks the experience to change genii parameters! So where are these web pages? I even tried youtube.

It's amazing to think that Baker probably came up with that initially using a SLIDE rule and experience that only a full time optical designer can acquire. I had my time with a slide rule but not on optics.

Also can you tell me what the correct rad would be for a 70% neutral zone? I spent some time with 6fig log tables at home in my youth so using the 70% doesn't surprise me. Less rays. Trouble is that I couldn't entirely get my head round what I was doing. More recently I tried reading Conrady.

John
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MKV
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5668752 - 02/08/13 11:15 AM

John, there is a saying you can lead a horse to the water but you can't make him drink it. I can't do your homework for you. You've been given enough hints to get to the water, but you'll have to do the drinking part.

First, you should have no problems finding help for OSLO optimization online. I just don't buy that you can't find anything.

Second, you need to learn some fundamentals about optics. Open a book such as Kinglake's Lens Design Fudamentals, or Warren Smith's Basic Optical Engineering, or even Rutten and van Venrooij's Telescope Optics, and read. If you don't understand the math then open calculus and geometry books.

Conrady is not light reading, so I don't recommend it. As for Baker, I doubt that he used a slide rule. Probably Conrady's equations. But even if he didn't, he could have retro-engineered the corrector by raytracing.


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Mike I. Jones
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Re: Baker Reflector Corrector help new [Re: MKV]
      #5668844 - 02/08/13 11:57 AM

I would also recommend downloading and giving Don Dilworth's "Synopsys" optical code a try. The fully functional version is available at http://www.osdoptics.com/, with the free version limited to 12 surfaces (compared to only 10 with OSLO). The interactive design tools in Synopsys are the best in the business, MUCH easier than OSLO, Zemax or CODE-V.
Mike


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Ajohn
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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5669299 - 02/08/13 03:45 PM

I have been thinking of looking at that Mike mainly as Olso's software standards don't seem to be too good. Being able to write code for it is useful though but I expect there may well be some hidden problems in edu otherwise some one with the right skills could make it work more or less as premium.

Telescope optics is too noddy to be of much use. One of the problems with the "next step up" is notation. There seems to be more than one standard and even where it's actually mentioned. There can be peculiarities eg something I looked at earlier today used a small p in an equation. Curious thing in this instance the text then talks about a P rather an a p, the P is then defined in an equation, not p. In some branches of mathematics capitalisation has very distinct meaning.

Examples in books always work as they have often been "predone" one way or the other. Conrady was a well known source of initial designs to modify. There are others. His books are tough reading but do give some insight into the basics that lie behind lens design as pressing a button on a PC on a design from scratch in all probability wont achieve anything other than layout a scope to an existing design.

Calculus - taking the corrector plate as an interesting instance there is lots on the web but taking the coefficients oslo uses no mention of how they achieve the shape. I'd guess that they represent dimensional changes in the radius of the base curve but they could be dimensional changes that are always along the axis of the system, changes in slope or any number of things. That leaves me and probably others using functions parrot fashion without any real basic understanding. Personally I generally wont do anything parrot fashion. Mathematical abilities do not even relate to that aspect.

I asked for links because of a comment some one else made relating to horses to water. I don't think there are any really just poorly described examples. Actually I used oslo a lot around 10 - 15 years ago and there seems to be a lot less useful info about now than there was then. Might be down to the knowledge = money aspect but more likely down to the lack of useful help which often causes people to loose interest. Also the general fact that many telescopes can be bough for far less than they would cost to make.

John
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Ajohn
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5672005 - 02/10/13 09:21 AM

Must admit I'm impressed by GENII now I know I can edit the operands but can't find a list of what they influence. Some are obvious. Also would like to be able to get rid of genii operands and use the direct normal operands without exiting oslo and starting it up again. These only seem to work axially though. I can't see any way of say pointing them at the 70% zone of the image. Is there one?

Maybe some on can help?

John
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MKV
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5672770 - 02/10/13 05:54 PM

Quote:

Must admit I'm impressed by GENII now I know I can edit the operands but can't find a list of what they influence. Some are obvious. Also would like to be able to get rid of genii operands and use the direct normal operands without exiting oslo and starting it up again. These only seem to work axially though. I can't see any way of say pointing them at the 70% zone of the image. Is there one?
Maybe some on can help?



You seem to be the only one who seems to have insurmountable problems with OSLO.edu, even suggesting it's flawed. I gave you the titles of several books by optical experts which would make the concepts involved comprehensible, especially Warren Smith's Modern Optical Engineering (Kingslake's Lends Design Fundamentals is much more manual raytrace oriented).

What you don't seem to understand is that your vertex radius detemrines where the "neutral zone" will be. You have to understand the nature of the optical path difference and how it is structured and only then you can proceed with OSLO. That's not the kind of subject you pick up on a forum's short answer list. OSLO is a bare-bones freebie but it does require some basic optical understanding to be used to its fullest extent.

The alternative is to simply raytrace Baker's system (primary plus field corrector), but without the aspheric corrector, determine the amount of uncorrected spherical aberration and, based on that, obtain solutions for the desired corrector. OSLO can do the rest without any sliders.


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Ajohn
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5672775 - 02/10/13 05:57 PM Attachment (22 downloads)

This is as near as I can get to what Baker seems to have intended - coma a slight problem at a semi angle of 3 degrees covering an 8in dia circle. Going on the MTF curve it looks like it even nearly meets Rayliegh's 1/4 wave limit at 3 degrees. Astigmatism seems to be the main problem there.20in mirror and 17in aperture.

John
_

Edited by Ajohn (02/10/13 06:03 PM)


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MKV
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5673377 - 02/11/13 12:35 AM

Quote:

This is as near as I can get to what Baker seems to have intended - coma a slight problem at a semi angle of 3 degrees covering an 8in dia circle. Going on the MTF curve it looks like it even nearly meets Rayliegh's 1/4 wave limit at 3 degrees. Astigmatism seems to be the main problem there.20in mirror and 17in aperture.



John, what are you doing??? The spots look good consideirng the angle, but in order to cover a 6 degree field your corrector will be 14 inches in diamater and the clear aperture is 17 inches! That's an 82% central obstruction! That leaves 32% of the clear aperture or equivalent to 5.6 inches inch telescope in light gathering power. You have a 20inch f/3 mirror and end up with the light of a 5.6 inch equivalent aperture, working at an effective f/14 or 15, and an 82% CO. Are actually thinking of making one of these?


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Ajohn
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Re: Baker Reflector Corrector help new [Re: MKV]
      #5673697 - 02/11/13 09:39 AM

His basic suggestion for any design is to follow the 17in corrector 20in F5 mirror example with a 50% obstruction = 8.5in in this case and the system comes out at F4.5. The 50% obstruction is a constant for any design as he sees it. He shows a spot diagram over 3 degrees but the scale is too small to compare really. The spots for an F4.5 parabola are shown above it. He points out that there is vignetting at both the mirror and the corrector. The recommended plate size for this one is 4x5in = 6.4in diagonal. All I have done is reproduce his spot diagram.

In a way the spot diagram isn't as it should be for photography. As he mentions the lens spacing has to be adjusted for the most even circles of confusion across the field.

John
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PS Yes if I can make it work in colour with a 220mm mirror. Field angle TBD. I need some info on Olso's schmidt constants in relationship to actual glass deformation and their relationship to the formulae the vac pan spread sheet uses. That one isn't provided in EDU.
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Ed Jones
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5674611 - 02/11/13 06:51 PM

Did you consider a Honders/Busack? I'm working on one myself; all spherical optics using ordinary crown glass.

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MKV
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Re: Baker Reflector Corrector help new [Re: Ed Jones]
      #5675023 - 02/12/13 12:00 AM Attachment (13 downloads)

I second that Ed, a Busack or a Honders-Riccardi f/3.7 or thereabouts is ideal.

John, here's a Honders-Riccardi 220 mm f/3.7 configuration. The corrector is a simple biconvex BK7 lens, and the primary is a Mangin mirror. The field corrector is an almost a pcx lens. All surfaces are spherical.

It covers a fully illuminated 44 mm FOV or 3.1 degrees.

I would rather do that than mess with aspheric plates and achromatic doublets. Baker's design was intended for monochromatic photography and it can be corrected extremely well for that purpose, but not for polychromatic applications.

I have no shop experience with aspheric plates, but my understanding is that they are not easy. Thank God there are viable alternatives.

As for your questions about the actual glass deformation for various zones as related to deformation coefficients, OSLO provides that information. The Schmidt vacuum method is well covered in literature and tells you exactly how much of a sag you will need for a desired vertex radius plate.

Edited by MKV (02/12/13 12:09 AM)


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Ajohn
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Re: Baker Reflector Corrector help new [Re: MKV]
      #5675393 - 02/12/13 08:30 AM Attachment (17 downloads)

The whole idea is a design based round a conventional parabolic mirror in my case but that one may be of interest at some point. I suspect that it wouldn't be as good at F3 as the Baker anyway and no need for a high quality chunk of BK7 for the mirror. Interesting though as I think Bk7 normal mirrors can be bought. I can also get the image out of the side of the tube. Not entirely happy with the way I can do that at the moment though.

On correctors MKV the vacpan info that is available to me is based round a corrector curve of Z=Ar^2+Br^4 where Z seems to be the actual numeric deformation of the glass. Oslo EDU doesn't offer that is uses a 4,6,8, and 10th power series and so far I haven't seen any indication of what this means physically on the glass. On none Schmidt scopes people get round the problem by using factors of a Schmidt plate's power. I'm not surprised some have problems. They would also have problems if they tried to put the correction on both sides as per the design you posted. Baker's F4.5 systems plate deviates from a sphere by about 5 waves. Trying to split that and centre it on both sides would be a joke. It usually is on all schmidts. There is also the possibility that Baker's plate deviates from a Schmidt plate. Basically it seems to form part of the colour correction. In blue light actually a very obvious choice of Schott glasses hardly makes any differences at all. Chromatically I'm 90% sure it can still be better than the spot diagram.

I still await an answer relating to the meaning of the olso edu coefficients.

As this is the Baker corrector thread I may as well post the spot diagram again. Pointing out that it still isn't as it probably can be. That's part of the other changes I want to make mentioned in the other thread.

John
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MKV
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5675509 - 02/12/13 10:09 AM

Quote:

the vacpan info that is available to me is based round a corrector curve of Z=Ar^2+Br^4 where Z seems to be the actual numeric deformation of the glass



Okay, John, the reason I am saying you probably need to read more is because the expression above is the formula for the depth of the aspheric plate at a specific aperture zone radius, r. The coefficients B, C, D, etc...are the 4th, 6th, 8th etc. deformation coefficients. The term A is not a deformation coefficient. This is all very, very basic, and if you don't know that the coefficients you have are the terms in the expression you posted above then you probably need to learn more about the subject.


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MKV
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5675571 - 02/12/13 10:44 AM Attachment (15 downloads)

Quote:

I suspect that it wouldn't be as good at F3 as the Baker



And what is your suspicion based on? Have you tried designing an f/3 of Honders-Riccardi type and compared it to the Baker?

I have, and here is a non-optimized 220 mm diameter f/3.01. The PSF shows the more realistic image of a point source at the very edge of the 1.9 degree semifield (22 mm off axis). All this with nothing but spherical surfaces and not a single achormat in the configuration, never mind aspheric plates! Oh, btw, the spectral range is from 405 to 706 nm. Try that with the Baker!

So, I am curious, how did you come to the suspicion that the Baker would be better?

Edited by MKV (02/12/13 10:55 AM)


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Mike I. Jones
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Re: Baker Reflector Corrector help new [Re: MKV]
      #5675586 - 02/12/13 10:55 AM

My guess is that he's trying to make use of the 220mm f/3 paraboloid he already has. I agree - dialytes like Honders, Busacks, etc. systems blow away almost anything else for field and spectral coverage in ATM-sized apertures. But John's wanting to work with what he has in hand.

Correct, John?
Mike


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MKV
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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5675602 - 02/12/13 11:03 AM

Quote:

My guess is that he's trying to make use of the 220mm f/3 paraboloid he already has. I agree - dialytes like Honders, Busacks, etc. systems blow away almost anything else for field and spectral coverage in ATM-sized apertures. But John's wanting to work with what he has in hand.



That seems like a good enough reason, Mike, but he seems to suggest that he's going with the Baker because he suspects the Honders-Riccardi "wouldn't be as good at F3 as the Baker", which is a totally different reason you give.

Edited by MKV (02/12/13 12:41 PM)


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Ajohn
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Re: Baker Reflector Corrector help new [Re: MKV]
      #5675907 - 02/12/13 01:52 PM

Thanks for answering for me Mike. It may finish up just being in some form of F15 scope but I like the idea of interchangeable ends and as that is a near life long desire want to look at the options. It all needs to go in the car easily too.

I looked at the spots and assumed it would be worse at F3.

Bakers for me has a big advantage - camera can go on the side of the tube for one as the image is further away from the lens than any other design I'm aware of. Not entirely happy with how that could be done at the moment. The other advantage is the parabola but at the moment a solution could use a spherical mirror providing a quality F15 scope is also viable. As an aside I have spent some time looking at that with a spherical mirror but advantages are dubious so far. There looks like there may be a spherical 2ndry solution and that would be an advantage but not a straight DK.

On it's performance it currently isn't any where near optimised for colour. The spots show near red optimisation which is obviously a bad idea. However I will never ever sort that aspect out without relating the usual schmidt aspheric profile formulae to the one oslo uses as currently correcting the plate for sa is very definitely likely to mess up the colour correction else where. As it stands it seems to be capable of sub arc sec photography. Not sure about IR and UV but until the colour correction is sorted out there isn't much point in looking. I wont be taking the filters of the cameras ccd either.



For a laugh I just let 3 of oslo's optimise routines try and sort SA out on something else from a flat surface. The results were awful. Hardly surprising really but if I look more closely I may find that they can be forced to work to closer limits on SA. Doing the correction manually as well showed just how messed up colour correction can get via oslo's constants.

I've asked the same question about the asphere constants several times and no answer. Interesting as it seems to be an insurmountable problem using edu.

John
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5676064 - 02/12/13 03:19 PM

Quote:

For a laugh I just let 3 of oslo's optimise routines try and sort SA out on something else from a flat surface. The results were awful. Hardly surprising really but if I look more closely I may find that they can be forced to work to closer limits on SA. Doing the correction manually as well showed just how messed up colour correction can get via oslo's constants.

I've asked the same question about the asphere constants several times and no answer. Interesting as it seems to be an insurmountable problem using edu.



Yeah John, OSLO.edu is just awful, flawed, even laughable through and through. If you know so much, why do you ask so many questions? Apparently you figured it all out and decided to fail OSLO.edu all on your own.


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Re: Baker Reflector Corrector help new [Re: MKV]
      #5676095 - 02/12/13 03:35 PM

I am beginning to think you are a rather offensive person MKV. Perhaps you just can't answer the question if that is the case there really isn't any need to be rude. On the other hand on the web Mike for instance and me in other areas are as helpful as we can be who ever it is who asks for help.

One thing for sure you haven't even read the part that you quoted.

John
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5676204 - 02/12/13 04:27 PM

Let me see if I can explain it.

The "depth" of a figure-of-revolution surface like your aspheric plate varies only with radius.

The depth "z" of a curve can be expressed as

z = (cr)/[1+SQR(1-(1+K)cr)] + Ar^4 + Br^6 + Cr^8 + Dr^10

where c = 1/(vertex radius) and K is the conic constant:

K > 0 oblate spheroid
K = 0 sphere
-1 < K < 0 prolate ellipsoid (like Dall Kirkham primaries)
K = -1 paraboloid
K < -1 hyperboloid (like Ritchey-Chretien or Rosin primaries)

All the A,B,C and D terms above do is change the local curve depth relative to the conic surface.

Enough? More?
Mike


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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5676446 - 02/12/13 07:09 PM

Quote:

I am beginning to think you are a rather offensive person MKV. Perhaps you just can't answer the question if that is the case there really isn't any need to be rude. On the other hand on the web Mike for instance and me in other areas are as helpful as we can be who ever it is who asks for help. One thing for sure you haven't even read the part that you quoted.



I am sorry you feel that way, John, especially in view of the fact that I gave you several alternate designs and suggested at least three well known books that may help you with the concepts, short of doing your own homework. Also, despite the fact that I gave you specific answers to your question in post #5675509 about the expressions, you still claim, only a couple of posts later that you "asked the same question about the asphere constants several times and no answer." Like I said previously, you can lead a horse to the water but you can make him drink it.

I just find it somewhat over the top for you to trash OSLO.edu as all but useless, and flawed, and laughable, when it is obvious that you don't know some basic concepts, refuse to accept friendly advice how to learn them, and conclude that OSLO doesn't have something or can't do something when in fact it does and it can. It that makes me "offensive", well, excuse me, Sir! I should have known better not to waste my time.


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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5676459 - 02/12/13 07:24 PM

Thanks Mike. I suspected it was Z as per what seems to be the more usual formulae but had no way of telling. There never is any info on something as basic as that. It might have been a slope at a zone for all I know.

From what I gather the conic constant for a schmidt plate would be as per a parabola in that formulae?

The usual formulae kicking about for schmidt plates is the other one I mentioned earlier but I have seen it with additional terms. Z=Ar^2+Br^4.

If I understand that one correctly the A and B terms are calculated on the basis of the schmidt that the plate is intended to be used on so that the neutral zone will be at 70%. That leaves me with the problem of either establishing a base curve to use optimisation with that ensures the neutral zone comes out at 70% or using the sliders in a way that does or even checking afterwards which would be tedious. One thing I have notices is that the 1st adjustment of SA can always be done with the first power term on the sliders but that always has to be backed off later. What I'm really asking now is how the oslo string of powers and constants can be handled to come out with the zone at 70%. I have been thinking about MKV's comment about a few rays determine what power of schmidt plate. I might manage that but it isn't something I do every day so may well get it wrong. Bound to really. Then I need to relate the one formulae to the other some how so that it can be entered into oslo edu.

Sorry MKV I missed an earlier post some how. I made a bad choice of words. I realised that the Z in that one was effectively the profile. Thinking about vacpans too so deformation came to mind.

I can't read Mike's post while typing this so may find that the Ar^2 term is the gubbins at the start and the vacpan method only uses 2 terms. To get down to small errors I have always needed more than 2 terms which makes the 2 term aspect more difficult to mentally relate to the one with more terms. I have to ask because there would be no point in guessing so if that is the case I need to know.

John
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5676474 - 02/12/13 07:41 PM

No hard feelings John. I am writing a reply to you and Mike that may help clear up some things. Ok?

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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5676499 - 02/12/13 07:54 PM

The conic constant and r coefficient (if accessible) should ALWAYS be set to zero and frozen during optimization of an even asphere (even powers only) like yours. The base radius and high-order terms are all that are needed to describe and optimize the surface. If you make K variable, the optimizer mushes it in with the higher orders and K often goes wild, like K=+8.25e+89 or K=-1.24e-125 or some stupid value like that. I have found to NEVER let the conic constant vary for a high-order asphere. K is also unstable when the base radius is very long, as in Schmidt plates, and can explode into meaningless numbers as well. Do all the aspherization design with the base radius and even powers of r only.

To confuse matters worse, I've seen people allow the r aspheric coefficient to vary as well. This has the crazy effect of changing the base radius without it showing up in the lens spreadsheet, since the base radius is already a function of r. A nice feature of OSLO-EDU is that it doesn't even allow you access to the r coefficient.

A good goal is to achieve the desired performance with the minimum number of high-order terms. Aspherization is sort of like the MacLaurin expansion of sine(theta). Low-order terms have the most influence on plate aberrations, and higher-order terms are often just unnecessarily gilding the lily. If you can pull off a suitable plate design with base radius, r^4 and at most r^6, you're way better off. Raising "r" to the eighth or tenth power introduces severe numerical sensitivity and instability that overshadow any real measureable benefit they bring to image quality. Only extremely fast systems like f/0.9 Schmidts need those higher order terms.

Mike


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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5676532 - 02/12/13 08:25 PM Attachment (14 downloads)

Mike, just so there is no confusion between the expression John mentioned earlier as z = AY^2 + BY^4... and yours

z = (cr)/[1+SQR(1-(1+K)cr)] + Ar^4 + Br^6 + Cr^8 + Dr^10

as both use ABC terms but in a different context.

Yours is the "complete" formula, with the (cr)/[1+SQR(1-(1+K)cr)] being the uiversal sgaitta equation, and A, B, C, D, etc. being the deformation coefficients of the 4th, 6th, 8th, etc. power by which a surface deviates from a conic.

John's expression is simplified as z = Ar^2 + Br4 + Cr^6, which John mentioned ealrier, where Ar^2 is NOT the same "A" as in your expression.

Rather, in this simplified version, the A is the coefficient of the vertex radius (Rv), such that Rv = A. The A can be found algebraically by r*D/[8*(n-1)*R), while B = -1/[8*(n-1)*R]. Here, the R is the radius of curvature of the mirror (or the equivalent radius of curvature of the mirror), r = Yz/Ym (zonal radius divided by the aperture radius), D is the aperture diameter (2Ym), and n is the refractive index of the glass used.

The expression A will therefore give an Rv depending where the "neutral zone" is located. The easiest way to find this Rv is using spherical aberration and from that value determine the value of A, and then the Rv. This is particularly helpful in compound telescopes which are OPD-equivalent to some single mirror. The OPD-equivalent mirorr can be found by Schwarzchild equations (coefficient G), or by raytracing, knowing that (1/G)^1/3 is the equivalent (or elative) OPD radius if curvature.

To the best of my knowledge OSLO.edu doesn't provide a way to determine the A coefficient or the Rv automatically, rod eos it ask for the "neutral zone" height. It requires a manual entry and therefore it requires that the operator know how to calculate the Rv.

Automatic optimization in OSLO can also determine the vertex radius but it doesn't allow you to pick the neutral zone. Depending on how the operands are set, this program will look for the best solution to match the operands.

So, this is not exactly simple and straight forward (but let's not forget that OSLO is free!) unless one knows what is needed and how to get it. But it's there. All you really need is to determine where your neutral zone will be, find A and obtain the vertex radius. OSLO will proceed from there and give you all the pertinent information about the plate profile. For example below is a profile of a Schmidt corrector plate of a 200 mm f/3 Schmidt camera in Text Window One (TW1).

As far as I know Schmidt' vacuum formula is somewhere on the net. This is from memory, so don't hold me on it, but I think it's as follows:

Rv = [16*(n-1)*(f/D)]*D, where D = diameter of corrector, n the index of glass, and f the focal length of the mirror. You can calculate the dagitta of that Rv by using (cr)/[1+SQR(1-(1+K)cr)], as Mike gave above, or simply approximate it with the usual (Y + z)/(2*z).

Mladen

Edited by MKV (02/13/13 11:39 AM)


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Re: Baker Reflector Corrector help new [Re: MKV]
      #5677461 - 02/13/13 11:10 AM Attachment (13 downloads)

Thanks that helps a lot but as expected Oslo wont do it for me.

I've spent a couple of hours looking for info in the help files for the sag table and for the location of the coefficients internally. No luck on either but found the sag table in the menus quickly. Defaults to surface 1 without asking but the command and syntax can be found from there by clicking on the blue output. Mentioned in case some one else is reading this that lacks the very basics.

No information at all on the table content though, Z (Sag) is obvious but there are also NVL,NVK and NVM and I have no idea what these are and have to hope some one else does in physical terms on the glass. I take it that the lowest values of NVL indicate the neutral zone? If it does though does this leave the power of the underlying sphere?

My current original Baker just converted to mm gives this. No good as I suspected.

John
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5677538 - 02/13/13 11:52 AM

I know next to zero about OSLO-EDU so I can't be of much help. I imagine (hope) the full-up OSLO can handle these kinds of aberration corrections in stride.

With almost 30 years experience in CODE-V (that's where the A,B,C,D nomenclature comes from) and 20+ years with ZEMAX, picking the "pinch point" in the merit function for Schmidt systems is kid stuff.

I did a little personal study years (decades?) ago to see how accurate the Schmidt plate writeup in ATM-3 was. In it, the author states that pinching the colors at the 70% zone will give a plate profile with the least material removal. However, to minimize color, the pinch point is more like at the 86% zone. I found that to be true in a general sense, although it did vary depending on the spectral band, focal ratio and field angles used. The 70% zone was consistenty not the best zone to achromatize to.

In ZEMAX's merit function, this pinch point is easily simulated by REAY (real ray Y-height) operands. I pick a zone on the plate at which all the colors should have zero Y-height at a common focus. I can then quickly change the zone, re-optimize and watch the residual color behavior. Easy Peezy.

I have no idea how to do the same thing in the little student freebie version of OSLO.
Mike


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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5677550 - 02/13/13 11:57 AM

John, NVL are tri-dimentinal direction cosines. If you read Kingslake or Smith you'll know what they are and how they are used in raytracing calculations.

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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5677651 - 02/13/13 01:01 PM Attachment (18 downloads)

Mike, CODE-V has been used by professionals at least since the 1960.s. ATMs continued to use the old z = AY^2 + BY^4...ZY^n format. I am not sure the student freebie OSLO version can find the "pinch" point by REAY, but this can be "forced" by the choice of the vertex radius and subsequent optimization. And the vertex radius can be found in a variety of ways, algebraically, as well as by raytrace results (long. sph. abberation). This is how Wright calculated the "relative" strength of his corretcor (the term used by authors such as Rutten and van Venrooij, etc).

When you use a three-decimal slide rule or log tables, or freebie versions of raytrace programs, you have to devise ways of getting to the desired result in a roundabout way. Manual raytracce was a an absolute must in those days.

Thus, the way Wright looked at the solution was simply by knowing that his oblate spheroid had twice as much spherical aberration as an ordinary sphere of the same radius of curvature using the (1+e) coefficient of SA, where e is the positive oblate "conic" constant. His mirror was exactly the opposite figure of a paraboloid, so e = +1. And knowing that, he could easily figure out the OPD-equivalent spherical mirror -- i.e. a spherical mirror of a given radius R that would produces the same amount of optical path difference as the oblate spheorid of raidus R'. And knowing that sp. aberration is a cubic function, he found R simply by diving the R' by the cube root of 2 or about 1.26, i.e. R = R'/(2^1/3). Another way of saying this is that for an f/4 Wright mirror you need to make a corrector as if making it for a spherical (Schmidt camera) mirror of f4, i.e. 4/1.26 or f/3.175 (~f/3.2).

This can easily be obtained also by the Schwartzchild expressions where the coeff. of sph. aberration G = b/8f or simply b/R, where b is the cc and f is the focal lenght of the mirror. The OPD-equivalent mirror radius of curvature then is simply cube root(1/G).

And knowing that long. sph. aberr = G*f*y, where y = aperture radius, you get the OPD-equivalent sphere of radius R and calcuate its correctcor from that, including the vertex radius which is A in the z = Ar^2 + Br^4... series.
It is the A coefficient in this case which takes into account the "pinch" point and will vary accordingly.

You're absolutely right about the 86.6% zones being overall better than the 70%. I believe the 70.71% was popular/preferred because it requires less glass removal and because its RMS/PV error is the smallest, even tough inconsequental.

Below are the results of three independent 200 mm f/3 Schmidt cameras. The first one has a vertex radius Rv = "0" (actually infinity), and the vertex curvature curvature Cv = 0), so the "neutral zone" (NZ) is at the center of the plate. The next one has the NZ at the 70.71% zone and the last at 86.6%.

Notice in the picture below ow this affects the deformation coefficients ever so slightly but significantly.

So, as far as John is concerned, the student version of OSLO works as long as you can apply the old fashioned manual raytracing and/or know the concepts involved. You get more sophisticated results in a roundabout way, which requires more than the basic entry level knowledge of optics.

And BTW, every new version of OSLO seems to have more restrictions. I still have a working copy of OSLO 5.4 LT (which was a freebie way back), and many of the functions that are now restricted in the EDU version are available in the 5.4 LT. The 5.4 LT can also handle up to 12 instead of 10 surfaces.

Cheers,
Mladen

Edited by MKV (02/13/13 01:07 PM)


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Re: Baker Reflector Corrector help new [Re: MKV]
      #5677789 - 02/13/13 02:32 PM

Were you just using d,F,C wavelengths? Try really broadbanding it with the same scope, like 0.38m, 0.58m and 1.0m, with different NZ's.

Also, the color spread at max field angle counts, too.
Mike


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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5677910 - 02/13/13 03:56 PM

I'm nearly there with it Mike and as MKV and others say it's an amazing piece of software for free. The reason I used the term for a laugh is that I wouldn't expect a general purpose optimising routine to generate a perfect schmidt plate from a flat surface. There are several optimisation routines in oslo. Opic for instance seems to be very good for tidying things up. GENII can be directed to zones. :-) Or maybe it's the other way round. Then there are ray and aberration operands. It churns out Seidels etc. There is a lot there. My biggest problem with it is terminology such as what a specific term actually means on the glass. The macro language is rather basic C. Adequate and easy to learn. The commands it offers aren't so easy to learn though.

Basically I think it's a program largely aimed at keyboard use and probably flies when driven that way by some one who really does know what they are doing. I suspect their market share suffers because of that and it's appearance. Software is an area I really do know something about. Where it falls down in my opinion is certain aspects of convenience as software is supposed to help. I don't think that the documentation they provide with it is very good either but that is a common problem with technical software that is to be used by experts. That aspect can have a very distinct bearing on just how long it takes for some one to become an expert though. I'd guess that they sell with support. Common dodge to earn more money. I don't think that the examples they use cover the typical things that some one might want to do to a lens either as it's a bit like a design a schmidt on another site - "now set the sliders like this".

Baker used AY^2 ........ to 5 terms going on his papers that I have found so most probably worked the same way in the 1940's. I suspect the 70% zone relates to vacpans as it can't produce anything else. That's intuitive because it's hard to see how it could produce a neutral zone at a number of different positions and have a correct figure elsewhere.

The sag chart that I posted was chased down until oslo showed +/-5e-6 mm scale. The SA at that stage was S shaped and took up about 2/3 of the scale. Can't remember what the scale was before that one but it was very small and the change did improve all spots.

One thing for sure his reflector corrector is an amazing piece of work. I think I am beginning to get an idea how he balanced it all up - well at least a way that oslo can mostly cope with.

John
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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5677917 - 02/13/13 04:01 PM Attachment (13 downloads)

Quote:

The "depth" of a figure-of-revolution surface like your aspheric plate varies only with radius.

The depth "z" of a curve can be expressed as

z = (cr)/[1+SQR(1-(1+K)cr)] + Ar^4 + Br^6 + Cr^8 + Dr^10





The conic surface sagitta does not belong to the terms defining the Schmidt profile. The first term, which can be called the (corrector's vertex) radius term, is actually defocus term, which specifies how much of defocus is combined with spherical aberration at the paraxial focus. This goes to the very basics of the Schmidt profile, which is directly determined by the aberrated wavefront it is made to correct. It needs to produce a wavefront aberration that is identical in magnitude and shape but opposite in sign to the mirror aberration. Thus its shape is the shape of mirror aberration multiplied by the medium (light retardation) factor 1/(n'-n), n and n' being the refractive index of the incident and exit media.

Since the shape of wavefront deviation changes with the point of defocus, so does the Schmidt profile. Relative defocus L (from 0 at the paraxial to 2 at the marginal focus) is directly related to the relative height of the neutral zone N as L=2N^2. Best focus location for primary spherical is midway between the paraxial and marginal focus, thus with L=1 and N=(0.5)^0.5. Hence this is the Schmidt shape producing the smallest wavefront error in non-optimized wavelengths, thus lowest spherochromatism (it is also the easiest to make).

The complete profile is described as a sum of defocus term and as many spherical aberration terms as needed:

(2N^2*r^2*d^4)A4 + [(rd)^4]A4 + [(rd)^6]A6 + ....

where N is the neutral zone position, "r" the zonal height for semi-aperture normalized to 1, "d" the semi-aperture, A4=1/4(n'-1)R^3 the aberration parameter for primary spherical and A6=3/8(n'-n)R^5 the aberration term for secondary spherical, R being the mirror r.o.c.

Taking "d" as unit, and neglecting the A terms (which merely determine curve depth), Schmidt shape is proportional to the sum of

-2N^2*r^2 + r^4 + xr^6 +...

where the signs reflect the fact that the defocus error, as defined, is always opposite in sign to the spherical aberration error ("x" is the ratio in magnitudes secondary-to-primary spherical). This can be used to illustrate how these terms generate the final Schmidt profile. For the best Schmidt shape N=1, and the combined plot is proportional to (r^4-r^2). For the smallest blur, N=1.5 and the combined plot is proportional to (r^4-1.5r^2).

Note that the secondary spherical term is given for paraxial focus only, but it can also be used with its own defocus factor, which is generally preferable for fabrication (it also minimizes secondary spherochromatism, but that is negligible). All wavefront deviation shapes are exaggerated, and secondary spherical is exaggerated vs. primary.

All this said, in this particular design mirror has zero spherical aberration, and the corrector corrects spherical aberration of the field lens. Since this lens has weak curves, it is only its primary spherical that matters.

Vla

Edit: The primary s.a. aberration parameter A4 on the pic was incorrectly written as A6

Edit 2: the second plot from left (A4+a) was also mistakenly plotted as r^6, instead r^4. Sorry - just noticed that.

Edited by wh48gs (02/16/13 07:32 AM)


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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5677928 - 02/13/13 04:07 PM

I'll tuck the meaning of that term away for future reference MKV. I'm not sure I want to know at the moment.

What I really do need to know is which of those figure relate to the position of the neutral zone and if at that point the corrector has zero power or a power generated by the base curve the figuring has been applied too.

I think I can see a way of establishing the correct base curve to keep the other refractive optics happy. If I then "schmidt it" I need to know if that power will still be there. He does point out that he makes use of the hump in the middle of a schmidt plate so it may have to be figured by hand anyway. He doesn't really give any other info apart from a list of sags.

Hope you can find time to answer for me.

John
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5677940 - 02/13/13 04:14 PM

Simple question: Can't you adjust the NZ radius by the diameter of the support O-ring? If your O-ring is at the 70% diameter, then the vacuum will only have influence on the part of the plate within the 70% diameter. The larger the O-ring diameter, the more of the plate gets deformed by vacuum. That has to make sense. Now the question is, is the shape of the plate that springs back at 1 atmosphere after being ground and polished flat under vacuum anywhere near the right shape regardless of the O-ring diameter? Or does it only work when the O-ring is at or near the 70% diameter point?

Time to break out Roark's "Formulas for Stress and Strain" and wade through it, I guess. Just not enough hours in the day.

Mike


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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5678168 - 02/13/13 06:50 PM Attachment (11 downloads)

Quote:

Were you just using d,F,C wavelengths? Try really broadbanding it with the same scope, like 0.38m, 0.58m and 1.0m, with different NZ's.

Also, the color spread at max field angle counts, too.
Mike



Mike I am not sure what the point is. My point was to show that 86.6% NZ corrector gives better correction, as you said, but the 70.71% may be easier to make.

Other than that, the camera performs well in the spectral range from 0.38 to 1.01 nm, optimized at 0.58, keeping in mind that Schmidt camera would require a field corrector/flattener that would be suitable for CCD imaging and that most of the surfaces in color were done using astronomical emulsion plates with specific filters and then combined.

Mladen


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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5678184 - 02/13/13 06:59 PM

I don't think so Mike. Depress the centre of a disc with a support in from the edge and the rim will be forced to turn upwards in a rather odd way due to tension in the circumference. I shudder to think about getting to grips with the math for that. Celestron and other do it by having a form tool and sucking all of the air out and then grinding the curve. It seems the chinese now do this to an accuracey that doesn't need figuring on the 2ndry mirror in a SCT anymore. When they started doing this though they stopped advertising 1/10 wave. With the new Edge they are back to figuring the 2ndry but those have a very high quality field.

As I understand it the plate is ground flat and then supported at the rim and sucked down to some depth at the centre. A tool has been prepared by grinding it to a calculated rad and that rad is then ground into the corrector. When it's released from the pan it springs back and has the correct form. Air under the blank isn't of much use it has to be an uncompressable liquid. There is a company in the UK who made a replacement SCT corrector for some one and I would have thought that they would be well aware of the methods of doing it. I cussed them because when they made the vacuum pan it was only for one rather large size of corrector. It could have been stepped in for other sizes.

I have hours in the day problem too. That prevents be going any more deeply into a subject than I need too. Age also makes new learning more difficult. In this case it's more of a question of just how best to get oslo edu to do the job and interpreting the output it gives.

One thought struck me on schmit plates. As Vla pointed out these are calculated on a unity basis in some respects. Given a "correct" plate it can be scaled. Unless some odd scaling is involved a "correct" plate could be scaled to a certain diameter on the basis of it's oslo parameters and the power could then be varied by multiplying the coefficients only by a constant. If the scaling which I do know works on them is as simple as that it's a viable method of sorting it out with the neutral zone anywhere. In fact it would appear that this could be done with a slider.

Once again though I need an answer to a very simple question - does oslo scale correctors that way.

The other question about the neutral zone concerns a possible method of using oslo to balance out the aberrations in the scope. I had a lot of trouble with the reduction in F ratio the design gives and a lot less trouble with one that hardly changes the F ratio of the mirror. If I am to go through it again properly I need that info.

John
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5678254 - 02/13/13 07:55 PM

John, why not make a template out of aluminum the way Celestron makes the correctors? If I think there's much less of a chance for breakage and the blank is held over its entire surface rather than just at the edge. The sag would probably be no more than a couple of thousands deep. If I had to make a Schmidt corrector, I think I would go with that idea.

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Re: Baker Reflector Corrector help new [Re: MKV]
      #5678762 - 02/14/13 04:28 AM

If you wanted to make a very precise form jig like that would you make it out of aluminium mkv? I don't know what Celestron use but I know what I would use and after I had made maybe a dozen corrector plates with it I suspect they could come out as accurately as needed. I could go out an buy a super precision cnc profiling machine I suppose which would reduce subsequent hand work they crop up on ebay all of the time.

John
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5678853 - 02/14/13 06:51 AM

Celestron developed the method way before the CNC machines. I imagine it could be made by the same way we grind optics, except using some sort of speculum (metal) material. Also, I don't think having a CNC shop generate one in a 220 mm size would be prohibitively costly.

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Re: Baker Reflector Corrector help new [Re: MKV]
      #5678926 - 02/14/13 08:08 AM

I would look at using a rather large block of zerodor or something similar for production MKV. I believe there is one embryonic machining technique that might get to the sort of accuracy that is needed via an ion beam. As to profiling machines there have been a number of methods about for donkey's years that might meet long wave needs. Some ir optics are directly machined on super precision machines. I believe canon also produce a limited number of diffractive optics to the usual camera standard. It would be interesting to know how they do it. On the face of it apart from time and equipment it should be cheaper option but they tend to be rather expensive even if they are made in what might be nearly referred to as bulk quantities.

If suitable equipment is about it would be cheaper to get them to machine the corrector and a lot simpler. It might even work out at long IR.

John
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5680873 - 02/15/13 08:50 AM

Doh. It looks like schmidt's equation will scale due to the R^3 term based on the main mirror rad. This does have a finite set of solution in a way though so might prove useful. It could be used to establish a series of base curves where the neutral zone is where it's needed for interpolation. Oslo's constants don't seem to scale in any obvious way.

Problem though. In some respects it's not a schmidt plate as Vla pointed out. Worse still in some ways Baker seems to have put the "neutral zone" at 70% to minimise the amount of glass that has to be removed. In quotes as naughty me I assumed something. Mainly that it was desirable. The neutral zone in terms of the total sag zone doesn't seem to exist.

Looking at the figures more closely the aspheric depths from a rad don't have a neutral zone either other than if the power of the asphere overcomes the sphere. Might be possible with some other set of curves. At inch intervals they are
0.0,0.01,0.02,0.05,0.08,0.09,0.12,0.11,0.08,0.00
in thou's as they used to be called. The total sags show ever increasing depths indicating a sphere with a sag of 0.174 thou but he suggests starting from 0.2 so some of the form may project past the 0.174 sag rad. More likely margin for error on an analogue spherometer. These are for a 18in dia corrector. The scope has an 17in aperture corrector, 18in o/d. These needn't tie up as he expects the final figure to be put in by hand anyway. Basically it's a -ve asphere on a positive sphere. He also gives figures for a 40in corrector for an 100in FL mirror. The total sag does drop of near the outer rim of these figures from around a 15in zone height.

If the system is scaled for focal length first for a smaller faster mirror than he uses it's possible to finish up with a slight reduction in F ratio rather than an increase in speed. It's much easier to play with without getting severe astigmatism problems.

In days of old when knighst were bold and having plates coated was rather difficult it seems people put slight concaves on the none aspherised side of the corrector to avoid problems with reflections.

John
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5681173 - 02/15/13 11:05 AM

Aspheric coefficient scaling is simple:

Let r = radius of the aspheric aperture
n = power,
Cn = nth order aspheric coefficient, and
S = the desired scale factor

A general aspheric deformation term is Cn (r^n). n can be both even and odd integers.

Scaling the system or particular aspheric surface by S scales the aspheric coefficient as

C'n = Cn * S^(1-n)

The scaling routine in OSLO should already do this properly. Have you tried using it?

Mike


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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5682861 - 02/16/13 05:57 AM

Thanks Mike. I did a quick check on what happens to the ^4 term and a scaling of 0.6 on the whole scope produced a 10:1 change. What I was getting at is the schmidt formulae is set be etc/4(n-1)R^3 so power can be changed by simply multiplying it by a factor as the R^3 term sets it. So if there is a spec of some shmidt corrector with the zone in the correct place it can be scaled to a power to suit other types and the zone will still be in correct place. A tedious way of getting round the edu problem as it could be used to narrow down the rad needed on the plate to get the neutral zone in the right place - assuming that the optimisation then does it's job correctly.

Scaling the ^4 powers etc would be even more tedious as olso wont scale the plates power on it's own. MKV has posted a plate design with the neutral zone in the correct place and in principle that could be scaled to suit any scope that needs one while keeping the neutral zone in the right place.

Mentioned as an aside really as I'm fairly sure the Baker doesn't use a schmidt type plate.

John
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Re: Baker Reflector Corrector help new [Re: MKV]
      #5682896 - 02/16/13 07:28 AM

Mladen,

Quote:

My point was to show that 86.6% NZ corrector gives better correction, as you said, but the 70.71% may be easier to make.




The 0.707 zone is certainly easier to make, being less than half as deep as 0.866 zone profile. The profile dept is also directly proportional to the wavefront error of spherochromatism, so it also has less than half the spherochromatism. The only "advantage" of the 0.866 neutral zone is that it focuses at the smallest blur focus, thus produces the smallest geometric blur. Many sources (including Schroeder and Mahajan) state that it minimizes spherochromatism based on this criterion, but the criterion is flawed. We don't see the geometric blur, we see diffracted energy, and it is the wavefront error that determines its distribution.

It is easy to check: place neutral zone at either location and look at the wavefront error in the same unoptimized wavelength. The 0.866 zone will always have it more than twice larger.

Vla


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Re: Baker Reflector Corrector help new [Re: wh48gs]
      #5683014 - 02/16/13 09:17 AM

Vla, this is not consistent with (1) refereed, published articles and (2) my own analysis. I do respect your analytical abilities, though, so maybe this would be a good subject for a new thread, as this is sort of OT and buried too far down in this one.
Mike


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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5683306 - 02/16/13 11:38 AM Attachment (9 downloads)

Quote:

Vla, this is not consistent with (1) refereed, published articles and (2) my own analysis. I do respect your analytical abilities, though, so maybe this would be a good subject for a new thread, as this is sort of OT and buried too far down in this one.



I posted comparative results three 200-mm f/3 Schmidt cameras and they show that the geometrical blur is the smallest with the NZ at 86.6%, but it also confirms Vla's assertion that the wavefront error and chromatic aberration will be the smallest at the 70.71% NZ location.

Is it significant (i.e. perceptible)? I think not, certainly not photographically or interferometrically. I think the PSFs make that perfectly clear. A thing to remember is that geometric raytrace analysis of the image blur (spot diagram) does not show accurate energy distribution because it neglects diffraction effects.

Mladen

Edited by MKV (02/16/13 11:48 AM)


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Re: Baker Reflector Corrector help new [Re: MKV]
      #5683510 - 02/16/13 01:13 PM

I take it those are axial MKV? If as Vla suggests the profiles are distinctly different they will have differing degrees of colour correction off axis.

I would guess that the 86.6% wins out in that respect.

John
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5683763 - 02/16/13 03:47 PM

Optimal NZ is also a function of the desired spectral bandwidth and plate dispersion. Achromatization over F-C is different and easier than for 0.365-1.014um. Try comparing NZ's that way.
Mike


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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5684141 - 02/16/13 07:50 PM

Quote:

I take it those are axial MKV? If as Vla suggests the profiles are distinctly different they will have differing degrees of colour correction off axis.

I would guess that the 86.6% wins out in that respect.
John-



Yes, they are axial. This is a Schmidt camera. Its images are pretty much unchanged even 3 degrees off axis.


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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5684512 - 02/17/13 12:45 AM

Mike,

I do mention that many (including the respectful ones) sources erroneously state that 0.866 neutral zone minimizes Schmidt spherochromatism. And, like I said, it is easy to confirm with raytrace that the wavefront error for non-optimized wavelengths is more than twice smaller with 0.707 neutral zone (it is also directly implied by the diffraction theory, which places best s.a. focus midway between the paraxial and marginal, i.e. coinciding with 0.707 zone focus)

That may change if other refractive elements are present. For instance, this particular system has a field lens made of common glasses that produces both longitudinal and lateral color error. They cannot be both minimized at the same time with the field lens alone: when the lateral color is corrected, red and blue foci are separated, and vice versa. Increase in the optical power of the corrector by heightening the neutral zone can bring the red and blue together, without affecting (corrected) lateral color.

Vla


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Re: Baker Reflector Corrector help new [Re: wh48gs]
      #5686451 - 02/18/13 05:23 AM

I have a suspicion that he has actually used a conic on the corrector. I had a play with that from the nearest sphere he gives which can be tied down approximately from the information. It takes a huge number on such a shallow curve but does remove most of the SA. Oslo of course applies the conic from the centre rather than minimal glass removal.

On Vla's point he mentions that the "bulge" in the centre is part of the colour correction even in just blue light. Optimisation routines tend to move that way too increasing it significantly.

I'm beginning to suspect my best bet is to try and optimise it at the original size with new glasses as that way I should gain when the size is reduced. The problem with what I have at the moment is that there is no real margin for error. The biggest problem is working on the lens to the exclusion of the corrector. The paraxial stuff isn't accurate enough.

John
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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5686458 - 02/18/13 05:39 AM Attachment (15 downloads)

This is Oslo's standard asphere formulae. Most is pretty obvious apart from the value of Cc it uses as it seems that can't be changed. Is the value zero?

John
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Re: Baker Reflector Corrector help new [Re: MKV]
      #5686524 - 02/18/13 07:46 AM Attachment (15 downloads)

Quote:

...chromatic aberration will be the smallest at the 70.71% NZ location.

Is it significant (i.e. perceptible)? I think not, certainly not photographically or interferometrically.




At 200mm f/3 it probably isn't, although it is always better to have less of the aberrations, than more, in the context of minimizing all error sources. But at f/2 it becomes significant, as illustrated by polychromatic MTF (typical CCD spectral sensitivity).

Vla


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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5686562 - 02/18/13 08:23 AM

Quote:

This is Oslo's standard asphere formulae. Most is pretty obvious apart from the value of Cc it uses as it seems that can't be changed. Is the value zero?




Since the Schmidt profile combines two wavefront deformations, defocus and primary spherical, and it is the former that defines the first term, being a parabolic function proportional to the zonal height squared, the corresponding conic is -1, and the first term comes to (r^2)/2R, where "r" is the zonal height defined in polar coordinates (i.e. in the pupil) as (x^2+y^2)^0.5, and curvature is 1/R, R being the vertex r.o.c. of the corrector, i.e. of the applied defocus wavefront deformation.

The OSLO formula is identical to one posted by Mike, and I caught myself in not seeing the obvious, which is that if the specific Schmidt profile formula uses parabolic (defocus) term, as it does, it can be also expressed using the general conic sagitta relation. It isn't revealing what the actual profile parameters are, but is formally correct.

Vla


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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5686943 - 02/18/13 12:42 PM Attachment (9 downloads)

John, the first term, cvr/ [1 - sqr(1 - cvr(cc+1)] is simply the so-called universal sagitta expression. The (cc+1) is known as the relative spherical aberration term.

You're probably more familiar with the specific sagitta expressions for a sphere (using the same x-y coordinate notion as OSLO): z(s) = R - sqrt(R - r), or, as Vla mentions, the parabola sagitta z(p) = r/2R, where R is vertex ROC.

In the case of Schmidt plates, the cc = -1 (parabolic) because that's the only conic that has zero axial sphericla aberration (i.e. cc + 1 = 0) over the aperture. When cc = -1, then, as Vla says, the whole first term defualts simply to the familiar r/2R.

In ATM3, the profile (z values) of the Schmidt corrector is given algebraically, avoiding the deformation constants, by what is called a biquadratic parabola equation. Remember though that this equation is a 4th order formula and incorporates only the first two terms in the expansion series,

z = (r^4 - kr^2y^2)/[4(n-1)R^3], where y = zonal height, and R = ROC of the mirror you're trying to correct, and n is the refractvie index of the glass used.

One more thing, OSLO can correct a perfect sphere (cc + 1 = 1), by using nothing but deformation constants, as shown below. Setu up a sphericla mirror, D = 200, R = -1200, leave conic = 0 and enter the deformation constants listed below. You get the same results as if you hand entered -1 for conic.

The OSLO formula however does not give you the vertex radius, which is not the same as the ROC of the mirror. And the vertex radius is the tgeoretical radius at the very cnete rof the corrector plate to which the plate is deformed.

Also, notice that the OSLO equation does not account for refractive index of the glass used. It is therefore much better to use the alternate equation that does: z = Ay^2 + B y^4 + Cy^6...etc. The term A = [(y/r)D]/[8(n-1)R]. Once you have A, the vertex radius Rv = 1/2A. The 4th terms is even simpler. For anything faster than f/3 you're probably fine with these two terms. Thus B = -1/[4(n-1)R]. Your total z, then is simply Ay^2 + By^4, where y = zone along the semidiameter of the corrector.


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Re: Baker Reflector Corrector help new [Re: wh48gs]
      #5687258 - 02/18/13 04:20 PM Attachment (10 downloads)

The following is the result of something that as far as I know of, simply can't be done in OSLO-EDU. This is a high-resolution ZEMAX optimization by an 8-CPU machine that required about 35 hours to run. The system is the 200mm f/3 Schmidt system we've been using for comparisons: UBK7 plate, 10th order aspheric on rear surface. I used 12 equally weighted wavelengths from 0.365-1.01m and four equally weighted field angles (0, 0.75, 1.1 and 1.5). The optimization targets were ONLY minimization of polychromatic diffraction MTF values at 100, 150, 200, 250 and 300 cy/mm relative to diffraction-limited values. This technique allows for automatic optimization of the neutral zone radius based strictly on maximized MTF performance. As can be seen, when using system polychromatic MTF values as the sole criteria, which fully account for diffraction at 1024x1024 resolution, the optimized neutral zone converges to the 76.68% zone.

This is interestingly about halfway between the 70% and 86.6% zones. The study I did years ago that gave NZ's more in the low-to-mid 80's was encircled energy-based, which does not appear to be the best metric for image optimization of wide-band linear-response sensors like CCD's.

Just thought you'd find this interesting, and worthy of further study.
Mike


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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5687260 - 02/18/13 04:22 PM Attachment (17 downloads)

Here is the resulting optimized MTF curve. It is about as close to being diffraction limited as numerically possible.

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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5687322 - 02/18/13 05:01 PM Attachment (31 downloads)

OK, I entered it into OSLO-EDU for you to analyze.
Mike


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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5687493 - 02/18/13 06:22 PM Attachment (13 downloads)

This is what I get.

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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5687501 - 02/18/13 06:26 PM

Mike, how do you use CCd processors on a curved filed? In the old days of film photography and non-linear recording, all you needed was a mechanically bent film or a simple planoconvex lens right at the film emulsion. Today's Schmidt systems comes with elabroate field correctors.

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Re: Baker Reflector Corrector help new [Re: MKV]
      #5687535 - 02/18/13 06:48 PM

Thanks for the help earlier. I will check in the morning but I'm fairly sure that Oslo fixes cc at 0 and wont allow a conic to be set as well.

Vla's point about the base curve of the corrector allows the SA curves of any 2 colours to coincide. As I have it at the moment bringing red and green in throws blue way out.

John
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Re: Baker Reflector Corrector help new [Re: MKV]
      #5687581 - 02/18/13 07:08 PM

I thought the point of this discussion is the best NZ radius for a given configuration already under study. None of the other 200mm f/3's discussed here included field flatteners. The post was more for Vla than anyone, as we were discussing optimum NZ radii, not whether or not a field corrector was being used. I was showing the optimum NZ radius for a Schmidt with spectral correction over 0.365-1.01. I remember from looking at this before how the optimal NZ changed with corrector glass and required spectral passband.

And what, specifically are you referring to about "today's Schmidts"? Can you post up prescription files or patent numbers so that we might discuss them analytically and quantitatively, or are you just guessing it might be true?
Mike


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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5687702 - 02/18/13 08:13 PM Attachment (13 downloads)

Mike,

Quote:

The following is the result of something that as far as I know of, simply can't be done in OSLO-EDU. This is a high-resolution ZEMAX optimization by an 8-CPU machine that required about 35 hours to run. The system is the 200mm f/3 Schmidt system we've been using for comparisons: UBK7 plate, 10th order aspheric on rear surface. I used 12 equally weighted wavelengths from 0.365-1.01m and four equally weighted field angles (0, 0.75, 1.1 and 1.5). The optimization targets were ONLY minimization of polychromatic diffraction MTF values at 100, 150, 200, 250 and 300 cy/mm relative to diffraction-limited values. This technique allows for automatic optimization of the neutral zone radius based strictly on maximized MTF performance. As can be seen, when using system polychromatic MTF values as the sole criteria, which fully account for diffraction at 1024x1024 resolution, the optimized neutral zone converges to the 76.68% zone.




That amounts to a computer exercise for this specific case. It combines aberrations in the first four terms to reduce the aberration toward IR, at a price of increasing it in the violet. Since the optimized wavelength (462nm) is shifted significantly away from the range's center toward violet, the aggregate error toward IR is greater than toward violet, thus this results in the slight overall error reduction vs. corrector with this neutral zone that would simply correct the first two terms (other terms are entirely negligible here).

This optimized version is still not better than one with 0.707 neutral zone (Rc=-180,000, A4=2.74e-10, A6=2.85e-16), as the graph shows. For the frequencies it is optimized for, it is actually slightly inferior.

But the real world CCD has even (maximum) sensitivity only in the 0.5-0.54 micron range (approx.), falling below 50% at 0.4 and 0.7 micron. At about 0.8 microns, its sensitivity is near zero. With such sensitivity profile, optimization like this, that compromises correction in the optimized wavelength in order to reduce error in the wider sub-range of a decentered spectral range - and mainly in those wavelength toward the end of that sub-range - wouldn't work.

A small shift from the optimal (0.707) neutral zone location could be probably compensated by inducing slight overcorrection to the optimized wavelength, which would slightly more reduce the (larger) error toward blue-violet, than increase the (smaller) error toward deep. But it still wouldn't yield better performance, and couldn't be controlled in the process of making a plate anyway.

Vla


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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5688003 - 02/18/13 10:51 PM

Quote:

Thanks for the help earlier. I will check in the morning but I'm fairly sure that Oslo fixes cc at 0 and wont allow a conic to be set as well.



You can enter cc = -1 ; it won't make any difference. Deformation coefficients determine correction. The vertex radius is practically irrelevant because it is blocked by the central obstruction. The vertex radius only reflects the position of the NZ, which can be anywhere along the corrector, but it is most useful between 70 and 87 percent of the corrector radius. It can just as well be on axis (the corrector then resembles a bowl) but its residual OPD will be worse than at either of the above mentioned positions.


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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5688074 - 02/18/13 11:39 PM

Mike I know none of the other examples had a field corrector. I was just curious if you have seen or done field flateners that can be used with CCD devices. I remember seeing Schmidt-like cameras with very elaborate three-or-more-element correctors instead of the old pcx lens, such as

this one.

You hardly ever read about Schmidt cameras nowadays since other configurations (i.e. dialytes) can pretty much come close in performance and speed, but I wonder if it is also due to the fact that old-fashioned Schmitds are simply not suitable for ccd imaging over a wide field due to to field curvature.

Mladen


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Mike I. Jones
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Re: Baker Reflector Corrector help new [Re: wh48gs]
      #5688084 - 02/18/13 11:50 PM

Question: what sampling resolution was your MTF? I found very slight differences like you are showing can be a non-trivial function of FFT resolution. 64x64 and even 128x128 MTF's can give different answers than at very high resolution relative to P-V OPD, like 1024x1024 in this case, which is what I ran the ZEMAX design at. Using Longitidunal Aberration curves to assess image quality doesn't work well for me, as the depth of focus increases to infinity as entering ray heights approach the optical axis. MTF is the best metric for imaging devices, while encircled energy is the better metric for spectrographic instruments and fiber optic coupling.

As I remember, your assessment of CCD QE curves does not apply to all devices, only green-sensitized ones. Si-based detectors can even image Nd:YAG laser light at 1.064m if their filter window allows it. I've done it repeatedly.


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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5688395 - 02/19/13 07:22 AM Attachment (11 downloads)

There is from a paper by Ross on the Polamar Schmidt relating to K. He uses this table to show that for min ca k can vary from 1.5 to 1.75. He then adds a plano convex flattener using the same material as the corrector and finds that K=2 is best but drops back to 1.75 as there is little difference and it's easier to make. s is the slope of the corrector plate which is corrected for 4861. The more modern corrector plates seem to use a bi convex flattener sometimes with a meniscus ahead of that. The flattener is always close to the focal plain as it's part of the vacuum system and has to be stress analysed as well.

John
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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5688747 - 02/19/13 11:57 AM Attachment (9 downloads)

Quote:

Question: what sampling resolution was your MTF? I found very slight differences like you are showing can be a non-trivial function of FFT resolution. 64x64 and even 128x128 MTF's can give different answers than at very high resolution relative to P-V OPD, like 1024x1024 in this case, which is what I ran the ZEMAX design at. Using Longitidunal Aberration curves to assess image quality doesn't work well for me, as the depth of focus increases to infinity as entering ray heights approach the optical axis. MTF is the best metric for imaging devices, while encircled energy is the better metric for spectrographic instruments and fiber optic coupling.

As I remember, your assessment of CCD QE curves does not apply to all devices, only green-sensitized ones. Si-based detectors can even image Nd:YAG laser light at 1.064m if their filter window allows it. I've done it repeatedly.





It's diffraction-based MTF, assuming continuous image. Thus it should nearly coincide with high-resolution sampling MTF.

LA plots are only to illustrate the difference in the overall mode of correction for the two plate profiles. But the compensatory scheme for the 0.767NZ profile is not as simple as I thought at first. The 0.707NZ profile actually has smaller error in both extreme wavelengths, as well as in the optimized wavelength, but it has larger error in the red r line (706nm), etc. so it's more complicated.

By "typical CCD sensitivity" I meant unfiltered, which is most responsive in the green. It does drop near zero at about 0.9 microns, but it actually hits zero beyond 1.1 micron.

Strictly talking, 0.707NZ minimizes spherochromatism only for the profile determined by defocus and primary spherical alone (i.e. the first two terms in profile equation). When secondary spherical is significant, as it usually is, correcting the profile results in a small shift of the NZ, the magnitude and sign of which depends on the term applied for its correction. If it is the conventional A6=r^6 term, which corrects secondary s.a. at its paraxial focus, the profile is deeper and the NZ shifts lower, to about 0.67 zone. Secondary spherochromatism is 2.5 times larger than when secondary s.a. is corrected at the best focus, in which most of the extra deepening is around 0.7 zone, and the NZ shifts slightly higher, closer to 0.72 (that can be the direction for optimization, especially when secondary s.a. is relatively large).

The secondary s.a. can be also simply minimized by adding approx. as much of primary spherical of opposite sign - which is similar to correcting it at its best focus by the appropriate secondary s.a. term - in which case NZ remains at 0.707 zone, and slight residual ("balanced") secondary s.a. remains (obviously, it's next to impossible to control the profile to chose between the two).

Note that secondary s.a. is usually much smaller vs primary than shown (here, A6p=0.2r^6 and A6b=0.2(r^6-r^2))

Vla

Edited by wh48gs (02/19/13 12:07 PM)


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Re: Baker Reflector Corrector help new [Re: Ajohn]
      #5688854 - 02/19/13 12:54 PM

John, Ross is simply showing that for the Palomar Schmidt the best overall NZ value is 0.866 for the given wavelengths. K is the NZ factor defined as 2[(Yz/Ym)], Yz = zonal height and Ym the marginal radius of the corrector. Thus for K = 1.5, NZ = 0.866 because 2(0.866) = 1.5. Likewise, when K = 1, NZ = 0.7071, because 2(0.75) = 1, etc.

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Re: Baker Reflector Corrector help new [Re: MKV]
      #5689079 - 02/19/13 03:20 PM

He is arguing something similar to the content of the posts MKV. He derives the 1.5 constant 1st and then points out that it isn't the only value that could be used. If you look at table 3 is shows total error over the wavelengths in the other table. There is no difference between 1.5 and 1.75. Later he adds a flattener using the same glass as the corrector and the same style of table shows a K of 2.0 being best.

The paper seems to be the basic design paper for the corrector done after the mirror had been made. It seems they used Crystalex glass which he states is similar to Schott K5.

John
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Re: Baker Reflector Corrector help new [Re: wh48gs]
      #5689232 - 02/19/13 04:34 PM

Untrue on MTF and PSF sampling frequency - the sampling frequency of the pupil and OPD makes a clear difference in the calculation accuracy, with higher being better accuracy-wise. 32x32 or 64x64 MTF's give much faster results, but MTF curve accuracy suffers, and can even exhibit aliasing (undersampling). One must experiment with the MTF sampling frequency for a given lens with given OPD behavior over spectrum and field, by increasing the pupil sampling frequency until the MTF values stabilize to 3 or 4 digits. That's why I ran my ZEMAX MTF sampling at 1024x1024, which is very accurate but slow as Christmas.

A useful general rule for sampling frequency that avoids aliasing is OPD <= 2^(n-5), where "n" is the log2(sampling frequency), from which

n >= 5 + log2(max OPD)

This is just enough to avoid aliasing (undersampling). A safe value for "n" for accurate MTF calculations is

n >= 7 + log2(max OPD)

If a lens has Max OPD = 1 wave, the minimum n = 5 + log2(1) = 5+0 = 5, and accurate MTF calculations start at n=7+0 = 7.

Thus if an optical system has 1 wavelength of maximum OPD anywhere across the spectrum and field, then the bare minimum MTF/PSF sampling frequency to avoid aliasing is n=5, giving a 2^5 or 32x32 array. But useful accuracy is achieved at n=7, giving 2^7 or 128x128 array sampling.

Oddly, I don't see a way to change MTF sampling in OSLO-EDU. The sampling frequency for Point Spread Functions can easily be selected by right-clicking and changing sampling frequencies. I don't see that same option for changing sampling frequency being carried over to the MTF routine.

Mike


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Re: Baker Reflector Corrector help new [Re: Mike I. Jones]
      #5689552 - 02/19/13 07:31 PM

Mike,

Quote:

Untrue on MTF and PSF sampling frequency - the sampling frequency of the pupil and OPD makes a clear difference in the calculation accuracy, with higher being better accuracy-wise.




I did not say the sampling frequency does not affect MTF/PSF (it is helpful to quote what one responds to). I said that OSLO gives diffraction based (direct integration) MTF, and the only sampling is that of the wavefront. The default is 11 points; I went up to 1000 points and there is no difference in the shape of this MTF, which implies that there shouldn't be a difference vs MTF calculated for high sampling resolution.

There is FFT (sampling) based MTF option in OSLO, but it is not working in the freeware version.

You can also verify the MTF by running the system with 0.707 NZ.

Vla


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Re: Baker Reflector Corrector help new [Re: wh48gs]
      #5691477 - 02/20/13 06:24 PM Attachment (8 downloads)

I need to keep and eye on where oslo focuses by the look of things. Is there any way of getting it to default to a spot diagram something like this? I can't find anything other than right clicking on the graphic and setting it up each time I need it.

John
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