PST mod, resolving potential theory

[GlassWalker]

Anyone well versed in optical theory around here? Got a bit of a question regarding resolving power...

If we take ideal refractors for now (diffraction limited), let's assume they're all the same focal length, and we vary the aperture size. My understanding is, a bigger aperture gives proportionately more resolving potential. If you take, say, an 80mm circular aperture scope, and put a 40mm circular mask in front of it, it would behave like a 40mm scope. Note for this scenario, focal ratio and light gathering capability are not important and may be disregarded.

Question 1: what happens if the 40mm mask is not centered on the optical axis? e.g. what if it was off centre touching the centre and outer edge of the 80mm objective?

Question 2: Imagine we have a perfect SCT. We already have a centre obstruction, so if we say have a 200mm aperture, and put a 40mm aperture mask on that away from the centre obstruction, does it resolve like a 40mm ideal scope or differently?

Question 3: Still with the SCT, what if we have multiple 40mm aperture masks, say, one each at extreme opposite sides of the 200mm objective. What would be the resulting resolving capability of this system? equivalent to 40mm, 80mm, or 200mm? Or something else?

Why am I asking this? I have a PST (was 40mm objective) black box which I want to try using with an 8" SCT (200mm objective). Now I'd need an ERF to use this safely, but I haven't seen a 200mm ERF. Even if it exists, I couldn't afford it as it would be in the thousands. My thought is to use an array of deep sky H-alpha filters strategically placed on a mask in front of the SCT, and use the PST etalon assembly on the SCT rear port. Light loss isn't important as there's tons of it from the sun. I understand the centre obstruction will reduce contrast, so arguably a bigger obstruction would impact that further. This may or mat not be an issue. I just want the resolving ability of 200mm vs. the 40mm I currently have! I know, I'll probably be seeing limited way before this anyway...

I think the only risk of using a Ha filter instead of ERF is do they block enough longer wavelength IR? They're generally optimised for imaging use and most sensors lose sensitivity by 1000nm or so. As this application is imaging only (not observation) I don't think it would be too big a deal anyway. Even the Baader D-ERF starts passing IR from 1400nm+...

[JamesF]

I wouldn't personally like to take the risk of damaging the scope or the camera in case my assumptions were wrong. I think when the time comes for me to do a PST mod I shall look for a 100mm or 120mm 'frac and put a smaller D-ERF down inside the OTA.

James

[GlassWalker]

The SCT itself needs some kind of ERF in full aperture usage, which would also help at the PST black box. The use of a H-alpha filter was one possible solution, but thinking more an ND filter may suffice if I can find one of suitable strength. The Baader solar film (even ND3.8 version) will be far too strong in this application. I would be even happier if there was something cheap that reduces IR without impacting visible red as that would be ideal.

I know the Tal 100 + D-ERF mounted internally is a popular PST mod option, but I know there is scope to do far better with what I already have without spending nearly as much.

Having said all that, my original goal of using Ha or even red filters is still likely the blend that best balances cost and risk. But I need to understand the resolution implications. Look at existing (radio) telescope arrays. They don't have full aperture coverage, and usually have some triangular based sampling pattern. I assume I need something similar to that optically.

[michael.h.f.wilkinson]

In principle, a 40mm off-axis mask is fine, but does not gain anything with respect to a PST. Multiple off-axis masks are more problematic, as you could interpret them as a scope with very thick spider vanes. Not nice at all. Full aperture use of a C8 for solar is possible but only with an objective filter (like the Baader ones). Anything else is dangerous. DayStar produces masks to use with a sub-aperture ERFs.

The PST black box contains an etalon much smaller than the 40mm of the aperture (20mm if I am right). You could mount this at the back of an SCT with suitable sub-aperture mask and ERF, but you run into another problem: the blocking filter size. The image will be much larger than at the 400mm focal length of the PST, so the blocking filter needs to be bigger to see the whole disk. This is seriously expensive. The etalon will also have a comparatively small sweet spot, in which the image is selecting the desired wavelength

PST mods can be made from cheap refractors much more effectively.

[JamesF]

That's a good point that I'd not thought of. The focal length of the C8 would work against you if you were after full disc images.

James

[GlassWalker]

I'm not after full disk images, since I have that already. The whole point of going bigger aperture is to make use of the increased focal length and resolving potential to get into the details further.

Also I'm not looking at using a single small aperture, but multiple small apertures as required to restore the spatial resolution.

I know the PST black box isn't the best in the world, but it's the best I'm going to get without spending buckets of cash... put it this way, the "traditional" upgrade route of a 100mm refractor and D-ERF would cost in the ball park of £500. If I can get away with a few filters that would be significantly less than that, and I can think of several higher but acceptable risk even lower cost alternatives. There will be limits for sure, but I'm not going to find them by playing it too safe. I wouldn't be bothered if I ended up toasting a camera or PST black box as they're sacrificial, although I'd prefer not to toast the scope...

[Zakalwe]

If I can get away with a few filters that would be significantly less than that, and I can think of several higher but acceptable risk even lower cost alternatives.

Have you priced up a few H-a filters? 2" filters are about £200 a pop....

I think a cheaper route is a 120mm Skywatcher achro, a ERF buried in the tube and the PST Etalon further down.

[GlassWalker]

There are much cheaper options, but I still need to go through the details and optimisation process.

I'm just not in the mood for another refractor...

[Zakalwe]

If you use 2 sub-aperture openings, then surely you've just made a Hartman mask?

http://www.astropix.com/HTML/I_ASTROP/FOCUS/METHODS.HTM#HM

[GlassWalker]

Doesn't matter what it's called, it's what its effect is that I'm not 100% up to speed on. The application of a focus mask and what I propose is quite different.

[Zakalwe]

have you asked on Solar Chat?

http://solarchat.natca.net/index.php/en/this-is-solar-chat/12-solar-scope-modifications

[Peter Drew]

I've been experimenting for a few years now with PST type mods. I've made a range of refractor based versions from 80mm to 220mm aperture. I would not advocate 200mm+ apertures for solar work as the seeing conditions seldom permit a good image, 150mm seems to be the most effective upper limit. I tried a 125mm SCT conversion as I have a 145mm ERF, although it worked the results were not as impressive as with a 125mm F10 refracting system, a pity as the SCT was much more compact. To the possible downsides of your hypothetical multi aperture etalon prototype, I would add that the etalon is only half of the equation, the other half being the blocking filter, it maybe that just one blocking filter fed by the multiple filters, could cause additional problems.

[Merlin66]

My thoughts...

If you could fit an array of say eight 2" filters around the inside edge of the corrector....the effective aperture would be (2x2)x8=32...this would be equivalent to a 5.5" and have half the light grasp of the 8" - not a big deal for solar.

The resolution would be impacted by the changing PSF...think about it....it would be an 8" aperture with effectively a ragged 6" secondary (66%!!)

There would be a significant impact - I can check Suiter's book for you.

IMHO it's very easy to verify.....

Just make up an aperture mask with the eight holes and view the Moon, Jupiter and a couple of target stars/ double stars. That will very quickly show the possible results.

[GlassWalker]

That book, would that be "Harold Richard Suiter's Star Testing Astronomical Telescopes: A Manual for Optical Evaluation and Adjustment"? I'm curious what's in it, although so far it looks like it'll cost me £50 to find out.

Good idea about making an aperture mask and testing its impact. I don't think I'll wait until I can see the moon again, and it could be a very long wait. But a daytime terrestrial subject may suffice.

[Merlin66]

Yes, that's the one.

It contains what it say's on the lid...a manual for optical evaluation and adjustment. Covers all types of telescopes and the possible/ probable optical problems....

[allcart]

This might help Glasswalker.

http://cs5538.userapi.com/u11728334/docs/70647d387cfa/Suiter_H_R__Star_Testing_Astronomical_Telesco.pdf

[markt]

I don't think this idea will work. A refractor option is going to give you much better results.

Firstly, each of those 40mm apertures is going to need an ERF - you would be looking at a "2 Baader filter for each of these as a minimum (£££££££££).

Secondly the f-ratio of the SCT secondary mirror does not match that of the native PST assembly (f10) - as such image will show big sweetspotting and will go off band across the fov very quickly. Then there's less than ideal field angles on the etalon because the apertures are off axis...

In terms of resolution the maximum resolution you will get is limited by poor daytime seeing, which is much worse than what an 8" is capable of.

[michael.h.f.wilkinson]

The F-ratio of the secondary is irrelevant (it is negative to be precise). The only thing that counts for the PST black box is that it accepts an F/10 light cone, which is what the SCT delivers. If I am not mistaken, an F/-10 negative relay lens is then used to produce parallel beams before passing through the etalon, followed by a positive lens (F/10) which produces the final image. I am planning to build something similar once a secondhand ST80 arrives, using either two F/5 positive lenses or a positive/ negative pair as above, to relay light through the 35mm etalon of the LS35 I have. This set-up gives me a focal length of 400mm so I should be able to use my old blocking filter. A new ERF is needed (Baader D-ERF 75mm placed between etalon and objective).

Later I could upgrade the blocking filter, and attach any larger F/5 objective smaller than or equal to 6" roughly.

Multiple aperture scopes produce nasty point-spread functions that require complicated post processing to get good results. Visually they are not good at all.

[markt]

The F-ratio of the secondary is irrelevant (it is negative to be precise). The only thing that counts for the PST black box is that it accepts an F/10 light cone, which is what the SCT delivers.

The F-ratio of the secondary is far from irrelevant, infact it is the most relevant thing... The C8 is comprised of an f2 primary and (-)f5 secondary mirror, this make the f ratio of the system as a whole f10, however in Ha setup proposed the collimating lens of the PST etalon unit would be seeing a f5 light cone - it's the field angles here that are important. Now, if the focal ratio of the collimating lens is greater than the focal ratio of the incoming light cone then there will be vignetting in the system, however if the focal ratio of the incoming light cone is greater than the focal ratio of the collimating lens then we are not utilising the full 20mm of etalon that we have availble. Both scenarios will 'work' but won't provide as good an image as is possible if the f-ratios match.

[michael.h.f.wilkinson]

The F-ratio of the secondary is far from irrelevant, infact it is the most relevant thing... The C8 is comprised of an f2 primary and (-)f5 secondary mirror, this make the f ratio of the system as a whole f10, however in Ha setup proposed the collimating lens of the PST etalon unit would be seeing a f5 light cone - it's the field angles here that are important. Now, if the focal ratio of the collimating lens is greater than the focal ratio of the incoming light cone then there will be vignetting in the system, however if the focal ratio of the incoming light cone is greater than the focal ratio of the collimating lens then we are not utilising the full 20mm of etalon that we have availble. Both scenarios will 'work' but won't provide as good an image as is possible if the f-ratios match.

Sorry, but that is not right. If this were true, SCTs would be hard on EPs, as hard as an F5 frac or Newtonian. This is not the case, as the light cone is as narrow as that of a regular F/10 scope (basic geometric optics will show that). This is also borne out by Peter Drew's experiments with an SCT for a PST mod. I for my bachelor project worked on an IR spectrograph which allowed an F/15 input light cone, but no wider. Using the Cassegrain focus of the 1.5m IR telescope of the Arcetri observatory was no problem. Likewise, for my MSc project, I worked on a Fabry-Perot-interferometer-based stellar seismometer, which also needed a narrow light cone. Again the Cassegrain focus of the 3.6m telescope at the ESO was no problem.

Your assumption that F/2 and F/5 yield F/10 is not correct either. Assume we have an F/2 primary and an F/(-)2 secondary with the focal points coinciding. In this case the secondary acts as the negative eyepiece of a Galilean telescope, and will produce parallel rays of light coming from the rear, or a focal length of infinity. As can be seen, the light rays do not come out at an F/4 light cone. In fact, in the normal Cassegrain setup (and Schmidt or Maksutov variants are no different), the convex primary acts just like a negative Barlow. The magnification factor is determined by the ratio of the distance of the secondary image plane to the secondary (or Barlow), divided by the distance of the primary image plane to the secondary (or Barlow).

I think the confusion arises from the fact that the primary image plane coincides with the focal point of the primary, whereas the secondary image plane lies much further away from the secondary than its focal point. According to your theory, the light cone at the secondary image plane is equal to that of the focal ratio of the secondary. However, if I make a light cone with the focal ratio of the secondary mirror at the secondary image, it will have a width of the secondary mirror one secondary focal length from the secondary image (obviously). However, the secondary is much further away, so this light cone is much wider when we reach the secondary. If the secondary is 5x further, it will be 5x wider than the secondary mirror. Therefore, if we reverse the rays in this light cone, only light from the inner 1/5ths of the cone, and hitting the image plane can come from the secondary mirror.

For the maths see this page:

http://www.alpo-astr...sh/Cass_Equ.htm

The diagrams there also show that at Cassegrain focus the light cone is narrow

[markt]

Interesting stuff Michael, thanks for that link. SCTs for PST mods are an incredibly rare beast, I know of only 3 or 4 maximum, and they tend to be smaller models. I tried with my 90mm ETX and while it 'works' it is nowhere near as effective contrast and detail wise as a similar sized refractor PST mod (using the same donor etalon), I have also tried off axis briefly with my C8 and the view was appalling If it not the f5 assumption (in my case for the C8) there is definitely something something going on with the light cone and the etalon - can see how the view not only goes off band but also gets a wider band pass across the field of view; this is symptomatic with the field angles of the entrance cone not being ideal. Reading the article I wonder if the issue could be related to back focus? The etalon collimating lens needs to be set at the magic -200mm position, and while we can alter the 'focus' of our SCT by moving the mirror to get this, I wonder if the SCT is 'designed' for its main mirror to work as effectively from it's normal position? I would start to expect issues with spherical aberation to be creeping in when used out of design spec - I guess the SCT spherical aberation would be designed for a fixed back focus? Would we also start to cut the effective aperture by shadowing the outer edge of the primary with the baffle tube? What are your thoughts on this?

[Peter Drew]

As mentioned earlier, I experimented with a SCT/PST mod. I used a Celestron C5 with a full aperture ERF and a standard PST body. The results were by no means bad but compared to the same PST and ERF used in conjunction with a 5" F10 refractor the image seemed less contrasty and had a little more scatter. Overall I felt that the benefit of the compact package of the SCT was outweighed by the reduction in performance. I would support Mark's comment about a SCT's focal position causing correction problems if produced too far from the optimum design position, I recall reading a paper to this effect some time in the past.

[GlassWalker]

Since I started all this I guess I should catch up again...

On the SCT vs. refractor, then it is well know for equal aperture a well designed refractor should be superior due to not having the central obstruction, the presence of which reduces general contrast. Actually, if you dig deep enough that isn't the whole story, since the obstruction has effectively a constructive interference effect at some higher spatial frequencies where it can have a boost over the refractor. Anyway, all that theory is fine, except I don't have an 8" refractor so the argument is rather moot.

On the focusing, it was a while since I looked at it, but in short I will have two focuses to worry about. The sensor should be 200mm from etalon, and the objective adjusted to suit that. I'll worry about just how to do that if I see the sun again.

Back to the original idea I wanted to try... I still haven't done a test of it, nor priced it up. I never said it would be cheap, but I'm aiming for much cheaper than if I were to go the traditional route. Whoever said seeing would probably be limiting anyway, quite probably...

[michael.h.f.wilkinson]

Interesting stuff Michael, thanks for that link. SCTs for PST mods are an incredibly rare beast, I know of only 3 or 4 maximum, and they tend to be smaller models. I tried with my 90mm ETX and while it 'works' it is nowhere near as effective contrast and detail wise as a similar sized refractor PST mod (using the same donor etalon), I have also tried off axis briefly with my C8 and the view was appalling If it not the f5 assumption (in my case for the C8) there is definitely something something going on with the light cone and the etalon - can see how the view not only goes off band but also gets a wider band pass across the field of view; this is symptomatic with the field angles of the entrance cone not being ideal. Reading the article I wonder if the issue could be related to back focus? The etalon collimating lens needs to be set at the magic -200mm position, and while we can alter the 'focus' of our SCT by moving the mirror to get this, I wonder if the SCT is 'designed' for its main mirror to work as effectively from it's normal position? I would start to expect issues with spherical aberation to be creeping in when used out of design spec - I guess the SCT spherical aberation would be designed for a fixed back focus? Would we also start to cut the effective aperture by shadowing the outer edge of the primary with the baffle tube? What are your thoughts on this?

Getting critical distance is one matter, but I think the main issue might well be central obstruction, perhaps compounded by tube currents, which might be worse in a short tube with no real baffles, than in a long tube (preferably with a few baffles).