RMS guiding errors and their consequences...

[Slawomir]

Hi all,

While waiting for clear skies, I started pondering, if it would be of any benefit to one day in a distant future get a bigger telescope.

My current setup allows for imaging at 1.61 app at f/4.5 and at 1.21 app at f/6. Taking seeing out of the equation, the most important aspect affecting actual level of detail in the data is guiding. From what I have seen so far, my mount has been guiding with RMS errors between 0.2-0.4 arcseconds. So during worse nights, and assuming standard distribution, about 68% of guiding will be within +-0.4 arcseconds, and the mount will be able to keep guiding to within +-0.8 arcseconds at all times (100% of samples). This suggests 1.6 arcseconds variation in total, about 1 pixel at f/4.5 and about 1.3 pixels at f/6. Worse guiding is most likely a result of worse seeing, so this would probably be masked by the seeing anyway.

However, for the better nights and with the mount performing the best it has so far, with RMS 0.2 arcseconds, meaning it kept on target to within +-0.2 arcseconds at 68% of the time, and at all times (100% of the samples) +-0.4 arcseconds = 0.8 arcseconds total variation, which is about half a pixel at f/4.5 and 0.7 pixels at f/6.

From those rough estimates, given I did not somewhere commit a mathematical crime, it looks like for exceptional nights it might be okay to put a slightly larger telescope in order to capture that extra level of detail with my current camera. Another option to justify buying a larger telescope could be upgrading the camera to one with larger pixels :lol:

Okay, enough of that, where are those clear skies?

[Atmos]

I guess what it really comes down to is image scale more so than focal length. Taking weight and money out of the question entirely, an ASA 14" F/3.6 Newt with a FLI-16803 will give an image scale of 1.45"/pixel. It is all about matching telescope and camera.

So far I am managed 5 minute subs with a FWHM of 1.7 at 1.158"/pixel, not entirely sure if that is seeing or telescope limited, suppose I'll never know unless I get some truly amazing seeing :P

So the simple answer to your question, yes, you can get a bigger telescope :)

[gregbradley]

Simple, bigger is almost always better - hehehe.
Besides I thought for the average site 1 arc/pixel is the target.

Greg.

[Slawomir]

That a nice FWHM Colin :thumbsup:

Since you are using a premium mount my guess is that most of the time you are seeing limited and much less often image scale limited.

What I was curious about is how far we can push image scale until we become mount limited.

I remember that my AZEQ6 could occasionally guide at 0.4 arcseconds RMS, but usually was guiding at 0.6-0.7 RMS, so there would be not much benefit in imaging at 1 app with it. Since RMS error is for 68% only, guiding would be +-1.2 to +-1.4 arcseconds at all times = about 2.5 to 3 pixels error in total at 1 app (given there are no unexpected sudden large guiding errors). So light that should fall on one pixel would end up on up to 9 pixels on good nights.

Greg - I totally agree with you. 1 app is the target but few have mounts that will accurately guide to take advantage of such image scale.

My conclusion is that we can often aim for large scopes that will give us excellent image scale for those rare nights with exceptional seeing, but rarely we carefully take into account our mount's typical RMS guiding errors.

[Shiraz]

FWIW, I think that you can probably get a bit of a handle on the significance of guiding etc. using a simple approximation that assumes that the FWHM terms add in quadrature.

FWHM = SQRT(seeingFWHM^2 + scopeFWHM^2 + (2.35*guidingRMS)^2)

there are some complications : the scope and camera FWHM is not exactly the same as the scope resolution, since the camera will introduce more spreading via sampling point variations and crosstalk. In addition, the guiding RMS is definitely not independent of the seeing (as assumed in the above equation) and it will also vary with guide update rate and Dec drift rate (polar alignment accuracy). However, the above still gives some idea.

In general, all of our imaging will be dominated by seeing, often to the extent that guiding/scope FWHM contributions may not be all that significant, so there may not be too much point in aiming for perfection in mount and scope performance. In particular, on a night of good seeing, the mount guiding will be better than on a poor night, so the mount/guiding error tends to automatically keep itself within the seeing FWHM. Although of course, systematic errors (mainly backlash and residual PE) that result in non-round stars are generally not acceptable and will be more noticeable in good seeing. With appropriate sampling, a big scope will not really resolve much better in Australian seeing - compare your images with those from the 3.9m AAT, there will not be much in it. The main advantage of a big astrograph is in how quickly it can get to a desired SNR.

[Slawomir]

Thank you Ray, Greg and Colin very much for sharing your thoughts on the topic :hi:

[PRejto]

Sorry, not right on topic but related in terms of resolution. I don't understand this. This is from the Astrophysics site re the BARADV barlow used on the AP175. I always thought that theoretical resolution is determined by aperture and that this is rarely if ever achieved due to seeing. Yet here it seems that going from f7 to f14 there is an increase in resolution.

From the site:

"These two images compare the resolution with and without the Advanced Convertible Barlow using a QSI 683 (5.4 micron pixels) camera with the AP 175EDF at 1400 mm focal length. The left image is shown at 400% screen size and the right image with the Barlow is at 200% screen size, keeping the two images equal in perspective"


George (of AP) commented in a discussion on the TEC discussion group that he believed that pix size was a factor here where at f7 perhaps the pix are too large to permit enlargement to match image size at f14. If true then a longer focal length would have the potential to increase resolution. I don't know what to think! I do know that 4 years ago I took a pretty high resolution photo of M83 using this barlow on my TEC140. I'm curious what you all think about this.

Peter

M83: http://www.pbase.com/prejto/image/151603452

[Atmos]

It actually looks very similar to what I notice between drizzle integration and just standard integration. There are details that under standard integration that don't look that great but really pop after drizzle integration.

[Slawomir]

Interesting question Peter.

While I agree with Colin that it looks similar to a result of drizzle integration, the main difference is that higher resolution data acquired with a Barlow is not a result of mathematical manipulations as it is the case with drizzle integration.

But if both methods produce similar results, then why bother with large telescopes? Unfortunately I don't have an answer to your question Peter, but sometimes I ponder whether the reason for us seeing more detail in some splendid amateur space images is not because of them being taken with larger telescopes, but more so because of premium mounts being used, better cameras and filters, and perhaps even more importantly, inspiring results are due to superior data processing skills of those few truly gifted and experienced amateur astrophotographers.

[lazjen]

It's also a bit harder to compare. After all it's easier to get the smaller scopes - they're effectively everywhere, so therefore you'll have more results overall using them. Larger telescopes are more expensive and so there won't be as many around - lesser pool to work with...

I think for, um, "scientific purposes", I should be given a large telescope to get some data for comparison. :)

[PRejto]

In the case of the Astrophysic's barlow on the AP175 I think we can assume that both images were taken with a state of the art mount and OTA!

Peter

[lazjen]

You're most likely correct Peter, I was more referring Suavi's last paragraph and question. I think more "inspiring" results are just because of the pool of processors for the small telescopes far outweighs those for the large telescopes.

[Shiraz]

Maybe take the images with a grain of salt Peter - I doubt that even AP has managed to find a way around atmospheric seeing and sampling theory.

It is only claimed that the images "compare the resolution" - in the little info I have seen, it is not claimed that they are separate images taken under identical conditions, one with and the other without the Barlow. Do you know of any info on how they were taken?

Might be wrong, but my guess is that the image without the Barlow has been synthesised from the one "with" by heavily downsampling and then resampling back up. ie, it is intended only to illustrate in general terms that a Barlow can sometimes produce better results - which is what you want if you are selling them. The presence of strong processing artefacts in the "without" image may possibly be a clue as to what has been done. An alternative possibility is that the camera is a Bayer camera - if it is, the results would possibly be a little more understandable.

If the seeing is really good and a non-Barlow system is undersampling, then a Barlow can certainly help, but that comparo looks more like a guide than a true result.

[PRejto]

Who knows, Ray. I only know what I've read on the AP site. When I think of a company like AP I find it hard to believe they would fabricate an image to sell a product. But, as I said, who knows?

The next time I see Roland I will ask him directly about this!

Peter

[Shiraz]

I don't know either, and would also be very surprised if they fabricated an image - but synthesising an image from real data to illustrate what they have observed is something different. Or maybe they just used a Bayer camera.

Whatever, angular resolution is primarily determined by aperture and/or seeing. Adding a Barlow only changes the image scale and, provided the sampling is right, it does not change the resolution for DSO imaging (if it was possible where would you stop - maybe a stack of 5x Barlows could get Hubble-like results and there would be no point in big scopes or AO)

I guess it would be interesting for someone to try it out.

[Atmos]

The one without the barlow looks undersampled with a OSC camera so increasing image scale will make quite a significant improvement. It kinda looks like a single exposure looking at the star colours, they're not overly uniform.
I think what Ray is getting at is that (and I agree) increasing focal length doesn't improve seeing :)

[gregbradley]

One thing I don't quite follow on this thread. In my experience you notice weak guiding at any image scale. Sure 2x2 binning sometimes rounds out guiding errors to some degree but not fully.

Having more arc secs/ pixel will not hide guide errors. Of that I am quite certain. I have imaged at lots of different image scales. They all show guide errors.

In fact I find the CDK17 most forgiving of guiding and easiest to get round stars on and that has the lowest arc/sec/pixel of my setups.

So 1 arc sec/pixel it is for those with average seeing of around 3 arc secs.

Greg.

[Slawomir]

That is very interesting observation Greg that goes against ones intuition. I do not have any experience in guiding at long focal lengths (longer than 1.2m), but I can certainly second what you wrote about binning - it does not fully hide guiding errors. When guiding was bad with my previous mounts, even binning 3x3 resulted in eggy stars in some subs, in spite of my hopes that stars will be perfectly round in all subs.

It seems that accidentally I started a quite interesting and useful discussion :-)

[codemonkey]

I suspect we (or at least I) get better seeing than people assume is typical in Australia. I routinely get 1.8" FWHM L subs with my Esprit 120. Using Ray's handy spreadsheet I can reverse-engineer an approximation of the seeing at my site based off:

0.12m aperture
0.6" RMS guiding
1.8" FWHM stars in the resulting images
= ~ 1.28" seeing

Again using Ray's handy spreadsheet, upping my aperture to 0.2m would reduce the FWHM of stars in the resulting image to approx. 1.63"

I realise these are approximations, but don't know exactly how accurate Ray's formulas are. I do know the aperture of my scope, typical RMS guide errors and resulting star FWHM with confidence though.

[Atmos]

For me to get a FWHM like that happens very rarely. I am usually closer to 2.5" on average. The best I've ever got was a night around 1.5" up at Heathcote for a while.
I've had 1.7" briefly in Ha one night in Melbourne. Well that's two instances of below 2" :P

[Shiraz]

the assumptions make it a bit ropey to backcast like that Lee, particularly in extricating seeing from the effects of guiding RMS. The actual seeing is likely to be in between what the spreadsheet gives with your measured RMS and with zero RMS, but there is no way of being any more precise, so it is what it is and that is still useful information.

you are fortunate to have seeing that good, but it is not unheard of in Australia - just not available in all locations http://articles.adsabs.harvard.edu//full/1995PASA...12...97W/0000101.000.html
pretty good here tonight as well - between gusts it is well under 2 arcsec:D.

yeah, you need a bigger scope ..... and a bigger mount and .......

[Slawomir]

Speaking of bigger mounts, I'm not sure if it is always plausible to assume that bigger aperture, even from the same manufacturer, will necessarily yield tighter stars given the same level of guiding is maintained with a heavier telescope. It is curious that for example Orion Optics states that for their fast Newtonians 12inch will yield the smallest spot size on and off axis, while their smallest 8" as well as their largest 16" Newtonians both have the largest spot sizes. Or is spot size unrelated to the FWHM we can expect in our images?

[Atmos]

At shorter focal lengths poor spot sizes will yield soft images while it becomes less important as focal length increases.
For instance, at 16" F/3.8 has a focal length around 1544mm. If used under the kinda average 2" seeing conditions that we've all grown to know and love, a star will cover 15 microns.

An 8" F/3.8 has a FL of 772mm and stars will cover 7 microns at 2" seeing.

[Slawomir]

Thanks Colin. Would then a 12" f/3.8 from OO, with stars covering 11 microns yield better data than a 16" when seeing is about 2", since spot size for 12" is less than half of an 16"? Would this suggest that smaller aperture telescope is not always inferior to a larger one in terms of resolving power, even from the same manufacturer?

[Atmos]

Location location location!
If I was at the top of Atacama or in Chile I would be getting the 12" and whacking a FLI ML-814 (same chip as the QSI690) as it would be imaging at 0.68"/pixel. Considering the sky clarity and spot diagrams, it allows for drizzle integration for some serious resolution.

Out in the average Aussie burbs however, it doesn't matter a great deal :P

[codemonkey]

Thanks Ray :) I should probably correct myself in that I routinely get 1.8" (sometimes better, but rarely) for part of the night, definitely not all night. As the target drops in the sky and I shoot through more atmosphere the FWHM goes up.

If I was to get a bigger scope I'd be looking at an 8" RC or Edge, both of which are smaller and lighter than the Esprit. But getting one would only be sensible if the resolution gain I'd get from the greater aperture wasn't offset by less great optics.



I don't know much of anything about spot size, or optics in general. Doesn't seem to be published for the Esprit either. I think I've seen Colin posting recently about the ideal spot size for a given camera, but I'm not sure of the details. Colin, can you (or someone else) elaborate on this?

[Atmos]

I have a quite limited knowledge on spot diagrams (can spot bad ones but struggle to read the difference between good ones), MTF curves and the like. Mostly I can spot bad ones and glean some very basic information, something I am slowly trying to teach myself :)

What I thought I would show is two images that I have taken. Same target, same lens, roughly the same integration time but different cameras.

LMC with Nikon D700 & Nikkor 85mm F/1.8G (http://www.astrobin.com/full/269173/0/)

Nikon D7200 (http://www.astrobin.com/full/286072/0/)

The first was taken with the Nikon D700 which has 8.445 micron pixels and an anti-aliasing filter which means that I can never get better than a FWHM of ~8 pixels. It was taken wide open at F/1.8 so when I saw a little bit of blue/purple around some stars I really wasn't too surprised. The stars are showing some slight deformity at the edges of the FX frame. Also not too surprised at F/1.8.

The second is with a Nikon D7200 which I think has 3.91 micron pixels and no anti-aliasing filter. It was taken at F/4 so a far cry from wide open. It shows a LOT of purple (the outer star forming regions look purple and not blue) and you can see the stars deforming quite easily in the DX chip. There is however ~3500 galaxies in the PGC catalog in this image!

What these two show is that even an average lens can show almost zero aberrations if quite large pixels are used. Small pixels really show any optical imperfections, especially when small pixels are matched with a higher QE and lower read noise.

In some ways this also points back to what Greg has seen with shorter scopes with small pixels vs larger scopes with larger pixels. On average, most of the shorter focal length telescopes are cheaper and have smaller cheaper cameras and lesser quality correctors so even when you're imaging at the same scale, optical imperfections are more likely to be an issue.

I have recently been looking at short focal length optical nirvana, looking at telescopes like the Tak Epsilon series (F/2.8-3.3) or a Boren-Simon Power Newt 8" F/2.8 (8" F/4 with an ASA 0.73x Corrector/Reducer). These are on the cheaper side for their size and focal ratio and it shows when using cameras like the ASI1600.
Of course then there is the large price increase to the ASA 8" F/2.8 H which has spot diagrams that just make one drool which is effectively what you end up paying for.

[Slawomir]

Very interesting discussion and I really enjoy reading what everyone has to say about the topic. Colin, I certainly prefer the look of the image taken with D7200 - and both indicate quite a few interesting regions for potential targets! As you can probably imagine, I really can't wait to finally test my new small refractor and see if it is capable to collect photons more elegantly than the best telescope I have owned until now - a TS 4" doublet.

As for spot diagrams for apochromatic refractors, below is an interesting excerpt from an article written by Pal Gyulai, optical designer from CFF Telescopes. I hope it is okay to quote entire paragraph.

In fact, if we construct a fast triplet APO lens of F/6 focal ratio and the optical design is optimized for the "best looking" spot diagrams, then after actually building the lens and testing it under the sky, the image quality will not be optimal. This is not surprising, as the classical method cannot be used for optical systems approaching (or at least getting reasonably near) the diffraction-limited quality. Today we expect better than diffraction-limited performance everywhere between the blue and red colour wavelengths, so, the classical methods (that can't explain why we see an Airy disk surrounded by diffraction rings in the eyepiece) cannot be used anymore. This methodology was perfect to design car headlights, room lighting and slow focal ratio achromat lenses and (judging by today’s standards) semi-APO lenses. But it is not usable to construct modern, fast APO systems.

[Atmos]

That is a really interesting read Suavi, something that I wouldn't have expected. My general assumption would be that when you have the best spot diagrams you would have the best performance, i.e. light it being focused at its best and most efficient within that system.

I've still got so much to learn!

[Slawomir]

I reckon we all have a lot to learn, but that is arguably the best part of this hobby :-)

It makes sense to me that when we talk about diffraction-limited performance, we should consider light as a wave not particles. That is not to say that spot diagrams are not useful- they certainly have their place and are also relatively easy to read.

[codemonkey]

Cheers Colin (and nice images both!). I've got a basic understanding of spot diagrams, can spot basic aberrations etc. My main question is what are you looking for in relation to pixel size? Is there a specific ratio that will yield optimal results?

Interesting quote, Suavi! Certainly for me at least, it's very difficult to compare scopes and make a decision that's better than a gamble.

[Atmos]

I don't think there is a ratio that you can use perse. You also need to consider the sensor size, the ASI1600 has the pixel density of a 65MP full frame sensor but you wouldn't want a full frame sensor with 3.8 micron pixels as there isn't many telescopes available (they're all VERY expensive) that can handle that pixel size off-axis. The shorter the focal length the less seeing conditions have an effect.

Shooting with a 50mm lens will ALWAYS be lens (and camera architecture) limited where as a 24" F10 will always be seeing limited unless using something like 24 micron pixels.

[Shiraz]

for anything but a very small scope, suggest that the pixel size in arcsec be 1/2-1/3 the seeing that you expect if you want the optimum DSO combo of sensitivity and resolution.


good point but maybe you could take it a little further - a 24" scope will always be seeing limited even if it has significant aberrations. eg, if a big scope has say 1/2 wave of SA, it's FWHM will blow out by say a factor of ~2x - to 0.5 arcsec. But that will still be way less than typical 1.5-2 arcsec seeing FWHM, so it will not matter (quite a bit worse could be tolerated - which is why scopes with horrendous central obstructions still work OK). Optical quality is a major factor with lenses and small scopes, but it is almost of secondary importance with big ones - unless your seeing is exceptional.

[codemonkey]

Cheers guys. Yep, Ray, I've been under the impression that 1/2 - 1/3 the seeing in "/px is what you should aim for, but Suavi's earlier comments have me wondering, specifically in regard to the assumption that a bigger aperture is going to mean better resolution: what if it does the opposite because the optics suck?

As mentioned earlier, my "best common case" seeing is about 1.8" with a 120mm scope and 0.6" RMS guide error. We established earlier that puts my actual seeing (approx) between about 1.6" and 1.8".

So lets say I want to make the most of it, err on the side of resolution and oversampling so we'll use 1.6". Again erring on the side of oversampling, I'll go with 1/3 of the seeing in "/px - that tells me I want to be sampling at about 0.53" / px

Given the above, an RC8 combined with the ASI 1600 looks like a good fit. Increasing the aperture (assuming all else is precisely equal) should have reduced my FWHM to 1.6" instead of 1.8"... but how can I be sure that the RC8 is going to be a good choice? What if it's just plain "not sharp"? What metric can I use to compare my options before making such a purchase?

Funny thing this hobby... the longer I'm involved with it, the more I realise what I don't know.

[billdan]

To put things in perspective I have attached some photos from Sky and Telescope in 1997 (20 years ago).
The first is a typical pixel planner for planetary or DSO imaging, and the second the difference in quality of large pixels on DSO images.

How things have changed with respect to cameras, as 9 micron is about the largest you can buy today and the average around 5 micron, with the newest cameras at 3 micron or less.

Cheers
Bill