Astrophotography resolution: what should "good" look like?

One of the interesting challenges of astrophotography is that there are so very many factors that go in to the result. Basically, it can be difficult to determine what went wrong. Pull down your face shields, we're going to do something similar to science...

I'm going to use my rig as an example, because, well, I did this math already. But that's ok because you can use use it to get some idea of things. I'll give you the math if you're really inspired to scribble on a big chalkboard and draw diagrams to impress your ladyfriend (or gentleman friend...and.... like other species geeks and nerds come in a variety of standards and even non-discrete units- gender/sexuality can't be determined by Millikan oil drop).

The non-variables:

• I have a 6" f/4 telescope with optics of unknown quality
• Through these optics, each pixel represents 1.46 arc-seconds of sky/star
• My tracking scope (ST80) and its little camera reproduce 1.93 arc-seconds per pixel
• I have some messy data from my tracking scope in operation (used below)
• The angular diameter of Sirius is 0.006 arc-seconds

I obtained the arc-seconds/pixel numbers for the two scopes by plate solving images taken from them using the wondrous tools at nova.astrometry.net.

So very simply, if the angular diameter of Sirius is less than one pixel of the sensor, and if everything was amazingly perfect it should look like this when magnified:

Not real life

If you claim to have seen such a thing you're a liar and a scoundrel.

Any telescope's resolution is limited by the physics of light, simply because the quality of an optic, and how cleanly it reflects is proportional to the wavelength of light itself. Even if the optic is beyond the light's wavelength, the pinpoint of light will reproduce a central disk with rings of interference around it in a ratio of 84% in the middle, 16% in the rings. How long you expose the image will determine how bright the rings are, up to a point that they no longer appear as rings on the sensor and are instead a larger disk. This is why images of bright stars fill more pixels than dim ones. The size of this disk is determined by the diffraction limit, which is:

1.22x wavelength(cm)

----------------------

diameter(cm)

in radians. So light somewhere in the middle of the spectrum: 0.00005cm and diameter of 15.2cm, we get 0.83 arc-seconds. Astro-Tech lists the scope's resolution as 0.76 arc-seconds. Isn't that interesting? At any rate, that's the area of the central disk. So in theory a short enough exposure would still render a single pixel. The diffraction rings, which look a bit like this:

Not to scale with the other fake pixels

would render as pixels something like this with sufficient exposure:

Real life if you're in space

That's looking more like a star in a telescope like we're used to. This takes care of your Dawes numbers, Raleigh, or whatever else you subscribe to. Don't get too picky on the differences between those, we're taking pictures from the bottom of a deep pool.

Being in Florida I'm looking through about 30 feet of water in a best case scenario. It's a swampy, swampy state with a lot of dense, wet air starting at sea level. This produces  "seeing" quality issues. The dense/wet air refracts light the same way that a glass (refactor) telescope does, except that it is constantly shifting with air currents, hundreds of times per second. If I were on Mauna Kea again that would distort the location of a given star (and its diffraction rings) by about 0.4 arc-seconds on a good night. Here? It's probably 2 arc-seconds on a good night, and likely 3 most of the time. Let's go with 2.5, or 1.7 pixels. Yes, I'm skipping over the concept of FWHM here because it's a calculus problem and you don't really need it for this sort of back-of-the-envelope look at things. Maybe another time. New image:

Scuba/Swamp Vision

That's basically my expected detail if I get everything else completely right with a significant exposure. Shorter exposures of course could render a smaller image. In fact if the exposure was shorter than the frequency of eddie currents causing the seeing conditions (and I got lucky with a current that got very little distortion), and short enough to not expose the diffraction rings it could take up a single pixel. Instead, this is what I've got:

This should really only take up 4 or so pixels

The shift of colors from red to blue tells me there's chromatic aberration, and because I can see it on other more significant things in that image comatic aberration as well. How do I know the stretch isn't tracking?

PHD2 unfortunately doesn't like my camera and won't let me put in a pixel size value for it, so it only reports deviation in pixels. Since I was able to plate solve an actual image from the camera though, it's easy math (arc-seconds = 1/(pixels per arc-second*deviation)):

• Average deviation of 0.45 pixels = .87 arc-seconds
• peak deviation of 1.5 pixels = 2.95 arc-seconds

Those are for the ST-80, so arc-seconds being the common here that means going the other way for for the AT6IN/Fuji combo:

• average deviation of .87 arc-seconds = ~0.6 pixels
• peak deviation of 2.95 arc-seconds = ~2 pixels.

The image is stretched over at least 3 pixels, so the only other candidate beyond my optical issues is focus. I'm focusing using a Bahtinov mask, which results in one of those scientifically accurate levels of focus that I can't determine by looking at pixels alone.

So...collimation, optics, aberration.

For reference, here's a bright star with a longer exposure. It's a little harder to tell what's going on there, but you get the idea:

Astro-probs.

Astrophotography updates, buying problems for myself

New optics!

The main scope (for imaging) is an Astro-Tech AT6IN, and the new tracking scope is an Orion ShortTube-80, or ST80. There's a dozen versions of the ST80 of different names, all made by Synta for the various retailers.

I wanted something with a wider field of view, in this case the focal length is 610mm. Where the previous scope (a Celestron C6 SCT) rendered about 1.1 arc-seconds/pixel on my Fuji X-T1 camera, this renders closer to 1.5. In other words, it sees more sky.

This offers a few advantages:

• Tracking does not need to be as precise (we'll get to how much...)
• I can image larger objects, such as the Pleiades, Rosette, and Horsehead/Flame nebula
• Being the same aperture (6") but wider, that also means it's getting much more light every second the shutter is open.

How much more? If the previous scope was more or less F6.3, and this is F4, that's about 2.5x more light. So if I needed a 60 second exposure before, this would need a 24 second exposure. 

And now I'm going to tell you why this was a terrible decision.

A short focal length Newtonian is a mess. It naturally has a ridiculous amount of comatic abberation, which is inherent in all large optics, but is exaggerated the shorter the focal length. Without a corrector this scope is basically worthless.

The coma corrector (made by GSO) mostly helps this...but your collimation (having all the optics at perfect angles to each other so that the light path is focused evenly/flatly on the image sensor) has to be really, really perfect. I've seen some estimates that at F/4 the image breakdown occurs when the light path deviates by as little as 0.45mm from accurate.

0.45mm. Let that sink in. You know how wide the bullseye is on a typical laser collimator? About 4mm. Part of that is because the output optic for a typical laser diode is 3mm.

So what you're doing is taking a really nice, wide angle image that should be able to get beautifully sharp and subjecting it to something that will begin breaking down at a level of accuracy that is 8-9x more accurate than the equipment you're going to calibrate it with.

Now suppose you're like me, and are the type that will stretch a thin film over your collimator so that you can see when the return light path, which is focused to much smaller than the exit light path, makes a nice bullseye in the exit path. Assuming you also loaded your collimator in a lathe at some point and centered that path to within a few mm at 50ft, you're probably able to get it within the margin of error.

If.

If the rest of your optics are aligned correctly, which... mine were not. Worse, they were not able to be: if you have a closer look at the image above you'll spot some extra holes where the secondary is mounted. My secondary mirror was too far down the tube to align correctly. Yay.

And then it still won't be good enough.

You'll hang a heavy imaging train off the side of the scope, which will cause the focuser to flex off of center on its mount. Your imaging train will have to be especially awkward because there's a heavy corrector optic in it, which then has a spacing of about 75-80mm (mine does best at 78mm) before it finds an imaging plane, which is probably a mirrorless camera or DSLR. This will shift things out of alignment by a couple mm. Which is enough to notice.

I think Newtonians might just be a bad idea anyway.

Once you've done all of this, you'll have a system which is very out of balance for the mount. The camera will sit at a different axis from the finder and tracking scopes (otherwise it will be in their way). You could add weights opposite of the focusing assembly, but of course this stresses the mount even more.

So...now what?

I don't know. I'm going to keep playing with it for the moment, and try not to get any farther down the rabbit hole unless I think I can make it truly work out. I have managed to take a couple ok-ish images with it, but far short of what I think my setup could otherwise do:

Pleiades, stack of several 180s exposures from the Astro-Tech AT6IN and Fuji X-T1. Of course from my fully light polluted Central Florida skies.

I like the wider field of view very much. Note: this was taken when I was still trying to get the coma corrector spaced out just right, so it shows worse on here than it is in some of my tests.