Out Out Damn Spots! .... Swatting at Celestial Gnats, Part 2

Maybe you don’t feel guilty about your astro imaging post processing (PP) the way Lady MacBeth did for her crime, but sometimes I do. I know I should learn to do more with my Photoshop. I’ve even contemplated starting to learn PixInsight, but I’m just too busy with other things.

I rationalize my avoidance of PP by saying I like to experience the sky first hand. This attitude is a form of photon fixation I’ll return to at the end of this posting, although with smart scopes we’re really operating cameras so this rationalization doesn’t work too well. I often try to “science the shit out of it” to quote Matt Damon in The Martian. That’s what I’ll do now to the challenge of stellar images and what they do to our images.

In the previous post I looked at the numbers of stars we start to encounter as we go to fainter magnitudes. (And note that in astronomy, many quantities are backwards to what they might be. Fainter magnitude stars are higher numbers.) I also thought a bit about how we actually need lots of stars in our FOVs so that the scopes can orient, find, and then track objects. I found the exercise very interesting because it started to tell me about the engineering of the smart scopes.

This second posting is going to now look at the sizes of the stars in our images. It seems everything is getting bloated these days, from portions at a restaurant to my waist. Let’s try to understand what’s happening in celestial imaging and see what we can do to have some control over it.

I will also give one of my usual caveats. I know there are some of you who are far more proficient at the science and practice of astronomical imaging. I consider myself an amateur amateur astronomer. So, please correct or add to this posting in the comments if you have ideas and thoughts that can help with PP stars.

REAL STAR SIZES

The first thing we need to realize is that the star sizes on our images basically have nothing to do with actual star sizes. I have to be careful here because two stars at exactly the same distance, that are exactly the same temperature, but differing in diameter will actually emit different amounts of light and the bigger one will yield a bigger digital image. But this isn’t the major effect. We’ll stick with the difference in sizes on our images due to different apparent magnitudes.

Except for the above image of Betelgeuse by the HST, the JWST nor our smart telescopes can directly measure the size of a star in a simple image. All stars should be regarded as point sources no matter what their brightness.

If we imagined our Sun at an “extremely” close distance of 1 pc (=3.26 light years), it would only be 0.01 arc seconds in diameter. That’s 100 times smaller than the theoretical resolution of my eVscope and 172 times smaller than one of its pixels. Placed at a more typical distances of maybe 10 to 100 pc, it would be just that much smaller. Even Betelgeuse would only be about 4 times bigger and just at the limit of HST’s abilities in orbit. Note that the JWST will be worse than the HST even though it’s a much larger diameter. That’s because it operates at infrared wavelengths and longer wavelengths mean poorer resolution.

So, I hope this convinces you that the star sizes we see have nothing to do with measuring their real diameters. What determines their sizes are their apparent brightnesses. Stars with smaller m’s will appear larger in our images.... It’s astronomy remember, relationships are bassackwards…. ;-)

DIGITAL STAR SIZES

Now, what’s really curious, to me at least, is that the diameters of the stars are all the same when they finally get focused by our scopes. What? Yes. I mean that a 15th magnitude star and a 1st magnitude star will come to focus in the same size spot. Now, our scopes will not be able to show that difference — mostly because of the sky brightness — but the stellar images all spread out to the same size.

Since the stars start out as point sources, there are only two things that affect how big they will be when brought to a focus. The first is the diameter of the telescope’s primary objective, whether it is a mirror or lens. Light behaves like a wave when it comes to our optics, so there’s a theoretical image diameter, which is approximately the wavelength divided by the diameter of the light. This gives and an in radians, which is not useful to us. Converted to arc seconds it is 114/D(mm). Here are some theoretical limiting resolutions for three different smart scopes, the Unistellar scopes, a Vespera and then a Dwarf II. (If you have a different diameter you can figure yours out using the formula.)

Diameter Resolution

112 1 arc second

50 2.3 arc seconds

24 4.8 arc seconds

Thus, the first rule of getting smaller star images is:

1. The bigger the aperture of your smart scope, the smaller the stellar images will be.

My highest resolution scope is my eVscope. Even at 1 arc second for the optics, the pixel size is 1.72 arc seconds across. So, that means that the optics are really not a limiting factor. For the Vespera, the pixel scale is 2.99 arc seconds. Both scopes “undersample” in their imaging, which basically means they could go to finer pixel scales to take advantage of the theoretical resolution.

But, that really isn’t good to push these puppies too far. Undersampling might yield slightly lower resolution final images, but it does lead to better signal to noise and make it easier for the telescope to do do long enough exposures. I’m not going to mess too much here with resolution. I’m more interested now in what gives a star the size it has. In our cases here, the telescope optics aren’t really a problem, especially considering how these scopes work. So, what else makes our stars bigger?

ASTRONOMICAL SEEING

Astronomical “seeing” refers to optical distortions imposed upon incoming light from the stars. The Hubble Space Telescope achieves its high resolution because it doesn’t have to contend with any blurring, changing air. Given that we have to operate from our planet’s surface, we can’t avoid the atmosphere. It is maybe the secondary problem we encounter after the light pollution.

Typically seeing is measured in arc seconds and can range over at least an order of magnitude from fantastic 0.5 arc second to horrible 8 arc second seeing. It can’t be avoided. 3 arc seconds of seeing combined with the resolution of my eVscopes optics yields a theoretical image width at half max which is the square root of 3^2+1^2, or 3.2 arc seconds.

So, if the seeing is bad, it is usually the most serious factor broadening the star sizes. The second rule of reducing star sizes is then:

2. The smallest stellar images will be recorded when the seeing is best.

I should add one thing that might make us feel a little better because our apertures are not that large. Larger aperture can lead to bigger problems with atmospheric seeing. Maybe not so much in the sizes of modest amateur telescopes, but it is noticeable with the 11 and 16 inch ones. So, if you’re feeling aperture envy, this should be another reason why the smaller ones are actually better.

IMAGE SIZE AND THE DREADED AIRY CURVE

Now I can put most of this together to explain the image size phenomena. After combining the effects of a finite aperture imaging a light wave, with the atmospheric seeing distortions, a point source of light like a star will result in light falling onto the sensor like the curve above. It's named for the astronomer who first explained it, G. B. Airy (who was an Astronomer Royal)!

The half width is the same for all brightnesses of stars. It’s just for fainter stars the peak is lower relative to the sky background. So, fainter stars will show less of their Airy curve “girth.” Bright stars, which blast above the background will show that half width and then some.

Of course there is possibly an issue with the number of bits our scopes can record, but I don’t think that’s the major factor here. It’s the light distribution curve of the of different magnitude stars relative to the background.

POST PROCESSING (PP) IMAGE SHRINKERS

Aside from the two ways to image smaller images described before, there are ways to reduce or even eliminate stars by manipulating the images. I’ve mentioned that I’m not as heavily into PP as many of our colleagues, but I can tell you what I know and what works for me.

The best results really require an intelligent filter. Since we know the stars will basically be Airy curves, the filters work by reducing the half width. But, they have to do it carefully so as not to leave artifacts.

If I want to reduce stellar images, I’ve had some success with a Photoshop plugin called StarShrink by RC-Astro. I believe they have one for PixInsight too, but I’m too lazy, at this time, to learn PixInsight. Photoshop and Affinity are really all I use and I’m not exactly tht proficient with either. Here’s a side by side example of what StarShrink can do when pushed hard.

A FINAL WORD ABOUT PHOTON FIXATION

I can hear some of my colleagues saying, well, in a “real” telescope when looking through the eyepiece, the star images are very small. And, indeed they can be. I understand that.

But what I don’t really get is the idea that people like to be able to experience “real photons” on their retina. Just because our smart scopes go through the process: photons -> electrons -> more electrons-> photons doesn’t mean this is a totally artificial process.

And as for capturing photons directly onto our eyes, well, we actually capture them even without telescopes. I did a basic calculation and here are the numbers of photons falling on the retina of one of our eyes without a telescope for different magnitude objects:

Magnitude No. Photons

1 1,200,000

5 31,000

10 313

15 3

So, indeed, if you know where to look, even Pluto is slapping a few photons onto your retina. We can’t really detect them, but they’re there — even if Pluto** isn’t a real planet…;-)

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P.S. I received a request a while ago to go to black on white type to make the blog entries more readable. As usual, it took me a while to figure out what I was doing. But, I hope that helps. Thanks goes to whomever made the request.

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• HST Image Credit: Andrea Dupree (Harvard-Smithsonian CfA), Ronald Gilliland (STScI), NASA and ESA

** I shouldn’t be too hard on little Pluto. He’s a great target for smart scopes. I’ll do an entry on him when he starts coming into view later this year.