I often see comments from smart telescope users who want to drastically shrink or even eliminate (!) foreground stars in their images of nebulae and galaxies. I must confess that this desire bothers me a bit. When I see a nebula with no foreground stars it seems naked and without its stellar context. After all, the nebulae are either clouds associated with the formation of new stars or the ejecta of dying stars. Taking the stars out is like eliminating all but the youngest babies and great grandparents from a family photo album.
In this posting and the next I’m going to step back to think about the stellar context of our imaging. I’ll admit I’m an astronomer and more interested in the astrophysics than I am in image processing (IP). I will also confess that my IP skills are more limited than many of my smart scope peers. But I do think I can convince you that the stars are our friends and critically responsible for the magic of our scopes.
This first stellar blog entry will be about the numbers of stars and how they figure into the mysterious processes of initializing and tracking done by our smart telescopes. In it I hope to convince you of how the engineering of these scopes was optimized to make them operate like championship hunting dogs.
The second stellar blog, which I hope to finish in the next week, will then look at the formation of the digital stars and how we can cope with their sizes to at least be able to get a handle on them with a couple IP apps. In that one I also hope to help you understand the immense challenge we have in dealing with points of light that range in brightness over factors of millions with just a few bits of data. Furthermore — the atmosphere gets into the act to smudge them as well so that no amount of resolution can get the better of mother nature with the scopes we use.
I invite you along now as I show you how I think about the “problem” of stars. It won’t be precisely rigorous, but I do promise you I’ll think talk about them in quantitative ways that might help us understand our situations better.
JIT APPARENT MAGNITUDES
JIT stands for “just in time.” I’m sure you don’t want to be dragged back through your Astro 101, but I do think I should do a quick review of some concepts from time to time. And this time we need to be comfortable with the topic of apparent magnitudes in astronomy.
Stellar brightnesses are a problem we face in astronomy. It seriously presented it self when we began to chart naked eye stars thousands of years ago and it continues in our age with digital imaging chips. Our eyes see brightness differences in a logarithmic way. This means that the sensitivity of our eyes to brightness changes is not linear. (BTW, We perceive sound logarithmically too and use decibels instead of magnitudes.) You’ll see next time that our chips do not see logarithmically, they respond linearly. For all their advantages, their linearity presents a major challenge too.
So, stars we might see in the sky with our naked eyes have traditionally been ranked into 6 broad classes, with 1 being the brightest and 6 the faintest. We started calling these rankings magnitudes and it has stuck. 1st magnitude is reserved for the brightest stars and 6th for the faintest we might see in a dark sky (Dark sky, what’s that?). Now, this is a very old fashioned scheme and we can be made very precise with photometers, but we don’t need to get into that here.
What’s curious is that if we were to measure the actual visual intensity or apparent brightness of these stars we see with our eyes alone, we would learn that they actually emit a range of light that is a factor of 100. In other words, a 6th magnitude star delivers just 1% the amount of light to our eyes as does a 1st magnitude star.
And, it can get more extreme — much more extreme — when we use telescopes. Even our smart scopes can record brightnesses that are millions of times fainter than a 1st magnitude star. That gets us down to an apparent magnitude of about 17. Or at least that’s the faintest I’ve recorded. I’ll come back more to this magnitude challenge in the next posting because digital devices simply can’t deliver such brightness ranges from individual pixels. For now, let’s just consider how many stars there are in the sky as a function of apparent magnitude, m.
STAR COUNTS
We live in a galaxy made of many billions of stars. Within it we cannot possibly reckon them all without large professional telescopes or satellites and infrared detector, but we do know how they stack up in our vicinity. If we make the extremely crude assumption that the density is uniform and their absolute visual magnitudes are the same we find that the number of stars at each magnitude class scales like 10^(0.6m). This means that the number of stars we count goes up almost a factor of 4 each successive magnitude.
So, if there are 22 first magnitude stars, these assumptions will lead to a simple model of 88 seconds, 352 third magnitude stars, and so on. Of course this model is a bit absurd because it ultimately would lead to a uniformly bright sky as we added on more and more stars. This is the famous Olber’s Paradox.
We won’t go into it that concept here, but I will list hear some of the numbers from a much more accurate model for fainter magnitudes that are important to our smart telescopes. And I will do one more thing. I will divide the number of stars expected for each magnitude by 41,253. This is an important number in astronomy — it’s the number of square degrees in the entire sky.
m # Stars per Sq. Deg.
10 3.6
11 22
12 55
13 136
Why are these numbers useful to us? Well, to me at least, they tell me a lot about our smart telescopes. Here’s why.
When I multiply this last column’s numbers once more by the field of view (FOV) of a smart telescope I find an interesting result. The FOV of an eVscope1 is 0.24 square degrees. So for magnitude 11, it yields an average 5.3 11th magnitude stars on average per random direction on the sky.
The photo here shows a recent snap shot of my screen just after my scope initialized and started tracking from a random location of the sky. This is, of course, before any image stacking. I’ve connected some triangles and a couple quadrangles. I like to think of these as smart telescope “mini constellations.” Sure they’re tiny, but they’re important. Traditionally, there are 88 constellations. At the scale of this image if there were two of these for every square degrees, the sky would be filled with 2x41,253=82,500 smart telescope mini constellations! It’s about a thousand fold increase! Those 82,500 "mini constellations" are the way that scope “sees” the universe. Now, I wouldn’t take my musings to be precisely accurate, but in round numbers, I’m sure this is the right way to think.
I also have a Vespera. It’s FOV is 6 times greater than my eVscope. So, it only needs to detect 10th magnitude stars to come up with ~5 stars in its FOV. But, of course its aperture is about half the diameter of the eVscope, so all other things being equal (chip sensitivity and integration time) it will always be a magnitude or two “behind” the eVscope. But its FOV compensates by imaging more stars in total.
I know the other smart telescopes coming on board now work nearly the same way. All they need to do is get enough light to capture enough reference stars in their FOV. So, actually, smaller, wide field optics are a good way to go.
I seriously hope you’re following this line of argument. I really don’t want to get more technical than I need. I will also admit that I don’t have any inside information from the manufacturers, either.
PLATE SOLVING
Here’s what this star counting is telling me. These scopes have been carefully engineered to enable them to “plate solve” easily. What’s plate solving? Well, it’s the computer algorithm that their little Raspberry Pi brains use to figure out where the scopes are pointing. These scopes all have a database of stars and a way to represent the “mini constellations” mathematically.
I’m not precisely sure, but I think the plate solving programs then look for small patterns of stars because they are the fastest way to identify a star field. They can’t use individual stars, of course because one looks just like another without spectroscopic information. And they can’t see wide enough parts of the sky to ID the real constellations, which are quite large (Orion is 594 square degrees). Instead, I believe the plate solving routines store lots of stellar triangles and quads. The scope then measures numbers for the triangles (triads) and quads in its FOV and generates what are called hash codes of four numbers to compare with a stored table. It turns out that the information specified in a couple small triangles or quads in your FOV will be quite distinctive and easy to sort out.
(I’m also sure the telescopes pay attention to how the stars are moving when it’s stationary to also fine tune the regions of the sky to check for hash codes.)
Thus, these scopes need to have at least 3 to 6 good stars in their FOVs to make all their way-finding possible. But, based upon my informal tests with the eVscope (which shows me what the scope is seeing to do its orienting before stacking) I easily see 11th magnitude stars — that gives me the magic number of 5. I hope to test this hypothesis more carefully with calibrated star clusters like M23, but just haven’t been able to do that yet with all the weather and smoke problems of late.
Interestingly, smart telescopes don’t need to be any larger aperture than they are in order to do the plate solving. And, in fact having a much smaller field of view, which would make planet imaging acceptable, is actually maybe not possible with these apertures. So, those of you who would like to put in field magnification lenses would find that your scopes couldn’t do the basic initializing because they would have enough stars in their FOV’s.
A much larger aperture and a more powerful computer would be needed to have a scope that performed in the same way and could go to higher magnification and measure triads and quads down to magnitude 15, which might be required. At least that’s what I think. (If you have a traditional Go To telescope you know that it relies upon our knowledge to orient the telescope to a handful of reference stars. They don’t do it automatically.)
DOGS HUNTING CHAMPAGNE
I often tell people my smart telescopes are like good hunting dogs. They orient themselves quickly and find their prey on command. These tasks are the primary thing our scopes have to do. All other performance, even the amazing image stacking and processing is secondary to orientation. This all reminds me of the decision making NASA/JPL has to do with Mars rovers. The engineers have the first say, because if they can’t land the robot safely, then there will be no science.
So, next time you’re cursing the stars in your image, please realize that without them we would be lost. Truly …. Count your lucky stars! Better yet, toast your smart telescope with champagne some time and remember what Dom Perignon exclaimed upon tasting the first bottle of bubbly.
“Come quickly, I am tasting the stars!”
Next week I hope to then address the challenge of stellar digital images how to tame those starry gnats can be reduced if you insist. Until then.... Cheers!
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HST Image Credit:
Sgr Star Cloud: AURA, STScI, NASA, Hubble Heritage Project (STScI, AURA)
Interesting article on possibly how are eVscopes are plate solving.