Building the TMT

So how are we going to build the Thousand Mile Telescope?  Once we get to the Kuiper Cliff, is there anything we can use?

We will do the usual thing, the same kind of procedure that we will use to build the rest of Solar Civilization: arrive with several general-purpose 'factories'.  Each factory is a system of machines that can:

• mine asteroidal materials
• refine the materials into useful forms
• make solar arrays for power
• reproduce themselves on a larger scale
• build cramped, cold, uncomfortable habitats for the grad students
• make the machines that will make the big mirrors.

 For the mirrors themselves, I propose using only three elements: silicon, oxygen, and aluminum.  The silicon and oxygen to be combined into SiO2 -- quartz -- that gets foamed into a volume much larger than it would be if solid, but still very rigid.  Probably a fractal kind of structure, like the inside of bones.  It it easy to foam stuff in zero-G because the bubbles don't try to rise.





Once you make the big low-mass, rigid disks, you use a polishing process that simultaneously creates a very slight paraboloid, and fuses the surface smooth.  Use a directed-energy thing, like those Martian death-rays.  The green ones.

To get optical smoothness you have large polishing machines crawling around the surface for a year or so, doing final polishing.  And finally the biggest vacuum-deposition gadgets ever made -- no need for a "chamber" -- to apply the aluminum coating over the entire surface of each disk, resulting in an optically-smooth aluminum coating a thousand Angstroms thick or so.





OK, maybe I don't know every last detail, but one must leave something for the engineers to figure out or they will become irritable and despondent.

One note about cleanliness.  The entire mining, refining, and manufacturing process must be kept clean.  Any waste that cannot be used should be at least well controlled, for example by packing it into containers.  The last thing we want is a cloud of unused gas and dust floating around the mirrors, and us hoping that it eventually blows away in the practically nonexistent light pressure.  We are making telescopes here, let's not simultaneously make smog around them.






How much material do we need?  Will there be enough?

Let's use enough SiO2 that, if it were solid, it would be a meter thick.  (It will actually be probably at least ten times thicker than that after foaming, but for those bubbles we will use whatever waste gas is handy.  Probably oxygen, there's gobs of that stuff.

So how much SIO2 do we need?

The total area of all the dishes is the same as a single 1000 mile dish, one meter thick.  500 mile radius is 804.5 Km radius, so the volume is

pi * ( 804500 m )^2 * 1 m 

== 2e12 m3

== 2e18 cm3

* 2.6 g cm-3 ~= 5e18 grams

We need 5e18 grams of SiO2.  Can we get it?

I think the Kuiper Belt probably has two distinct populations of objects in it: the fluffy ones and the stony ones.  The good ones for us are stony, like Pluto, which is maybe 70% stony stuff like rocky asteroids, and 30% water-ice.

Let's assume we can find more things like Pluto.  (Because I don't want to rip apart Pluto, just for old time's sake.)  What kind of composition will we find?

Silicon is always the limiting factor, because there's so much oxygen.  And that's without counting the water ice!  Silicon is about half of the mass that we need, so let's be generous and call it 3e18 grams.  And silicon is about one-fifth of the mass of the stony planetesimals in the Kuiper Belt, so we will need to process a total of about 15e18 grams of material total, assuming the worst case that it's all mixed together evenly.

How much rock is that?  Assuming (conservatively) a density of 2 grams per cm3, we need to process 8e18 cm3.  Or 8e12 m3.  Or 8e3 Km3.

That's a sphere 25 kilometers across.

That is not a very big rock.

It's smaller than the Earth.

( In each of these pictures, the two objects are shown in proper scale with each other.)

Earth and Moon

It's smaller than the moon.

Moon and Pluto

It's smaller than Pluto.

Pluto and Vesta

It's even smaller than Vesta.

Vesta and the TMT rock.

That's it -- the little thing to the right of Vesta.  That's the size of the rock we need to build the Thousand Mile Telescope.  It would just about make one of the larger craters on Vesta (which is the third-largest main-belt asteroid.)

In the Kuiper Belt, we are going to be able to find a zillion rocks this large.

And each time we find one, our machines and graduate students will go to work on it.

Mining a little rock.

And we'll start making dish-arrays out of it.

A Dish Array of the Thousand Mile Telescope

And I suppose we could make some habitats too.  Even grad students need someplace to live.

Where to Put the Thousand Mile Telescope

But where can we put this monster?

Siting the Thousand-Mile Telescope is probably going to be non-trivial.  We can't just find some wasteland that nobody cares about -- for example New Jersey -- and cover that up.  The telescope is too big.  It has a surface area a little larger than Mexico.

And there are all kinds of problems even more serious if we locate dishes on the Earth's surface -- like gravity, wind, vast and immediate climate changes, disruption of the lithosphere with massive strip-mining to get the materials.  We would probably cause the deaths of a couple billion people, which seems likely to make the instrument unpopular with the survivors.  So -- not on the Earth.

Problems Likely at This Location

No, our dish-arrays really can't even be on the moon.  Still too much gravity to be able to maintain such large paraboloids -- which will also have to be extremely thin to avoid using inconceivable quantities of material.  Such big thin things would flatten out like a coat of spray-paint even in lunar gravity.

Getting colder, but still not cold enough.

No, it has to be in zero G.

But then that brings up another couple of problems.  First -- where are we going to get all this material?  Even with the disks being very thin, a thousand-mile disk uses a lot of mass.  If we have to boost it up out of a strong gravity well, we are doomed.

And second -- if we build them anywhere near the Sun -- well, we will basically be building the biggest sails in the history of the human species, and the wind from the sun will blow them away like little soap bubbles on a breeze.  We do not want to make these things just so we can watch them receding into the infinite distance.

No, we need a place where:

• We can get lots of material with practically no gravity.
• It's far enough from the Sun that light pressure is negligible.

As it happens -- I have just the place!  But we will need to zoom back a ways.

The size of the Sun in this picture, by the way, is to scale with the size of the orbits.  The Sun is very big, very powerful, very calm, very special.  Anybody who tells you that the Sun is an 'average star' has no faintest clue what they are talking about.

We need to get out past the orbit of the Earth, only 500 light-seconds away, where the intensity of Solar radiation is nearly a Kilowatt per square yard.

We need to keep going, out beyond Mars.

We might pause and think about the asteroids for a bit, but the sunlight is still too intense, and Jupiter keeps sweeping by cheerfully disrupting everything, throwing his big gravity field around and hurling hundred-mile lightning bolts in all directions.  It's like having a neighbor who plays loud music all night.

No, we have to get well away from mighty Jupiter.  There is a better place, but it's still far away.  Keep going out, while the light-minutes turn to light-hours.

Out past ringed Saturn and Uranus.

Look, I know it's going to be hard to get people to come out this far, but a lot of the work can be automated, and anyway there will always be astronomy grad students.


We keep going past the orbit of Neptune, the final planet we know about ...

Until at last we see it.  Five light hours from the Sun, the real asteroid belt of the Solar System -- the vast Kuiper Belt.

The Kuiper belt has zillions of little rocks and ice-balls, some of them ranging in size all the way up to that of Pluto.  In fact, Pluto is probably just a large and close-in Kuiper Belt object.  The belt has a total mass of 5% of the Earth or so -- which is a very great deal of mass which we will be very happy to get our hands on -- spread out over an area of four thousand square AUs -- 40 million trillion square miles.  So it's spread kind of thin.  But that's OK, we will find some decent-size chunks and go use those.


And specifically, we will go to a magical little band of the Kuiper Belt -- well, 'little' meaning only 100 million miles wide --

The 'Kuiper Cliff' -- a band where there are very few floating things, but which is right next to regions that are nice and thick with material we can use.

Here, we are 40 times farther from the Sun than is the Earth.  Solar radiation is 1600 times weaker.  Even on our gossamer dishes such weak wind will do next to nothing.

It's cold, it's dark, it's lonely.  Nobody who didn't already know exactly where to look would be able to find our little dishes in a million years.

It's perfect.

The Thousand-Mile Telescope

Next week I will go back to talking about my algorithm, but right now it's snowing when it should be springtime, it's colder outside at this time of the year than it has been ever before in my life, and I think it's time for me to come out of the closet and tell you what I really want.

I want a Thousand-Mile Telescope.

Does that sound like an awfully long focal length for a telescope?  After all, the CDK700 I am using right now is only 15 feet.  Well, however bad it sounds the truth is a lot worse.  What I want is a telescope a thousand miles in diameter.

OK, so the first questions we should ask are Why Do You Want a Thousand-Mile Telescope?  And after that, How Can We Make a Thousand-Mile Telescope?

One Million Dishes in One Hundred Arrays.

Actually, these two questions are related, and I need to answer a little bit of the second question first.  We are going to build a Thousand-Mile Telescope by first making a One-Mile Telescope, and then making 999,999 more just like it.  A million One-Mile telescopes add up to have the surface area of a single Thousand-Mile Telescope. 

But!  What can we do with a telescope that's made of many separate mirrors?  There are two ways of combining the dishes so that they become a single instrument.  The easy way is to simply add the images together.  (We will need 40-bit per channel color images.  Heh heh.)   But that only gives us the light-gathering power of the TMT.  Not the resolving power.  Can we get the resolving power?

Yes, but we'll have to work at it a little.  We need a 2D array of dishes a thousand miles in diameter, constructed such that it is possible to know the location of each one-mile dish relative to the others to an accuracy of about 1/4 of a wavelength of violet light, or about 4 millionths of an inch.

Now we can't possibly do that with all million dishes, so what we'll do is we'll make an array like this:

That's a circular array 1000 miles across, containing ten thousand dishes.  Well, close enough.  (And only a few are shown, to give you the idea.)  The dishes are arranged on aluminum trusses that can move them precisely and measure their positions.  This array, with a little bit of computing power, can simulate the resolving power of a TMT.

So we make 100 of these, and add all the images together.  Boom!  You have both the resolving power and the light gathering power of a true TMT.

What Can It See?

The resolving power of a telescope, in radians, is 1.22 * wavelength / diameter.  The wavelength we care about is the worst case (longest) wavelength of visible light, which is red, which is 25 millionths of an inch -- 2.5e-7 inches.  Our diameter is 1000 miles, which is 6.3e7 inches.  1.22 * 2.5e-7 / 6.3e7 == 0.48e-14 radians -- call it 5e-15 radians.

At a radius of 1 light year, 1 radian is .. um .. 1 light year -- about 6e12 miles.  Multiply that by my 5e-15 radians and you get 30e-3, or 3e-2 miles.   So it's about 1 mile at 30 light years,  5 miles at 150 ly, and so on.

With this telescope, here is what our planet would look like at 1000 light years:

The Earth from 1000 light years with the Thousand Mile Telescope

 



Now it wouldn't really be all lit up like that, because ... um ... the Sun would be in the way.  But whatever you could see of the planet would have that level of detail.

And here it is from 25,000 light years -- the distance to the galactic center.

The Earth at the distance of the galactic center, with the TMT.

With the Thousand Mile Telescope, you can see half the galaxy well enough to know whether you would like to live there.

And over a distance of a thousand light years -- a volume containing 10 million star systems -- you can see planets well enough to see this:

Lights in the Night

That's why I want my Thousand-Mile Telescope.

Taking the Halos out of the Heavens

OK!  So we have found the bright stars by using an automated thresholding routine, and we have gobbled them up with a region growing algorithm.  So where we now?

Here is what our example image looks like after having all the bright stars removed.

Bright Objects have Halos

Close, but no cigar.  The bright objects have halos around them, and these halos are themselves much brighter than the dim objects that I want to look at.

This is happening because we have only done region-growing on the pixels that were at the maximum brightness that this image could represent.  But those bright stars and galaxies don't just cut off at 255 in this images.  They fade and fade and fade into the darkness.  Halos.

OK, so here's what we do.  We use our knowledge of where the bright regions are, and knowledge of what the dark image looks like, to get rid of those halos.

We will take a statistic of all the pixels in the image remaining after removing the bright regions.  Then, for each bright region, we will grow its perimeter as a separate region.

Finding the Perimeters of Bright Regions

It's easy to get these perimeters: for every pixel in the bright region, check its neighbors.  If any of them are not in the region -- add them to the perimeter region.  (I suppose that is not the most efficient possible method for large regions.  Exercise for the interested reader.  Or for me if I ever get to do this with a Big Telescope.  An actual perimeter-following algorithm is almost as easy as what I did here.)

Now the fun part.  We have the statistic for the dark image (image with bright regions removed.)  So look at the average pixel value of that perimeter.  If it is more than N standard deviations above the dark-image mean (I think I chose N==1.)  then the perimeter is 'bright'.  Add it to the region.

So we iterate, finding new perimeters and adding them to the regions until the perimeters are not significantly brighter than the dark images anymore.

Here's our image after 5 such iterations:

and after 10.  (Some objects stopped growing a while ago.)

When all regions have stopped growing, we have eliminated all the bright halos!

Here is what our image looks like now:

That is beautiful.   At last we have an image of just the dark stuff.  All the bright stars removed, including their halos.


And now we can threshold this image, and find the bright regions in it.

At last we can detect all of the objects that were really faint in the original image.

The Faint Objects

We are now only a couple steps away from paydirt: the detection of moving faint objects.

Finding Bright Stars with Region Growing

What does it mean for a piece of software to 'find' a star in an image?  The star is already there in the image isn't it?

No, there is no star in the image.  The image has nothing but pixels in it.  To find a star, a program must build a data structure that makes knowledge about the star's existence and location explicit.  There are no stars but what we make.
 

There is no star in this image.

To make knowledge about stars explicit in my program, I will use a region-growing algorithm.  We will start out with a vanilla region-growing algorithm.  Later, we will add something strange and wonderful.

Here is a quick sketch of how it works:

1. select a threshold.  We will make regions out of pixels whose values are greater than or equal to that threshold, and ignore all others.  Let's call pixels bright if they are >= threshold.
2. Find a pixel in the image that is bright.  Start a new region with it.
3. Look at all its neighbors.  If any are bright, add them to the region.
4. For all the ones you just added, look at all their neighbors.  Add to the region any that are bright.
5. Keep doing this, until you get to a point where you don't add any new pixels to the region.  Then stop.

Here's an illustration.



This is the image we will be using.  I've outlined all the pixels in red so you can see them.  All the bright pixels have been set to white, while all non-brights have been set to gray.

To find the first bright pixel, scan the image top to bottom, left to right, testing the value of every pixel until you find a bright one.

Start a new region, and add that pixel to it.

Actually, I will have several different groups of pixels in this region.  Let's call them current generation, region, and new generation.  I will color-code them.  Right now the pixel we just found is the only one in the new generation.

Now we can get started.
For all the pixels in the current generation, look at their 8 neighbors.  If any of those neighbors are bright, add them to the new generation.

After finishing checking the neighbors for all of the current generation, move all of the current generation to region.  Move all new generation pixels into current generation.  Then repeat the process.

I have numbered the generations here, so you can see how they get added to the region in layers.

Finally, you reach a point where, when you check all the current pixels, you find no new ones.  So you put the current generation into the region, and you're done.  There is nothing more to check.

Now we know explicitly where a star is.  We know how many pixels are in it, we know its centroid X and Y.  We can look at the original image, before thresholding, and know its average gray value.  We know all kinds of stuff.

That's how we find a bright star.

Autothresh

Here is a beautifully thresholded image of the night sky of 5 March, 2016.

By the way, my T27 images are 27 minutes of arc across.  A full moon would fit almost perfectly inside this box.

This is not the original image as it came from the telescope.  The original image has gray values that go from 0 to 65536, and on my screen it doesn't look like much.

In fact, the original looks like this:

Of course the original actually has much more dynamic range than my thresholded (I call it "sliced") version, but I don't care.

I don't care because:

1. My monitor can't display it.
2. My eyes can't see it.
3. My image manipulation tools can't handle it worth a damn.  (Maybe yje next version of the Gimp will do better.)
4. My algorithms need it.  The things I'm looking for are all down near the noise.

So I like my thresholded images, and I'll be using them.

Actually, it has been two-way, thresholded.  Like so.

Here is a histogram of the original image.  (On the x-axis it has gray-values, on the y-axis it shows how many pixels of that gray value are in the image.)

The graph actually goes all the way to 65535 on the right, but the little bumps of pixels up there are so small you can't see them on this scale.  The big normal distribution of pixels you are seeing here is the Dark Night Sky -- which contains practically all the pixels in the image.

But my 8-bit sliced image only has 256 gray values, so here is what I did:

The question is -- how can we automate this process?  I want to write software to do all this with no human intervention, so that my software can find asteroids while I sit on a beach and sip Piña Coladas.  So -- how can we find a nice threshold without me clicking on stuff with a mouse?

The trick is in the structure of that histogram.  Because we are looking at the night sky, it will always look like that: a great huge normal distribution of pixels down in the dark, and teensy smattering of pixels all the way to the right.

How can we describe the ideal threshold position, relative to the structure of that histogram?

The criteria for the Magic Spot are structural criteria: aspects of the structure of this histogram.  We want a spot that has a rapid descent on its left, but where the histogram is nice and flat to its right.

To find that kind of structure, we will create a structuring element.  Since the space we are looking at is one-dimensional (it's actually just a list of numbers) our structuring element will also be one-dimensional.  It will be two line segments, one to the left of the-point-we-are-looking-at-in-the-histogram, and one to the right.

The two halves of the structuring element both contribute to the total score for the point in the histogram that we are considering, but they do so in very different ways.  The left half generates a high score if the part of the histogram that it is overlaying has a large drop in value from left to right.  The right part of the structuring element generates a high score only if its part of the histogram is nice and flat.  Between the two of these, they generate the highest score right at the place where we want to start our 8-bit, 256 grayvalue image: the right knee of the histogram's big curve.

By the way, the right half of the structuring element is not looking at the original histogram -- it's looking at the first derivative of the histogram.  It just adds up all the values of the first derivative that fall under it, and thus gets an idea of the net up or down movement of the part of the histo it is on.

But here's a problem.

How big should this structuring element be?  I don't want to assign it an arbitrary size that I simply know will work (like I did at first, during development.)

We want to ensure that the left half of the structuring element covers a good fraction of the right half of the Big Curve, but we don't want it to exceed half of the Big Curve's 'wavelength'.  And we want to be able to determine the size fairly easily, because we are inherently lazy.

So let's just do this:

It's easy to find the highest point in the histogram, and easy to walk to the right until the value has fallen to half of the maximum.  The distance we move rightward is a nice size for the left half of my structuring element, and we might as well use the same size for the right half.

Using that strategy for sizing the structuring element, and using the structuring element to find me my lower threshold for the 8-bit image 'slice' is what gave me these lovely images:  (these are small crops from the main image)

 

Notice how, in this 3-frame movie, the background brightness doesn't change at all.  The auto-thresholder found good thresholds on all three images, even though the background brightness of the sky was increasing during the 30 minutes I was taking the pictures.  (I think the humidity was increasing, or something.)

Also notice how the trapezoid of stars in the upper left is preserved.  Those are some of the dimmest objects in the images, and the threshold is doing a good job of not knocking them out.

This is the thresholder I will be using, until it dies or I find somebody better.

What is a Good Threshold?

If we're going to identify objects in the night sky, we need to find a grayscale threshold that means: Above this value, the pixels are probably part of an object.  Below it they are probably not.

A threshold is just an integer -- the pixels in our image, brought to us by the miraculously excellent Proline camera, are 16-bit integers, whose possible values range from 0 to 65,535.

The reason we need to think about a threshold is because the background -- the dark between the stars -- is not perfectly black.  If it were perfectly black, then its pixel values would all be zero, and our threshold would always be "anything above zero".  But it's not.  In the images I have taken, the dark between the stars tends to be around gray value 1000.  The darkest sky I have seen so far (on March 5th, 2016) had a background around 650.

And that background is never perfectly smooth.  It has noise.  It has a standard distribution of values, so that, if you brighten it enough and zoom in enough, it looks like this:

Further, if we just wanted to find nice, reasonable stars, we wouldn't have to worry about setting a good threshold.  Nice, reasonable stars are so much brighter than the background noise that you could choose practically any threshold at all and it would work just fine.

But we want to see the faintest things that hide right down in the noise, so we need the best threshold that can possibly be found.

How do we know if we have a good one?

Here are a couple examples, from the lovely dark sky of 5 March 2016, above Siding Spring, Australia.

 

The image on the left has been thresholded at 500, the one on the right at 600.

Look at the trapezoid of 4 faint stars near the upper left of both images.  They are just as discernable in the right image as in the left.  In fact, there are no faint stars visible in the left image that are not also visible in the right.

If we go too far into the noise with our threshold, we are not making any new faint stars visible.  We are only brightening the noise.

What we want is the highest threshold we can get -- and thus the darkest background we can get -- that does not lose those faintest stars.  That will be our criterion for a good threshold.

It's easy to find a good threshold 'by hand', by slicing the 16-bit image at many levels and inspecting the results -- but we need to automate the process.  Next week we will look at a method of doing that.

Holophonos

As we start making algorithms, let's avoid the temptation of generality.  There are many different kinds of things that move in the night sky, and if we make algorithms to find all of them we will be wasting our time.

The thing we are looking for has never before made a pass close to the Earth.  It is far away, and dark, and moving really slow way out in the cold places beyond Jupiter.  It is in an odd high-inclination orbit.  All these factors have combined to ensure that no one has noticed it yet.

Of course, its stealthiness is only part of the problem.

Three or four years from now, if we are lucky enough to look in just the right place, and have software that is good enough to process the images in just the right way, we will see something very much like this:

Holophonos

This is Holophonos: the killer of all things.

It is a chunk of nickel-iron about 4 miles across and if we don't see it soon enough it will kill everything you love, everything you hate, everything you hope for or fear, the future and the past, faith, knowledge, history, technology, dance music, fine dining, cities, villages, languages, cars, candy, comedies, proms, pies, parades, breakfasts, basements, butchers, bakers, candle stick makers, and baby's first steps.

There may be more than one reason why there are human beings on this planet.  But if Life on Earth could speak, it would say that there's only one reason it cares about.

It would say:

You are here to stop that rock.  Do whatever you need to do, use whatever you need to use, but stop that rock.

We can't stop it if we can't see it.