First Light on an 8” Scope and 1/4 Lambda on a 6” Mirror — All in One Night!

Tonight, Jim K essentially completed his 8″ telescope by putting in the primary mirror, positioning it correctly in the tube by focusing it on the Moon, and achieved FIRST LIGHT!

He also put on the Telrad finderscope and used it to aim the scope accurately on the star Capella with no difficulty at all. I did a brief star-test on that star and found that the scope passed with flying colors! Jim started grinding the mirrors back in the 1970s, put it aside, and brought it to us for help in doing the final polishing, figuring, aluminizing, and designing and constructing the telescope. It looks great and works well, too!

In addition, Pratik T may have finished figuring his 6″ f/8 mirror that he’s been working on. Using the Foucault/Couder knife-edge test measurements I made, the program FigureXP declared it to be 1/4 lambda error on the wavefront. This may be good enough, but more testing would be a good idea, later on.

We are closed all of next week for the holiday.

Some Progress – AT LAST! – With Figuring the 16.5″ f/4.5 Thin Mirror That Headlines This Blog

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I have been wrestling with this mirror for YEARS. It’s not been easy at all. The blank is only about twice the diameter of an 8″ mirror, but the project is easily 10 times as hard as doing an 8-incher. (Yes, it’s the one in the photo heading this blog!)

Recently I’ve been trying to figure it using a polishing/grinding machine fabricated by the late Bob Bolster (who modeled his after the machine that George Ritchey invented for the celebrated 60″ mirror at Mount Wilson over a century ago). That’s been a learning exercise, as I had to learn by trial and error what the machine can and cannot do, and what strokes produce what effects. The texts and videos I have seen on figuring such a large mirror with a machine have not really been very helpful, so it’s mostly been trial and error.

My best results right now seem to come from using an 8″ pitch tool on a metal backing, with a 15 pound lead weight, employing long, somewhat-oval strokes approximately tangential to the 50% zone. The edge of the tool goes about 5 cm over the edge of the blank.

This little movie shows the best ronchigrams I have ever produced with this mirror, after nearly 6 hours of near-continuous work and testing. Take a look:

And compare that to how it used to look back in September:

 

Also compare that to the theoretically perfect computed ronchigrams from Mel Bartels’ website:

perfect theoretical ronchigrams for guy's 42 cm mirror

Part of the reason this mirror has taken so long is that after grinding and polishing by hand some years ago, I finally did a proper check for strain, and discovered that it had some pretty serious strain. I ended up shipping it out to someone in Taos, New Mexico who annealed it – but that changed the figure of the mirror so much that I had to go back to fine grinding (all the way back to 120 or 220 grit, I think), and then re-polishing, all by hand. I tried to do all of that, and figuring of the mirror, at one of the Delmarva Mirror Making Marathons. It was just too much for my back — along with digging drainage ditches at Hopewell Observatory, I ended up in a serious amount of pain and required serious physical therapy (but fortunately, no crutches), so this project went back into storage for a long, long time.

Recently I’ve tried more work by hand and by machine. Unfortunately, when I do work by hand, it seems that almost no matter how carefully I polish, I cause astigmatism (which I am defining as the mirror simply not being a figure of rotation) which I can see at the testing stand as Ronchi lines that are not symmetrical around a horizontal line of reflection. (If a Ronchi grating produces lines that look a bit line the capital letters N, S, o Z, you have astigmatism quite badly. If astigmatism is there, those dreaded curves show up best when your grating is very close to the center of curvature (or center of confusion) of the central zone.

Using this machine means controlling or guessing at a LOT of variables:

  1. length of the first crank;
  2. length (positive or negative) of the second crank;
  3. position of the slide;
  4. diameter of the pitch lap;
  5. composition of the pitch;
  6. shape into which the pitch lap has been carved;
  7. amount of time that the lap was pressed against the lap;
  8. whether that was a hot press or a warm press or a cold press;
  9. amount of weight pushing down on the lap;
  10. type of polishing agent being used;
  11. thickness or dilution of polishing agent;
  12. temperature and humidity of the room;
  13. whether the settings are all kept the same or are allowed to blend into one another (eg by moving the slide);
  14. time spent on any one setup with the previous eleven or more variables;

Here is a sketch of how this works

bolster's ritchey-like machine

Major Moving Day at Hopewell Observatory

Yesterday we moved a lot of heavy metal and glass to temporary quarters so that we can mount a modern, heavy-duty Astro-Physics 1600GTO mount on one of our piers.

One of our founders, Bob Bolster, had built with his own hands a very unusual 30-cm Wright-Newtonian telescope and an equatorial mount on a permanent pier. Unfortunately, the drive stopped working and he was unable to get it back into working order before he died. So yesterday we removed it from its mount – and it took five of us with a 2-ton chain hoist, lifting straps, and a custom-built cart to winch it out of the observatory and into our operations cabin.

We all had fun doing it, nobody got injured, nothing got damaged, and the night that followed was the clearest one I’ve seen in a long time! Great open clusters in Cygnus!

I attach some videos and photos of the move.

By the way, that large disk of optical glass you see in the last few photos is for sale. We aren’t sure what type of glass it is, but you can find details here at Cloudy Nights or Astromart. It is 55 cm across, 83 mm thick, and we measured its weight as 59 kg (130 lbs). We calculate its density as 2.99 g/cm^3, and the nearest match in the Schott catalog is N-SF64 which has that exact density, but N-KZFS4 and P-SK57 are close as well (3.00 and 3.01, respectively). It’s definitely way too dense for Borofloat, Zerodur, or any other borosilicate glasses. The glass known as BAK-4 has density 3.05, which I don’t think is close enough, since there are several others between 3.00 and 3.05.  For comparison, the relatively inexpensive optical glass known as BK-7 has a density of 2.5.

We are asking $950 for the blank. If you were to order a brand-new one from any optical glass company it would cost you much, much more!

Why Not Show Students the Beauty of Math?

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When I taught math, I tried to get students to see both the usefulness and beauty of whatever topic we were discussing. The most beautiful mathematical objects I know of are the Mandelbrot and Julia sets, which in my opinion should be brought up whenever one is studying imaginary and complex numbers.

To illustrate what I mean, here are some blown up pieces of the Mandelbrot set. Below,  I’ll explain the very simple algebra that goes into making it.

 

I made these images using an app called FastFractal on my iPhone. The math goes like this:

Normally, you can’t take the square root of a negative number. But let’s pretend that you can, and that the square root of negative one is the imaginary number i. So the square root of -16 is 4i. Furthermore, we can invent complex numbers that have a real part like 2, or 3.1416, or -25/17, or anything else, and an imaginary part like 3i or -0.25i. So 2-3i is a complex number.

Ok so far?

We can add, subtract, multiply and divide real, imaginary and complex numbers if we want, just remembering that we need to add and subtract like terms, so 4+3i cannot be simplified to 7i; it’s already as simple as it gets. Remember that i multiplied by i gives you negative one!

Interesting fact: if you multiply a complex number (say, 4+3i) by its conjugate (namely 4-3i) you get a strictly REAL answer: 25! (Try it, using FOIL if you need to, and remember that i*i=-1!)

Furthermore, let us now pretend that we can place complex numbers on something that looks just like the familiar x-y coordinate plane, only now the x-axis becomes the real axis and the y-axis becomes the imaginary axis. So our complex number 4+3i is located where the Cartesian point (4, 3) would be.

Ok — but what’s the connection to those pretty pictures?

It’s coming, I promise!

Here’s the connection: take any point on the complex plane, in other words, any complex number you wish. Call it z. Then:

(1) Square it.

(2) Add the original complex number z to that result.

(3) See how far the result is from the origin.

(4) Repeat steps 1 – 3 a whole lot of times, always adding the original z.

One of two things will happen:

(A) your result stays close to the origin, OR

(B) it will go far, far away from the origin.

If it stays close to the origin, color the original point black.

If it gets far away, pick some other color.

Then repeat steps 1-4 for the point “right next” to your original complex point z. (Obviously, the phrase “right next to” depends on the scale you are using for your graph, but you probably want fine coverage.)

When you are done, print your picture!

If we start with 4+3i, after one round I get 11+27i. After two rounds I get -604 + 597i, which is very far from the origin, so I’m going to stop here and color it blue. I’ll also decide that every time a result gets into the hundreds after merely two rounds, that point will also be blue.

Now let’s try a complex point much closer to the origin: how about 0.2+0.4i? I tried that a bunch of times and the result seems to converge on about 0.024+0.420i — so I’ll color that point black.

This whole process would of course be very, very tedious to do by hand, but it’s pretty easy to program a graphing calculator to do this for you.

When Benoit Mandelbrot and others first did this set of computations in 1978-1980, and printed the results, they were amazed at its complexity and strange beauty: the border between the points we color black and those we color otherwise is unbelievably complicated, even when you zoom in really, really close. Who woulda thunk that a simple operation with complex numbers, that any high school student in Algebra 2 can do and perform, could produce something so beautiful and weird?

So, why not take a little time in Algebra 2 and have students explore the Mandelbrot set and it’s sister the Julia set? They might just get the idea that math is beautiful!!!

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How Thick Are the Coatings on the Mirrors We Aluminize?

At the NCA ATM class at the CCCC, we are the fortunate inheritors of a 1960s-era vacuum chamber and aluminizer that was twice given away as surplus (first by the Federal Government or US military, and then later by American University), but which still works.

Much of the credit should be given to Dr. Bill Pala, who snagged it for AU from the US surplus system; the late Bob Bolster and Jerry Schnall, who together ran it for a long time; Dr. John Hryniewicz; Alan Tarica; and several others whose names unforotunately escape me at the moment but who have given excellent advice on repair and maintenance and even provided replacement parts.

Here are four photos of the rig, followed by two of our finished mirrors.

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032

The question came up: (1) how thick are the coatings we generally put on our mirrors, and (2) how efficient is it — that is, of the aluminum that we vaporize, how much of it actually lands on the mirror?

Thankfully, John H actually measured how thick the coatings are as we coated a mirror. He found that the average thickness is about 93.4 nanometers (billionths of a meter, or thousandths of a micrometer, or millionths of a millimeter), and that the coatings looked like this when blown up sufficiently: ”

 I have attached some scanning electron micrographs of the top of the film.  The grain structure is very fine, you can compare the size with the scale bar at the bottom that shows you the length of the total bar (10 ticks, between each pair of ticks is 1/10 of that number).  There are some particles or perhaps larger grains on top.  They are still very submicron, a couple of tenths at most.

The way the mirrors get coated is basically three steps:

(1) We get the mirror very, very clean, using both with a special detergent (Alconox) bbefore it goes into the vacuum chamber, and high-energy electron bombardment while the pumps are working;

(2) We get the pressure in the chamber very, very low, so that there are relatively few air molecules or atoms between a coiled tungsten filament and the mirror. (We get the pressure down to somewhere in the range of 7*10^-5 to 4*10^-4 Torr, depending on which gauge you believe. This is quite low indeed – roughly the air pressure at the altitude of the International Space Station; this is needed so that the aluminum atoms won’t tend to bounce of the molecules of nitrogen and oxygen and lose their energy.

(3) We melt, and then boil off, a small quantity of pure aluminum from the filament, which goes off in all directions, fairly evenly; the Al atoms that happen to be going in the right direction ashere to the mirror. There, they form a very even, reflective layer.

You may wonder, how do we prevent this layer of aluminum from oxidizing once it comes back into contact with the normal atmosphere? Answer: we don’t. Aluminum oxide is the main component of rubies, sapphires, and corundum, which are very hard. Since the stuff we deposit is relatively pure, it doesn’t have the red or blue color of those pretty and precious gems, and it is transparent, so it forms a hard, transparent, protective layer all by itself. If your coating tarnishes or gets extremely dirty, the aluminum-and-gunk layer is pretty easy to remove with a little bit of hydrochloric acid mixed with copper sulfate. Then you clean it off and re-aluminize.

(Yes, commercial labs do overcoat their mirrors with stuff like Silicon Monoxide and Silicon Dioxide (aka quartz), but we haven’t collectively figured out how to do that with our minimal budget.)

So, again: how efficient is it? What percentage of the atoms of aluminum headed to the mirror, actually adhere to the mirror?

To answer this, it helps to pretend that the filament is at the center of an imaginary sphere, shown below, and that the mirror (facing down, towards the mirror) happens to be at the top of this sphere. Recall that to a good approximation, the aluminum that evaporates off of the coil goes in all directions, i.e., it coats this entire imaginary sphere equally – or it would, if there wasn’t all sorts of pipes and wires and glass bell jars in the way.

The filament and aluminum is located at the center of this sphere.

I measured the distance from the filament to the mirror, and found that it’s just about 20 inches, or roughly 500 millimeters. Archimedes figured out long ago that the surface area of a sphere is equal to four times the area of any circle contained in the sphere, or 4*pi*r^2 in our current notation. So that imaginary sphere, on which the aluminum is deposited, has an area of about 3.1 or 3.2 million square millimeters.

imaginary sphere for aluminization

We currently use slugs of aluminum that are about 15 mm long (give or take a couple of mm) and cut (not at right angles, because the pliers won’t do that) from wire with a diameter of 5 mm (radius 2.5 mm). If we pretend the slugs are cylinders then the math is much easier: we can use the formula pi*r^2*h to get a volume of about 295 cubic millimeters, and we will pretend that all of the aluminum boils off (and none of it sticks like glue to the tungsten) and goes equally in all directions. (Probably not the case, but in practice it doesn’t seem to matter much.)

Now if we divide the 295 mm^3 of aluminum by the total surface area, 3.2 million mm^2, we get the average thickness. I get a result of about 9.1*10^-5 mm, which converts to 91 nanometers. Which is very close to the result that John H found.

On the other hand, most of that aluminum is wasted, because it’s NOT aimed at the mirror. If you have an 8-inch diameter mirror (about 20 cm diameter or 100 mm radius), its area is 10,000*pi square millimeters, or about 31,000 mm^2 – and that’s only one percent of the area of the entire imaginary sphere.

Oh, well, aluminum wire is quite cheap.

 

 

 

Difficulties in Using the Matching Ronchi Test on a 12″ Cassegrain Mirror

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The other regulars and I at the DC ATM group at the CCCC have been trying to test a 12 inch Cassegrain mirror and telescope manufactured nearly 50 years ago by a company called Ealing and currently owned by the Hopewell Observatory, of which I am a member. It hasn’t been easy. I discussed this earlier on Cloudy Nights.

Reports from several people, including Gary Hand and the late Bob Bolster, indicated that the optics on this mirror weren’t good at all. Apparently the folks at the University of Maryland’s observatory were sufficiently unhappy with it that they either sold it or gave it to National Capital Astronomers, a local astronomy club, who in turn gave it or sold it to Hopewell Observatory.

With a plain-vanilla Ronchi test, we could see that the mirror was very smooth and continuous, with no turned edge, astigmatism, or bad zones. With the Foucault/Couder zonal test (aka “Foucault” test) , I got results indicating that it was seriously overcorrected: some sort of hyperboloid, rather than the standard paraboloid characteristic of classical Cassegrain telescopes, which have a parabolic primary mirror and a hyperbolic secondary mirror.

However, I have begun losing my faith in my zonal readings, because they often seem to give results that are way out of whack compared to other testing methods.

So we decided to do some additional tests: the Double-Pass Auto-Collimation (DPACT) test used by Dick Parker, as well as the Matching Ronchi test (MRT).

The DPACT is very fiddly and exacting in its setup. We used (and modified) the setup lent to us by Jim Crowley and illustrated by him at his Astro Bananas website. Our results seem to show that the mirror is in fact NOT parabolic, rather, overcorrected, which confirms my Foucault measurements. If it were a perfect paraboloid, then the ronchi lines would be perfectly straight, but they definitely are NOT: they curve one way when inside the focal point, and curve the other when the tester is outside the focal point.

We also tested the entire setup on a radio tower that was about half a mile (~1km) distant. We found that the images were somewhat blurry no matter what we did.

We also attempted the MRT on the same mirror. However, requires very accurate photography and cutting-and-pasting skills in some sort of graphics programs. What you are inspecting is the curvature of the Ronchi lines. Here is the result that Alan T and I got last night:

matching ronchi for 12 inch cass

In black is the ideal ronchigram for this mirror, according to Mel Bartels’ website. The colored picture is the one we made with either my cell phone or the device I finished making earlier this week, shown in my previous post. Here are the two images, separated rather than superimposed:

IMG_1337

ideal ronchigram 12 inch cass ealing

The mirror’s focal length is 47.5″ and the grating has 100 lines per inch, shown somewhat outside of the radius of curvature. The little ‘eyelash’ on the lower left is simply a stray wire that was in the way, and doesn’t affect the image at all. The big hole in the middle is there because the mirror is a cassegrain.

I don’t know about you, but I don’t really see any differences between the real mirror and the theoretical mirror. Do you?

Conclusion

So, what does this all mean?

  • One possibility is that the mirror is in fact perfectly parabolic (as apparently shown by the MRT, but contrary to what I found with Foucault and DPACT) but there is something wrong with the convex, hyperbolic secondary.
  • Another possibility is that the mirror is in fact NOT parabolic, but hyperbolic, as shown by both my Foucault measurements and the DPACT (and contrary to the MRT), which would mean that this telescope was in fact closer to a Ritchey-Chretien; however, since it was marketed as a classical Cassegrain, then the (supposedly) hyperbolic secondary was in fact not tuned correctly to the primary.
  • The answer is left as an exercise for the reader.
  • A star test would be the best answer, but that would require being able to see a star. That hasn’t happened in these parts for quite some time. In addition, it would require an eyepiece holder and a mount of some sort. Or else setting up an indoor star…

Latest Ronchi or Knife-Edge Tester for Mirrors and Other Optics Using a WebCam

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Here is the latest incarnation of my webcam Ronchi and knife edge (or Foucault) tester. It’s taken quite a few iterations to get here, including removing all the unnecessary parts of the webcam. I attach a still photo and a short video. The setup does quite a nice job of allowing everybody to see what is happening. The only problem is setting the gain, focus, exposure, brightness, color balance, contrast, and so on in such a way that what you see on the screen resembles in any way what your eye can see quite easily.

IMG_1335

Observe the Stars at Lake Artemisia Natural Area, September 30

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On September 30, members of the public will have the opportunity to observe several planets, the moon, and other heavenly objects through some telescopes to be provided by local amateur astronomers, including members of NCA and NOVAC, at the lovely Lake Artemisia Natural Area in Berwyn Heights, MD.

The location has a wide open southern horizon over the lake, and is surprisingly well-shielded from lights from local highways and shopping centers. The address is

Lake Artemesia Natural Area, Berwyn Road and 55th Avenue, Berwyn HeightsMD 20740

Park Contact numbers are: 301-627-7755  or TTY: 301-699-2544

Normally this park closes at sunset, but it will remain open for this event, which is scheduled for 7:00 (just about sunset) to 11:00 pm (just after moonrise) on Sunday evening, September 30. The event is free. I’ve attached a couple of maps. Please note that Berwyn Road dead-ends at the Metro rail lines.

 

We should be able to see Venus, Jupiter, Saturn, Mars, and the rising Moon, if weather permits. Volunteers with telescopes would be appreciated!

Math – How Come We Forget So Much of What We Learned in School?

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This was a question on  Quora. Here is an answer I wrote:

In the US, judging strictly on what I’ve seen from my time in the classroom as both a student, a teacher, and a visiting mentor of other math teachers, I find that math and science was very often taught as sort of cookbook recipes without any real depth of understanding. The recent National Council of Teachers of Mathematics prescriptions have attempted to correct that, but results have been mixed, and the Common Core has ironically fostered a weird mix of conceptual math marred by teachers being *OBLIGATED* to follow a script, word-for-word, if they want to remain employed. Obviously, if students are really trying to understand WHY a certain mathematical or scientific thing/fact/theorem/theory/law is true, they are going to have questions, and it’s obviously the teacher’s job to figure out how best to answer said questions — which are not likely to have pre-formulated scripts to follow in case they come up — and which are going to take time.

Another thing that is true is that not everything in mathematics has real-world applications in every single person’s life. I taught a good bit of computer programming (aka ‘coding’ today), geometry, arithmetic, probability, algebra, statistics, and conic sections, and in fact I use a LOT of that every week fabricating telescope mirrors to amazing levels of precision, by hand, not for a living, but because I find telescope-making to be a lot of fun and good mental, aesthetic, manual, and physical exercise. But I’m a pretty rare exception!

Most people obviously don’t dabble in math and physics and optics like I do, nor should they!

In fact, I have made it a point to ask professional scientists and engineers that I meet if they actually use, on their jobs, all the calculus that they learned back in HS and college. So far, I think my count is several dozen “Noes” and only one definite “Yes” – and the latter was an actual rocket scientist / engineer and MIT grad and pro-am astronomer (and wonderful, funny, smart person) who deals/dealt with orbital rocket trajectories. (IIRC).

In France, when I went to school there 50 years ago and in my experience tutoring some kids at the fully-French Lycee Rochambeau near Washington, DC, is that they go very deeply into various topics in math, and the sequence of topics is very carefully thought out for each year for each kid in the entire nation (with varying levels of depth depending on what sort of track that the students elected to go into (say, languages/literature, pure math, or applied sciences, etc), but the kids were essentially obligated to accept certain ideas as factual givens and then work out more and more difficult problems that dealt with those particular givens. No questions allowed on where the givens came from, except to note the name of the long-dead classical Greek, French, Italian or German savant whose name is associated with it.

As an American kid who was mostly taught in American schools, but who also took 2 full years of the French system (half a year each of neuvieme, septieme, premiere, terminale, and then passed the baccalaureat in what they called at the time mathematiques elementaires, I found the choice of topics [eg ‘casting out nines’ and barycenters and non-orthogonal coordinate systems] in France rather strange. Interesting topics perhaps, but strange. And not necessarily any more related to the real world than what we teach here in the US.

Over in France, however, intellectuals are (mostly) respected, even revered, and of all the various academic strands, pure math has the highest level of respect. So people over there tend to be proud of however far they got in mathematics, and what they remember. Discourse in French tends to be extremely logical and clear in a way that I cannot imagine happening here in the public sphere.

So to sum up:

(a) most people never learned all that much math better than what was required to pass the test;

(b) only a very few geeky students like myself were motivated to ask ‘why’;

(c) most people don’t use all that much math in their real lives in the first place.