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Guy's Math & Astro Blog

Guy's Math & Astro Blog

Monthly Archives: January 2015

D’oh and Duh! 12 Inches in a Foot! My previous tables were all wrong!

09 Friday Jan 2015

Posted by gfbrandenburg in Uncategorized

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Oh, jeez, what an idiot I am. I overlooked the amazingly obvious fact that the focal lengths in my table were in INCHES. I somehow thought they were in FEET, but they weren’t.

As they say about scientific investigation in general, the easiest person to fool is yourself. I see that I did a pretty good job of doing just that. Thanks to those who pointed out my error, for example Mel Bartels. I guess that’s the great thing about these interwefts: you can get immediate feedback and have other, wiser souls point out your stupid mistakes in a matter of hours or minutes.

Here’s how the table should go:

corrected min distances for star testAs you can see, the distances are still pretty long,  but not nearly as long as I claimed. For our fairly-standard 8-inch (20-cm) f/5 mirrors, the distance we would need for a good star test would be 73 feet (22 meters). We still can’t fit that inside the CCCC building in one straight line. However, I guess that if we get some good first-surface flat mirrors, we could arrange for 73 feet/22 meters if we reflect the pinhole light a few times. I also bet we won’t need that lens to reduce the size of the pinhole, which you can see here.

A 12.5″ f/6 mirror will need 119 feet, or about 3 times the width of the CCCC game room. My 16″ f/5 will need a distance of 287 feet or 87 meters. That’s a long way; 7 times the distance across our largest room! I guess we’ll need a bunch of decent small flats from Surplus Shed, as well as precision tip-tilt devices to line all those mirrors up properly.

Introducing another telescope making blog

09 Friday Jan 2015

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David Collins has a nice blog where he’s been documenting his telescope making projects. His first scope, a 6″, is named the Riccioli, and his second, a 12″, is named the Schall von Bell. Beautiful workmanship and good optical practices as well. If you are interested in finding out why they have those names, you will need to read his blog.

The link for his blog is here.

Bad News on Star Testing

09 Friday Jan 2015

Posted by gfbrandenburg in Uncategorized

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OOPS. These were all in INCHES, not FEET!

D’oh!! and Duh!

every single number in that table was supposed to be divided by 12 because there are, duh, 12 inches in a foot.

I have some bad news for myself and friends on the star-testing front. It turns out that even though it’s quite conceivable to make a source of light appear as a point for all practical purposes, and not too far from the telescope, I was forgetting all about spherical aberration.

The problem is that we don’t design and fabricate our telescopes so that they can look at birds or neighbors or even distant trees. Instead, our goal is to focus on sources that are INFINITELY far away – hundreds of thousands of miles or kilometers away at the very closest (i.e., the Moon and some comets). Our mirrors are designed to be paraboloids, which reflect light perfectly and to a point IF and ONLY IF the rays of light that hit the mirror are perfectly parallel to each other and to the axis of the mirror. But if the object being viewed is closer, you get a distortion that is known as Spherical Aberration. If you have objects that are, say, 8 feet away, the surface you want is a sphere with a radius of 8 feet, NOT a paraboloid. If you test a mirror at distance of merely, say, 40 feet, like I was planning to do, then your results will be all bogus: if the telescope passes the star test at that distance, then it definitely will NOT work on the stars.

Which means that all of my rejoicing over having been able to make small holes is pretty much worthless. The source has to be much, much farther away than I thought. How do I know? I finally got a chance to re-read a section of Harold Suiter’s famous book Star Testing Astronomical Telescopes (2nd edition) and on page 2 he has a table that shows how much you have to multiply the focal length of the telescope to avoid spherical aberration.

He does not give these distances in actual feet or meters, so I thought I would calculate those distancers. It’s not pretty.

min distances for star test

So, for example, if you have an 8 – inch diameter telescope mirror, which you made to be f/5 (ie with a focal length of 40 inches, pretty typical with us), then you need for your point source to be 880 feet away from your scope,. In metric units, that would be a 20 cm diameter and a distance of 268 meters.

I do not have any idea how we are going to be able to arrange to hang a light source of any type at these distances. Notice that an 18 inch, f/5 telescope (46 cm) needs to have its point source be over 4400 feet away (1344 meters)!!!!

Thereare a couple of somewhat-distant radio towers visible from the parking lot of the Chevy Chase Community Center, but how on earth would we ever get permission to hang a tiny christmas tree ornament on one of them?

There is

The original Mémoire by Foucault, in French, which I apparently was the first to translate into English

08 Thursday Jan 2015

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I was given the original Memoire to translate by a now-deceased amateur astronomer (whose name escapes me). When he passed away, I figured I might as well publish it on my old blog.
Here is the link to Leon Foucault’s original article on making parabolic, silvered telescope mirrors from about 1859:

http://books.google.com/books?id=m6Y3AQAAIAAJ&pg=PA197#v=onepage&q&f=false

On Making an Artificial Star for an Indoor Star Tester

04 Sunday Jan 2015

Posted by gfbrandenburg in History, Telescope Making

≈ 2 Comments

Tags

artificial star, ATM, CCCC, couder, foucault, Hubble, NCA, Ronchi, star testing, Telescope

I help run the amateur telescope-making workshop at the Chevy Chase Community Center in Washington, DC, sponsored and under the auspices of the National Capital Astronomers. Both the NCA and its ATM group have been on-going since the 1930’s, well before I was born. In our ATM group, have the somewhat esoteric thrill of manufacturing incredibly accurate scientific devices (telescopes), from scratch, with not much more than our bare hands and a few tools. And then we go and use them to observe the incredible universe we come from.

Since these telescope mirrors are required to be insanely accurate, we need extremely high-precision ways of testing them. However, we don’t have the tens or hundreds of thousands of dollars needed to purchase something like a professional Zygo Interferometer, so we use much cheaper ways of testing our mirror surfaces.

Some of those methods are associated with the names Foucault, Couder, Bath, Ronchi, Ross, Everest, and Mobsby, or are described with words like “knife-edge”, “double-pass” and “wire”. They all require some relatively simple apparatus and skill and practice in measurement and observation.

We are of the opinion that no one single test should be trusted: it’s easy to make some sort of error. (I’ve made plenty.) You may perhaps recall the disaster that happened when the Hubble Space Telescope mirror passed one test with flying colors, and other tests that weren’t so good were ignored. When the HST finally flew in orbit, it was discovered that the mirror was seriously messed up: the test that was trusted was flawed, so the mirror was also flawed.

We don’t want to do that. So, at a minimum, we do the Ronchi and Foucault/Couder knife-edge tests before we say that a mirror is ready to coat.

But the ultimate test of an entire telescope is the star test.

In principle, all you need for that is a steady star, your telescope, a short-focal-length eyepiece, and a copy of Richard Suiter’s book on star-testing optical telescopes.

Unfortunately, around here, it’s often cloudy at night, and if it’s clear, it might be windy, and around the CCCC building there are lots of lights — all of which make star-testing a scope on the two evenings a week that we are open, virtually impossible. We aren’t open in the daytime, and even if we were, I don’t see any ceramic insulators on any telephone poles that are both small enough and far enough away to use as artificial stars in the manner that Suiter describes. (There are a few radio towers visible, but I doubt that their owners would let us climb up one of them and hang up a Christmas tree ornament near the top!)

So, that means we need to make an artificial star.

I’ve been reading a few websites written by folks who have done just that, and it seems to be a bit easier than I thought. The key is to get a source of light that acts like a star at astronomical distances — but close enough that we can fit it inside the basement of the CCCC, probably not in the woodshop where we make the scopes, but more likely out in the hallway or in the large activity room next door, both of which are about 40 or 50 feet long.

So here are my preliminary calculations.

First off, it appears that the resolving power of a telescope equals the wavelength being used, divided by the diameter of the objective lens or mirror, both expressed in the same units. The result is in radians, which you can then turn into degrees, arc-minutes, arc-seconds, or whatever you like, but it’s perhaps easier to leave in radians. In any case, the larger the diameter, the tinier the angle that your telescope can resolve if it’s working properly.

I am going to use a 16-inch mirror diameter, or about 0.4 meters, as an example, and I will use green light at about 560 nanometers (560 x 10^-9 m) because that’s pretty close to the green mercury line we have in our monochromatic light box. I then get that the resolution is 1.4×10^-6 radians.

resolution of lens or mirror

(We can convert that into arc-seconds by multiply that by 180 degrees per PI radians  and by 60 arc-minutes per degree  and by 60 arc-seconds per arc-minute; we then get about 0.289 arc-seconds. If we were to use an 8-inch mirror, the resolution would be half as good, meaning the object would need to be twice as big to be resolved, or about 0.578 arc-seconds.)

resolution in arc seconds

I read that one can make an artificial star by using an ordinary eyepiece and a small illuminated hole that is put some distance away from the eyepiece. The entire setup is aimed at the telescope, and then you have an artificial star. Here is the general idea:

artificial star setup

Supposedly, the equations go as follows, with all of the dimensions in the same units. I think I will use millimeters.

Star Size of artificial rigWe want to make it so that the size of the artificial star will be small enough to be below the limit of resolution of any telescope we are making. I am pretty sure that we can set things up so that there is 40 feet (13 meters) between our telescope rig and the table or tripod on which we sill set up this artificial star.

I also know that I can find an eyepiece with a focal length of 12 mm that I’m willing to use for this purpose, and I also purchased some tiny little holes from “Hubble Optics” that are of the following sizes: 50, 100, 150, 200, and 250 microns, or millionths of a meter. Those holes are TINY!!! So that takes care of H and F. I still need to figure out what SS should be.

A few lines ago, I found that for a 16-inch telescope, I need a resolution of about 1.4×10^-6 radians. The nice thing about radians is that if you want to find the length of the arc at a certain radius, you don’t need to do any conversions at all: the length of the arc is simply the angle (expressed in radians) times the length of the radius, as shown here:

angle arc radius

c=theta times Radius

So if our artificial star is going to be 13 meters away, and we know that the largest angle allowed is roughly 1.4×10^-6 radians, I just multiply and I get 1.82×10^-5 meters, or 1.82 x 10^-2 millimeters, or 18.2 microns.

Which means that I already have holes that are NOT small enough: the 150-micron holes are about 10 times too big at a distance of 13 meters, so my premature rejoicing of a few minutes ago, was, in fact, wrong.  So, when I make the artificial star gizmo, I’ll need to figure out how to make the ‘star size’ to be roughly one-tenth the size of the holes in the Hubble Optics micro-hole flashlight.

Or, if I rearrange the equation with the L, H, F and SS, I get that L = H * F / SS. The only unknown is L, the distance between the hole and the eyepiece/lens. For H, I have several choices (50, 100, 150, 200 and 250 microns), SS is now known to be 18 microns or so (36 if I want to test an 8-incher), and I plan on using a 12.5 mm eyepiece. If I plug in the 150 micron hole, then I get that L needs to be about 104 millimeters, or only about 4 inches. Note that the longer L is, the smaller the artificial star becomes. Also, if I replace the 12.5 mm eyepiece with a shorter one, then the artificial star will become smaller; similarly, the smaller the Hubble Optics hole, the smaller the artificial star. This all sounds quite doable indeed.

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