Tag Archives: foucault

Easy ways to show the earth is not flat

18 Friday Dec 2020

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Sharing Steve Ruis’ handy methods anybody can use to show that the earth is in fact round. Very clever!

An Open Letter to the Many Flat Earthers Now in Existence

by Steve Ruis

Dear Flat Earthers,
Many people have been derogatory of your belief that the Earth is flat. Please note that they are belittling your belief, not you per se. You, personally, are an idiot, but that is probably not your fault.

Here are any number of accessible approaches for discovering the shape of our beloved planet. Enjoy!

* * *

Use Your Phone!
On Christmas Day, here in Chicago, I expect there to be snow on the ground because, well, it is winter. On Christmas Day I can pick up my phone and dial up anyone in Australia and ask them “What season is it?” They will tell you that it is summer in Australia. You might want to ask your flat Earth mentors how it could be winter and summer simultaneously on a flat Earth.

Use Your Phone!
Go to a globe and pick a spot half way around the Earth (I know it is a false representation in your belief, but humor me.) In the middle of the day, phone somebody at or near that spot. Call a hotel, they are always open. Ask whoever responds “Is it light or dark outside?” They will tell you that it is dark where they are. You might want to ask your flat Earth mentors how it could be light and dark simultaneously on a flat Earth.

Look Up What Local Time Was
In the US there was this concept of “local time” which was that “noon” was when the sun was at its highest point in its arc. You could call up people on the telephone who were not that far away and ask them what time it was and they would tell you something different from what your clock was telling you. The farther away they were, the greater the difference would be. On a flat Earth the time would be the same everywhere.

Look Up What Time Zones Are
I am writing this in the central time zone in the U.S. These zones were created at the behest of the railroad industry whose dispatchers were going crazy making up schedules for trains when every place had their own times. By creating these “zones” everything would be exactly one hour off from those in neighboring zones, two hours off for the next over zones, and so on. If you don’t believe me . .  pick up your phone and dial up a friend who lives a considerable distance (east-west) away from you and ask them what time it is. The time they state will be a whole number of hours away from your time. Heck, even the NFL knows this. When I lived on the left coast, the games started at 10 AM and 1 PM. Now that I live in the central time zone, the games start at 12 Noon and 3 PM. Over New York way the games start at 1PM and 4 PM. Do you think those games are replayed in one hour increments? Nope, time zones!. You might want to ask your flat earth mentors how it could be that simultaneous games start at different times on a flat Earth.

Watch the Video
Astronauts in the International Space Station (ISS) have made continuous videos of an entire orbit of the Earth. It takes only about an hour and a half about the length of a typical Hollywood movie. During the whole movie the earth appears round, and yet it is clear that different continents are passing in our view.

Now you may argue that NASA made this movie as propaganda for the Round Earth Conspiracy. It is certainly within our CGI abilities at this point, but you may want to ask why NASA would want to do such a thing? Plus, many astronauts have taken their own cameras aboard and taken pictures for themselves and they show the same thing. How could the Round Earth Conspiracy have allowed that to happen? It must be incompetence! Conspiracies aren’t what they used to be!

Da Balloon, Boss, Da Balloon
Many amateurs, unaffiliated with the government, have launched rockets and balloons high up into the atmosphere to take pictures. Every damned one of those pictures shows that the Earth is round. How come all of those cameras ended up pointed at the curved edge of your round and flat disk Earth? Such a coincidence!

An Oldie But Goodie #1
Occasionally, during a lunar eclipse, you can see the shadow of the earth falling upon the Moon. The shadow is always circular. This would be true if the flat earth were always dead on to the Moon, but the Moon orbits the Earth and wouldn’t a flat Earth be edgewise, often as not, and wouldn’t that create a non-round shadow on the Moon? Inquiring minds want to know.

An Oldie But Goodie #2
It was claimed that one of the first demonstrations of the earth being round was the observation of ships sailing west from Europe/England could be observed for a while but the ship itself was lost to sight while the mast was still visible. This would not happen on a flat Earth. The whole ship would just get smaller and smaller as it sailed west.

For pity’s sake, I live 22 stories up and the shores of Lake Michigan and I cannot see anything directly opposite me in Michigan. All I can see is water, with any kind of magnification I can muster. And I am not looking across the widest part of this lake! If the earth were flat, the lake would be flat and I could see the Michigan shore.

And Finally . . .

All of the fricking satellites! Do the math. What kind of orbit is stable around a flat disk earth? Answer none! And there are hundreds of the danged things in orbit.

Also, just for giggles. Look up what a Foucault pendulum is, And explain its behavior based upon a flat Earth.

PS You may be getting good vibes in your special knowledge that you know something other people do not. However, would not that special feeling be more worthwhile were you to volunteer at a food bank or a day care center or senior center? Wouldn’t doing something worthwhile be more rewarding that making a statement about how those pointy-headed intellectuals aren’t so smart?

PPS I have seen the cute models with the Sun and Moon on sticks rotating around (see photo above). If that were the case, everyone could see the Sun and Moon all day, every day. (There is straight line access to both objects in that model from everywhere on the flat disk.) Do you see the Sun and Moon all day, every day? No? Maybe someone who had more creativity than knowledge came up with those models. They do sell well, I must admit, so maybe their interest is commercial.

PPPS Regarding the 200 foot wall of ice that supposedly exists at the “edge of the disk,” supposedly so all the water doesn’t flow off and be lost into space. By now don’t you think someone would have sailed next to that wall all of the way? That distance would be somewhere in the neighborhood of a 28,000 mile trip. Has anyone ever report such a thing? Hmm, I wonder why not

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

08 Saturday Sep 2018

Posted by in astronomy, flat, Hopewell Observatorry, optical flat, Optics, Telescope Making

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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

07 Friday Sep 2018

Posted by in astronomy, Optics, science, Telescope Making

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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

Trying to Test a 50-year-old Cassegran Telescope

07 Thursday Sep 2017

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We at the Hopewell Observatory have had a classical 12″ Cassegrain optical tube and optics that were manufactured about 50 years ago.; They were originally mounted on an Ealing mount for the University of Maryland, but UMd at some point discarded it, and the whole setup eventually made its way to us (long before my time with the observatory).

 

The optics were seen by my predecessors as being very disappointing. At one point, a cardboard mask was made to reduce the optics to about a 10″ diameter, but that apparently didn’t help much. The OTA was replaced with an orange-tube Celestron 14″ Schmidt-Cassegrain telescope on the same extremely-beefy Ealing mount, and it all works reasonably well.

 

Recently, I was asked to check out the optics on this original classical Cassegrain telescope, which is supposed to have a parabolic primary and a hyperbolic secondary. I did Ronchi testing, Couder-Foucault zonal testing, and double-pass autocollimation testing, and I found that the primary is way over-corrected, veering into hyperbolic territory. In fact, Figure XP claims that the conic section of best fit has a Schwartzschild constant of about -1.1, but if it is supposed to be parabolic, then it has a wavefront error of about 5/9, which is not good at all.

Here are the results of the testing, if you care to look. The first graph was produced by a program called FigureXP from my six sets of readings:

figure xp on the 12 inch cass

my graph of 12 inch cass readings

I have not yet tested the secondary or been successful at running a test of the whole telescope with an artificial star. For the indoor star test, it appears that it only comes to a focus maybe a meter or two behind the primary! Unfortunately, the Chevy Chase Community Center where we have our workshop closes up tight by 10 pm on weekdays and the staff starts reminding us of that at about 9:15 pm. Setting up the entire indoor star-testing rig, which involves both red and green lasers bouncing off known optical flat mirrors seven times across a 60-foot-long room in order to get sufficient separation for a valid star test, and moving two very heavy tables into said room, and then putting it all away when we are done, because all sorts of other activities take place in that room. So we ran out of time on Tuesday the 5th.

A couple of people (including Michael Chesnes and Dave Groski) have suggested that this might not be a ‘classical Cassegrain’ – which is a telescope that has a concave, parabolic primary mirror and a convex, hyperbolic secondary. Instead, it might be intended to be a Ritchey-Chretien, which has both mirrors hyperbolic. We have not tried removing the secondary yet, and testing it involves finding a known spherical mirror and cutting a hole in its center, and aligning both mirrors so that the hyperboloid and the sphere have the exact same center. (You may recall that hyperboloids have two focal points, much like ellipses do.)

Here is a diagram and explanation of that test, by Vladimir Sacek at http://www.telescope-optics.net/hindle_sphere_test.htm

hindle sphere test

FIGURE 56: The Hindle sphere test setup: light source is at the far focus (FF) of the convex surface of the radius of curvature RC and eccentricity ε, and Hindle sphere center of curvature coincides with its near focus (NF). Far focus is at a distance A=RC/(1-ε) from convex surface, and the radius of curvature (RS) of the Hindle sphere is a sum of the mirror separation and near focus (NF) distance (absolute values), with the latter given by B=RC/(1+ε). Thus, the mirrorseparation equals RS-B. The only requirement for the sphere radius of curvature RS is to be sufficiently smaller than the sum of near and far focus distance to make the final focus accessible. Needed minimum sphere diameter is larger than the effective test surface diameter by a factor of RS/B. Clearly, Hindle test is limited to surfaces with usable far focus, which eliminates sphere (ε=0, near and far focus coinciding), prolate ellipsoids (1>ε>0, near and far foci on the same, concave side of the surface), paraboloid (ε=1, far focus at infinity) and hyperboloids close enough to a paraboloid to result in an impractically distant far focus.

We discovered that the telescope had a very interesting DC motor – cum – potentiometer assembly to help in moving the secondary mirror in and out, for focusing and such. We know that it’s a 12-volt DC motor, but have not yet had luck tracking down any specifications on that motor from the company that is the legatee of the original manufacturer.

Here are some images of that part:

On Making an Artificial Star for an Indoor Star Tester

04 Sunday Jan 2015

Posted by in History, Telescope Making

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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.

Figuring (parabolizing) Your Mirror

16 Tuesday Dec 2014

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5. Figuring and Testing

 A. Polishing pads do a great job of polishing out the pits, but they tend to leave a rough surface that is not a true paraboloid or even a section of a sphere, unless you are very, very lucky. Most folks will switch to a pitch lap for the figuring process, which involves removing sub-microscopic amounts of glass from various zones on your mirror, in order first to make it into a section of a sphere, and then into the bottom of a paraboloid – the only geometric figure that will reflect all of the rays that come from distant stars onto a single focal point. Many treatises have been written about figuring, and I’m not going to add to that list. “Understanding Foucault” by David Harbour gives an excellent explanation of the figuring process, as does Mel Bartels here. However, here are some of the basics:

B. You will need a pitch lap, made either of Gugolz or Acculap or Tempered Burgundy pitch. The first two are synthetic products whose composition is probably secret; the third one is made from the sap of coniferous trees. I’m not going to describe the process of making a pitch lap here, but I combine some of the methods of Carl Zambuto and John Dobson when I make a new one; you can watch it as we do it for you. It’s much less work if you can use a pitch lap that was made by or for someone else who has finished their own project. Sometimes a previously-used pitch lap will have sat around too long and might need to be scraped off and remelted. We generally use roughly square facets, which allow the pitch to flow better and conform itself to your mirror. Without the facets, any high points on the lap have a hard time being lowered. We also tend to use netting or a single-edge razor blade to make minifacets, which further help the lap to conform to the mirror.

C. Pitch is weird stuff. When it’s warm, it flows and it’s very sticky. When it’s cold, it is fairly hard, and you can shatter it with a hammer. If you leave a pencil or a coin on a pitch lap overnight, the next day you can see all of the details of the pencil or coin reproduced perfectly in the pitch. We want the lap to conform itself to your mirror. Then we use the pitch lap to remove all of the irregularities that were left by the polishing pads. So, we warm up the pitch lap to soften it a bit (using a heat lamp or hot water), spread Cerox or rouge onto your mirror, and then press the two together briefly but firmly. We often use some netting to create micro-facets, which help the pitch conform to your mirror even more.

D. The figuring stage can severely try your patience, especially if the tests show a surface that looks weird. But relax! If you persevere and don’t drop the mirror on the ground, success is guaranteed, since it’s just a matter of removing the correct millionth of an inch or two (much less than a micrometer) of glass from the correct zonal ring to achieve near-perfection. One needs to make sure that the lap actually conforms to the mirror; bad contact between the two can cause trouble, and so can a pitch lap that is too hard, too soft, or too thin. All of those are fairly easily fixed, with remarkable results. And we are here to help.

E. One major problem that can affect mirrors is a Turned-Down Edge (TDE). Opinions vary on what causes this dreaded condition, but the evidence suggests to me that TDE appears when the lap is exactly the same size, or slightly smaller, than the mirror itself. To avoid a TDE, do not chip off the parts of the pitch lap that ‘mushroom’ out past the edge. Let them stay there.

F. You will be instructed in a specific set of strokes which will first make your mirror into a sphere. Then, you will be instructed in a different set of strokes that will make your mirror into a good approximation of a perfect paraboloid. Texereau, LeCleire, and many other books describe those strokes. So did Leon Foucault in his 1859 article, which you can find on this blog/website. In our workshop, we will test your mirror frequently with a combination of tests, many of them invented by Foucault but later modified.

G. A very fast qualitative test is the Ronchi test, which you can look up. It gives you almost instant feedback on the presence or absence of bad features like turned-down edge (TDE), zonal defects (high or low rings), astigmatism (lack of symmetry), roughness, and so on. It will tell you whether your mirror is a sphere or not – if the Ronchi lines are perfectly straight, then you have a sphere. If they are not straight, then the test can tell us if your mirror is on the way towards being an ellipsoid with the long axis perpendicular to the mirror (or parallel to it), or a hyperboloid, or your goal, a paraboloid. There are several computer programs that provide simulations of what a perfect mirror should look like under the Ronchi test, but I’ve found you can’t always trust those simulations. RonWin is one such program, and Mel Bartels has another on one of his web pages.

H. A more time-consuming test that I find is necessary is the Foucault test as modified by Andre Couder, also known as the numerical knife-edge test with zones. If the Ronchigram looks good, and the numbers in the knife-edge zonal test are also within acceptable limits, then the mirror is done. A slight modification of this test is known as the Wire Test, which works well on fast mirrors. David Harbour’s article does an excellent job of explaining this test. One can use a pinstick method for marking the zones, or one could write directly on the mirror with a Sharpie, but we use a version that uses cardboard masks with holes cut out at carefully-measured zones.

I. We have tried a number of other tests, such as the double-pass autocollimation test, the Mobsby Null test, and the Bath Interferometer test, and have had difficulties getting good results with them. Therefore, we are continuing to use the Ronchi and Knife-Edge Zonal tests.

J. However, the best test of any mirror is the Star Test, which is the subject of an entire book by Richard Suiter. Some do this in the daylight, using sunlight reflected from very distant insulators on electrical poles. Most do it at night, but it requires steady air (‘good seeing’) and a clear sky as well. The Star Test is much easier to perform if the mirror is already aluminized and in a working telescope, which brings us to….

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