Astronomy

Is it practical to hand grind a convex parabolic or hyperbolic mirror?

Is it practical to hand grind a convex parabolic or hyperbolic mirror?


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I know it's practical to hand grind a convex spherical mirror and that it's practical to make a concave parabolic mirror from a spherical one. But as I understand it, the procedure for doing so depend on tracking progress by using interference patters generated by focusing light off the mirror, and that procedure clearly can't be used (unmodified) with a convex mirror.

Short of floating the blank in a bath of index of refraction matched optical fluid and apply the concave procedure to the back side, does anyone know of a way to do that sort of grinding?

Also, I've never actually run across a procedure for finishing a hyperbolic mirror for either convex or concave, though I haven't spent much time searching on that one.


If you're asking in regards to testing methods, as indicated in the comments, the simplest setup for interferometrically testing convex conic mirrors is with a Hindle Test, shown below in a figure from the University of Arizona College of Optical Sciences. This setup can achieve a perfect null after adjusting the reference sphere to be focused at the focus of the test optic - the catch is that the sphere needs to be larger than your test optic, with a hole through it as shown.

In industry, it is much more common to use an aperture-stitching interferometer for small quantities of non-research-level optics. Larger, more precise, and higher quantity aspheres may use a set of nulling optics, or a diffractive/holographic element to create a null wavefront, as covered in better detail in the link below, which is a slideset from U of Arizona's optical fabrication and testing course.

http://fp.optics.arizona.edu/jcwyant/Short_Courses/SIRA/7-TestingAsphericSurfaces.pdf

If you're feeling especially ambitious, there is a concept for measuring surface form of a mirror by displaying points on a monitor and using an HD camera to see where the reflections come from, thus telling you the angle of the optical surface at that location. The data is then integrated to form a full surface map. In theory, this system could be developed at low cost, with relatively high performance.

https://www.osapublishing.org/ao/abstract.cfm?uri=ao-13-11-2693

Hope this (or at least some of it) helps!

-J


Apparently there is a way of testing a convex mirror by making it from optical grade glass and testing it through the back. The refractive part of the light path creates a situation that if you test it as a sphere or paraboloid in that way (I forget which) the actual curve you get is a hyperboloid.


Is it practical to hand grind a convex parabolic or hyperbolic mirror? - Astronomy

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Grinding, Polishing and Figuring

Thin Telescope Mirrors

Abridged from an article appearing in Telescope Making #12
Provided: Courtesy of Astronomy Magazine
Article's Author: Bob Kestner

For many years, amateur astronomers and telescope makers thought it essential that glass for telescope primary mirrors be at least one-sixth as thick as its diameter. In the last decade, however, it has become increasingly common to find telescopes with primary mirrors very much thinner than the standard 6 to 1 ratio giving excellent optical performance. In fact, the trend has now gone so far that it is unusual to hear of an amateur telescope project much over 12" aperture that has a standard thickness mirror.


Why has this happened? Is the 6 to 1 ratio a myth perpetrated by opticians of a past generation to obstruct the building of large amateur telescopes? Is the 6 to 1 ratio somehow wrong? The answer is no, it is not wrong- it has just been misunderstood. In the optical industry, 6 to 1 is a good compromise between making the glass so thick that flexure can almost be ignored, and making the glass thin but spending much more time and money seeing to it that the glass does not flex and will hold its figure in use.

The avid and somewhat uncritical acceptance of standard - thickness glass in the early years of telescope making - plus some notable failures with thinner glass - gave the general impression that telescope primaries much thinner than 6 to 1 were unmanageable. They are not, but without using the proper techniques, they can be extraordinarily difficult to figure.

However, with the right techniques, thin mirrors aren't much more difficult to make than ordinary mirrors, and for the purpose of large amateur telescopes, thin primaries are advantageous. They are less expensive than thick primaries, are lighter and easier to lift (more important than one might think at first), add less mass to the telescope, and equilibrate to temperature changes more rapidly.

Preparation

The purpose of this article is not to teach you how to make a telescope mirror if you have never done it before. If you have made mirrors before, it can guide you in adapting the techniques you already know to the problems peculiar to big, thin mirrors. But I offer this warning: if you have never made a mirror before, don't start with a large, thin mirror. It's a bigger job than you realize.

There are many different ways of grinding mirrors. The methods I describe are those I use when working at home, grinding and polishing entirely by hand. Where I refer to machine working, it's for your information, and not essential to making a successful mirror by hand.

The techniques described in this article are for mirrors of 16" and larger. Again, I consider it essential that anyone attempting a mirror of this size on his own must have made at least 2 mirrors successfully before, unless he or she possesses an extraordinary aptitude of optics.

Obtaining Glass


Obtaining glass is often a problem. As of this writing, there are no companies supplying thin mirror blanks to amateurs. Until somebody recognizes that there is money to be made supplying the glass, telescope makers will be forced to buy rough cut glass from glass companies not used to selling small quantities over the counter.

It will take some tact and understanding on your part to deal with these places, to outline what you do need, as well as what you don't need from them. Remember, if you tell them what it's for (people love telescopes-promise them a look through it), many businesses will bend over backward to help you. But don't expect them to - they'll probably lose money on you.

There are still places where you can obtain plate glass portholes. Try surplus stores in coastal cities. Many 16" and 18" diameter portholes 1" thick are still out there, ranging in price from $10 to $150 (1981). A reasonable price is whatever you're willing to pay. The problem is finding one.

Pyrex Sheet Glass


Pyrex sheet glass is available from those glass companies not used to selling to amateurs. Corning makes Pyrex in many different thicknesses, the thickest now available is 1.625" (Editorial Note:Corning now produces sheets in two thicker forms, i.e., 1.875" and 2.250"). They sell it to glass companies (Corning distributors) in large square sheets.

Most companies sell coarse annealed and fine annealed. I recommend fine annealed for telescopes. I don't know if coarse annealed would suffice because I've never tried it, It's probably a hit-or-miss thing - most will work and some may fail.

The prices for sheet glass vary quite a bit. The last time I checked (late 1980), pieces 16" diameter by 1.62" thick were about $225, and 24" diameter by 1.62" thick were about $500.

When you order from a company, specify the diameter(rough round) and thickness. They'll cut out a square piece on a saw that will yield your diameter. Then they cut off the corners several times until the piece is round. What you'll get is a piece of glass blank with 16 to 60 sides with the surfaces only roughly flat - to less than 1/8". Be sure to insist they cut lots of sides - you don't want just 8.

Next you'll have to contrive a way to grind the blank round and flat. Grinding it round is not very difficult, especially if your piece has enough sides - it's just a matter of grinding off the high spots. I use a hand-size piece of tile and #80 grit. Grinding by hand against the outside of the glass, I've made a 16" with 30 sides presentable in 2 or 3 hours.

The surfaces are not as easy. You must grind both flat - especially the back. This can take 20 or 30 hours per surface on a 16" if you're working by hand, but the grinding time may be much less depending on surface quality.

If you're lucky, you may find a company willing to diamond-generate your blank. They can Blanchard the back flat, edge it round, and generate the radius. This work on a 16" will run $100 to $200. The problem is finding a company willing to do it. Work of this sort is usually done at your risk - if your glass breaks, you've lost the blank. Although glass breaking is uncommon, chips occur more frequently. All these problems may seem insurmountable, but TM is constantly publishing information about suppliers, so some firms dealing with amateurs may eventually turn up. Until then, you will have to use your own resources. Someone possessing the ambition to make a large telescope mirror can probably overcome these supply problems with a few dozen phone calls and letters. When you succeed, let TM know about your results so others can gain from your experience.

Thin Pyrex versus Thin Portholes


I was going to skip this section and leave it to your discretion, but the subject can't be avoided. It's paradoxical that something inferior (i.e., porthole glass) works as well as something better (i.e., Pyrex), given reasonable circumstances.

Plate glass has a three times greater coefficient of thermal expansion than does Pyrex. It should, therefore, be worse for telescope mirrors than Pyrex. Yet, when a plate glass mirror is used in a solid insulated tube with a closed back (such as a big Dobsonian), after initial equilibration in the evening, temperature changes in the mirror are quite slow. The telescopes that I've observed with most have plate glass mirrors mounted in closed-back tubes, and I can testify that the figure change after equilibration during the night is quite small.

If the back of the mirror is directly exposed to the air, temperature changes in the air affect the mirror more directly. At times I've been annoyed with the changing figure of a plate glass mirror under these conditions.

A crucially important fact, however, is that portholes come round and 99% of them have surfaces flat enough to start grinding the curve right off. With Pyrex, you must start by making the surface flat, which is a lot of work.


Now the bad news! Plate glass is more difficult to figure than Pyrex, and sometimes the strain in portholes is not negligible. Figuring plate glass is more time-consuming and more tedious than figuring Pyrex. After you attack a plate glass mirror with a warm pitch lap, it's several hours before you can tell anything about the progress you've made figuring. That means when you're doing the final figuring, you'll wait three hours before you can test the mirror to see what needs to be done next. Considering the time it takes to get going again, it can take all day to work the mirror twice. If you plan on making a porthole mirror, don't let this stop you: just recognize it is plate glass, and allow for it.


Well, there it is. Pyrex is easier to manage than plate, but it takes much more work to get a sheet glass blank ready to grind. The choice is yours. These days, I work only Pyrex, but I can afford to discriminate. I can buy it easily and get all the starting work done on diamond-grinding machines - something most of you don't have access to. I've also figured a half-dozen plate mirrors larger than 16" and wouldn't trade the experience for a million dollars - not to mention the thousands of hours of excellent observing these mirrors have given in return.

The thickness you choose, if you have a choice, is determined by the diameter of the mirror and how you plan to mount the mirror in the telescope. For mirrors under 19", I would not use glass under 1" thick and if you're buying Pyrex, I'd use a 1.62" sheet.

For mirrors in the 20" to 25" range, I'd strongly recommend 1.62" as a minimum thickness, especially if the mount is not going to be mounted in a sling.

Last summer a friend and I made a 25.5" mirror on a 1.37" thick Pyrex mirror. The curve, f/6, was relatively shallow. We paid strict attention at every step of the way to prevent flexure, especially when testing the mirror in a vertical position. I remember wishing that we had had that extra .25" in thickness. On the other hand, when it turned out well, it seemed good to have a 25" mirror that could be carried with little trouble.

The 1.62" is just a recommendation on my part, since it allows you a little room for error especially in a 16" or 18" mirror. For mirrors around 30" in diameter, working by hand, 1.62" is the minimum thickness that I would consider. If you plan on working your mirror by machine, you'll run into problems that will increase the minimum thickness needed even more.

Choosing the Diameter


I recommend that you start your big, thin mirror career with a 16". By keeping your ambitions relatively modest, your chances of success are much higher than with mirrors over 20". Even though my current efforts are going into a telescope twice as big as a 16", my observing friends and I agree that we could live the rest of our lives happily observing with a 16" without the slightest regret.

In choosing a blank size, you should think of the outer 1/4" of your mirror as lost to a turned edge. You won't be alone in this - most big mirrors have a clear aperture at least 1/2" less than the blank diameter. If you find a 16.5" porthole, think of it as a finished 16" mirror. If you're buying sheet glass, add 1/2" to the diameter of the finished mirror you want.

Choosing the f/ratio

After the aperture, you must choose the f/ratio. The most important factor from the standpoint of an optician is that a longer focus mirror is easier to make, since it departs less from a sphere. From the observer's standpoint, a long focal length makes a big telescope too big! Unless you have an army of people to help you set it up, you should not let the focal length get out of hand. Don't minimize the problems of simply using a telescope longer than ten or twelve feet - you'll spend a lot more time clambering up and down the ladder than you ever dreamed.

At the lower bound of useful focal ratios, coma and eyepiece aberrations limit your mirror's performance. Furthermore, short focus mirrors - are very difficult to figure, and as a further practical consideration, remove valuable thickness from your glass.

My recommendation is to play fairly conservative, and choose a focal ratio between f/5 and f/6 depending on your circumstances and desires. For most observers, f/5 may be the best choice.

Solid Tools

In addition to finding a blank for the mirror, you will need another disk for a grinding tool. It may be either a solid glass tool or a plaster tool covered with hard ceramic tiles - once again, your taste, energy, and previous experience will dictate what you want to try.

The tool need not be as large as the mirror. You can use a tool 75% of the mirror diameter without much difficulty. Tools smaller than 75% have less tendency to produce a spherical curve during fine grinding. Although a 16" tool works well with a 16" mirror, for larger mirrors I would recommend a smaller tool simply because full size tools are heavy and awkward.

Usually, what is available dictates what tool is used. Take care, however, not to use a tool that's too thin. If the tool is too thin, it will bend while you are grinding, presenting two problems. First, astigmatism in the mirror will not completely grind out because the tool will conform to the astigmatic contour. Second, the weight of your hands on the back of the tool will force the center of the tool to grind harder on the center of the mirror, generating a curve deeper (i.e., more parabolic) than spherical curve. Usually, this is not a severe problem, but you'll find the mirror requires extra polishing to polish the center.

A 16" tool with an edge 1/2" thick is approaching a thickness where troubles start. A friend of mine recently used a 16.5" glass tool slightly thicker than this safely. However, I once used a 20" glass tool 5/8" thick at the edge, and got a bad case of astigmatism. We ended up pitch blocking a 16" diameter porthole 3/4" thick to the back of it, and then it worked well. While 3/4" would be a reasonable minimum for a tool this size, with either plaster or aluminum tools, a thicker minimum should be chosen.

There are two main types of grinding tools - solid and segmented. Solid tools are usually glass and segmented tools are usually plaster faced with ceramic tiles.

A solid glass tool can be a disk cut from sheet glass, as you are used to, or can be made by laminating thin plate glass disks together. You can buy circular plate glass from retail window glass companies. You may have trouble finding a piece thick enough to serve as your tool face for rough grinding - you do not want to grind through it into the next piece. Although it has been done, it increases the chances of scratching in fine grinding.

For grinding the flat surface on the back of the blank, just glue on a new piece of glass if you grind through the first. Aquarium cement is readily available and sticks to glass.

Segmented Tools

For mirrors with the curve already generated, or for those wishing to try a segmented tool, a ceramic tile grinder is the answer. Tile tools are made by blocking ceramic tiles onto a support. Such tools can be made flat or curved to fit a generated blank. The tile support can be plaster, aluminum or glass. Epoxy or hard pitch is used to glue the tiles into place. The greatest problem with pitch is that the tiles may fall off in rough grinding.

A plaster support is made by wrapping a metal or cardboard dam around the mirror a couple of inches high. Smear soap over the surface of the glass to keep the plaster from sticking, then pour on the plaster. If the mirror has a curve, this method will give a mating curve on the plaster.

I highly recommend Kerr Dental plaster, Vel-Mix Stone Pink. This stuff hardens like stone! (Call Kerr Co. at 313-946-7800 and ask them for the name of a distributor in your area. They have 400 distributors nationwide. It costs $12 for 25 pounds). Add water to it and stir until it is slightly thicker than cream.

Almost any glazed ceramic tile will do for the grinding surface. They should be around 1" to 2" square or round. Attach them with epoxy. Epoxy can be bought in cans at the hardware stores. It helps if you can buy an epoxy softening agent, making the epoxy less brittle.

To epoxy the tiles to the base, start by protecting the mirror surface. Smear a release agent on your mirror so that excess epoxy will not stick. (Buy a release agent with the epoxy - but I suspect grease or soap would work, too.) Place the tiles in the desired pattern in mirror. Space them no less than 1/4" apart. Pick them up one by one, and spread a thick coat of epoxy on them. Set them back in place epoxy side up. It is a good idea to get a friend to help you, because you must coat the last tiles with epoxy before the first ones set. After they're all coated, carefully set the support onto the tiles and let it harden.

You can see that it is important that the curve of the tool match that if the mirror, and also that the tiles are uniform in thickness. If you are using plaster, be sure it is sealed well. It would probably be a good idea to coat the face of the plaster with a thin layer of epoxy to help the tiles stick.

This is a very general discussion of making tools. Experimentation with the materials and use of your smarts to keep you out of trouble.

Working Place

My favorite method for working mirrors by hand is on top of a 55 gallon drum with 300 pounds of sandbags in it. You can buy drums at salvage yards, and sandbags can be brought at nurseries.

One reasonable substitute for a barrel is a sturdy counter - remember, you don't have to walk around your glass. Another is so obvious it's usually overlooked: I used to grind and polish on my knees with the mirror on the floor. This proved successful, but the trouble is learning to walk again after 1/2 hour of polishing.

It is ideal to have two working area --one for grinding and another one for fine grinding and polishing. For reasons of cleanliness and temperature uniformity, polishing is better done indoors. Grinding with abrasives larger than 30 micron is a messy and, depending on your climate, may be better done indoors. Grinding with abrasives larger than 30 microns is messy and, depending on your climate, may be better done outdoors.

Grinding the Back Flat

The first step in generating the optical surface is to grind both front and back flat. When I say "flat", I mean "regular" more than flat. The back can be a few thousandths of an inch convex or (preferably) concave, but it must be free from astigmatism, what opticians call "cylinder". But flat is best. Even if the back has been Blanchard ground, you will still need to grind it smooth with 220.

Grinding the flats can be done with a glass or tile grinder. The best way to do it is to grind two blanks, one with the other. This way you get two flattened for the work of one.

The front, that is the side the curve is to be ground on, needs to be regular to a much lesser degree. However, if grossly high and low areas are present near the edge, by the time you grind in your curve, you're still likely to be missing contact near the edge, and it will cost you a lot of work to bring the surface down to meet them. Remember: On the face side, you're concerned with low areas near the edge that might be left unground after the curve is ground.

To grind, place the mirror face up on something soft like an old piece of deep shag carpet so the glass won't rock. (The carpet will ruined.) Wet it down, add the appropriate amount of #60 abrasive, add a few pounds to the top of the tool if you wish, and grind like mad. When it stops making lots of noise, splash it off and start it again.

After three or four wets, wash it off and look at the surface of the mirror. The high spots will be ground and the low spots will still look unground. This will give you some idea of what you're up against. Look at your tool as well and look how it started. Keep track of the convexity and concavity of both surfaces with a straightedge.

If your mirror starts going convex, concentrate grinding on the center with short strokes.

If the convexity persists, grind with the mirror on top for a while. It's not a difficult thing to manage. John Dobson says, "Rough grinding is a caveman job do it like a caveman. Eat well, sleep well, and work like hell."

A few isolated low spots on the back can be tolerated it they are small. What absolutely cannot be tolerated is a cylindrical curve on the back, or a curve in one axis and a flat in the other. This will cause the mirror to bend during grinding and polishing, and you will happily polish away until you discover that the mirror has astigmatism. When you're satisfied with the flatness of the back, fine grind it through 120 and 220. When grinding with the fine abrasives, low areas will have coarser pits on them and you'll have no trouble seeing them. If the back has been Blanchard ground, it should not take long to grind it flat with 220, just a warning Blanchard grinding may give a perfectly plane surface - but grind it for planeness anyway. You're better safe than sorry.

Preventing Astigmatism

Grinding the back flat is just the first step in preventing astigmatism. The next step is the proper mirror support. Fine grind and polish the mirror face up. A thin mirror bends over the edge of the tool if it's worked on top, so the problem reduces to supporting the mirror from its underside. The best way I know is to support it on a piece of deep shag carpet. The carpet will support the mirror and will allow you to rotate the mirror with no trouble. The carpet goes between your mirror and your work surface which, by the way, must also be flat. (Plywood or particle board is flat enough.)

The key to the success of the techniques is to rotate the mirror on the carpet frequently while working. This prevents non-uniformities in the support working into the mirror and showing up as astigmatism. Every time you complete one turn around the barrel, then rotate the mirror almost constantly in the direction opposite the direction you rotate the tool. As simple as it sounds, this method is quite effective.

For machine working, it's not so easy because the mirror usually can't be rotated with respect to its support. This is why you don't want to make mirrors to be worked on machines too thin. For 16" to 18" mirrors, 1.62" thick is the thinness I would recommend.

There are several ways to support the mirror on a grinding and polishing machine turntable, but first make sure the turntable itself is rigid. It must not bend. If your machine lacks a sturdy turntable, one way to make one is to cast it out of Kerr plaster 4" to 5" thick.

One way to support the mirror is to block the mirror right to the base with pitch. This is somewhat risky because the pitch can deform the mirror. A more manageable way is to pour pitch on the base 3/8" thick. Groove it like a pitch lap with grooves about 1/2" wide. Cover it with a single pieces of paper, and set the mirror on the paper and tape it down. Be careful not to tape it too tight. Let the mirror sit on this lap for 24 hours. The back of the mirror should press the pitch to its exact shape. Each time you take the mirror off for testing, put it back in the same orientation and let it sit again for a few hours. You must not let the grooves in the lap under the mirror press together. When they start closing in, regroove them. Although this method is not without its troubles, it is widely used in the optical industry.

Another method is an 18-point flotation system. I've never used this method for support while working a mirror, but there are those who swear by it. The problem seems to be preventing the mirror from rocking under the lateral forces of grinding and polishing.

Rough Grinding

Once you have the back of the mirror ground flat through 220 and the face reasonably flat, you're ready to start roughing the curve into the mirror. I recommend #60 carborundum for rough grinding. By the way, as in all optical work, be sure that you always maintain bevel on the edge of the mirror throughout grinding.

If your mirror is light enough to grind on top, grind much the same way you would a smaller mirror. Your goal is to grind the curve from the middle out, timing it so that you reach the desired focal length at about the time the curve reaches the edge of the disk.

Start grinding by concentrating the center of the mirror on the edge of the tool. Use a long "W" stroke, occasionally stroking the center of the mirror out to 2" to 3" from the edge of the tool, progressing around the circumference of the tool rotating the mirror.

For mirrors ground face up, a small tool is desirable - 75% of the mirror diameter or smaller. Rough grind the curve by concentrating on the center.

As grinding progresses, you must monitor the focal length of your curve. If the Sun is available, splash water on the mirror and focus its image on a piece of cardboard and measure the distance to it.

Alternatively, you can keep track of the sagitta of the curve. Calculate the sagitta of your curve. Find something that can act as a gauge is a drill bit). Check the progress of rough grinding by slipping the gauge under a straightedge placed across your mirror.

Rough grinding usually produces a grossly hyperbolic curve. Toward the end of rough grinding, start using shorter strokes to produce a smoother, more spherical curve.

Shorter strokes also move the curve toward the edge.

It is not difficult to manage grinding so that the curve meets the edge at about the same time it reaches the desired focal length with a reasonably spherical form.

Placing the mirror face up and grinding with a moderate "W" stroke will also move the curve toward the edge, and tends to produce a more spherical surface. Leaving the mirror grossly hyperbolic will make fine grinding difficult.

Fine Grinding

We've all heard stories about fine grinding taking hundreds of hours. If done correctly, however, fine grinding takes a fraction of this time, and in fact, is one of the more manageable jobs in making a large mirror. Depending on your circumstances, about 2 hours of continuous work at each grade is usually sufficient.

Fine grinding rather naturally divides into two stages: before #220 and after #220. Before 220, you're getting the radius and a smooth curve. After 220, you'll need to pay attention to preventing astigmatism. I also switch from my rough grinding area to my polishing area at 220.

The fine grinding compound you start with depends on the condition of your mirror and fit of your tool. If you rough ground your mirror with 60 grit, you should start fine grinding with 120 grit before going on to 220. If you have been fortunate enough to have the curve generated, you can start with 220 providing your tool has a reasonable fit to your curve. If you are working with a machine, you can use 30 micron grit.

Fine Abrasives

For abrasives smaller than 120, I prefer aluminum oxide to carborundum because it has less tendency to cause large pits in the fine-ground surface. There are several sequences of fine abrasives you can take, but as long as you are careful to have completely ground away the last abrasive pits before going on, you'll be all-right.

More than anything else, your sequence depends on the quality of the abrasive you use. Most abrasives you buy have a few larger abrasive particles in them. For example, although #320 is mostly 320, there will be some grains closer to 220 size in it, plus some much smaller stuff. There is nothing wrong with this - but you must compensate for it by not taking a big step between abrasive sizes.

On the other hand, if you can get some really high quality abrasive like Microgrit(, (made by Micro Abrasive Corp) you're in luck. 30 micron Microgrit( really is 30 micron. There are no 32 micron grains and no 28 micron grains - just 30. As a result, you can spread out the size you use. For example, I use #220 followed by 30 micron, 12 micron, and 3 micron.

When using more conventional abrasives, such as those available from Edmund, the sequence should be 220, 320, 400, 600, E305. There is not too much difference - but the 3 micron is finer than the E305.

It is difficult for me to even guess how much abrasive you'll need. I've never kept track of it. Depending how you happen to use it, the amount can be quite small or large. If you clean the glass after each wet and start by sprinkling new abrasive on the wet glass, you may use as little as a tablespoon of the finer line abrasives for each grade. If you use the abrasive may not be enough. For 120 and 220 abrasives, the amount varies mostly with the amount of work you need to do. On the average, I've found 2 to 3 cups of 120 and 1 cup of 220 will do for me.


Getting a Sphere

Even the most careful finishing up job with 60 grit will leave the curve somewhat hyperbolic. After 60 grit, your main interest, besides removing the pits, is getting the mirror spherical. At this point, the support of the mirror is not at all critical, but using a piece of carpet under the mirror will allow you to rotate it easily.

Start by sprinkling the abrasive on the face of the wet mirror, as you did with smaller mirrors - not too much and not too little. Place the tool down edge first, and start grinding. Walk around the barrel, rotating the tool as you go, and also rotating the mirror every time around.

A solid tool traps abrasive in the center of the mirror and resists grinding the mirror spherical. When you first start a new and smaller abrasive, this shows up as a tendency to form a large bubble in the center, especially in the larger abrasives. Remedy this by using short "W" strokes and stirring the abrasive under the mirror every minute of so until the bubble is gone. To stir up the abrasive, just run the center of the tool clockwise around on the 50% zone of the mirror once or twice while you spin the tool clockwise. You will need to do this often all through fine grinding.

Because a segmented tool does not trap abrasive, a spherical curve will come a good deal more rapidly. A short "W" stroke serves well here, too.

When the wet comes to the end, stop grinding, separate the mirror and the tool, and more water and grit, then continue. If you have a tile tool, you can slop some water and grit on from the side without separating the mirror and tool, but don't drag the tool off on the edge of the mirror - this can roll off the edge. Instead, pull the tool three-fourths of the way off, then lift the tool up. In the finer abrasives this is difficult. A solid tool won't want to separate, and lifting will tend to pull the tiles off a tile tool - so take it easy.

As you probably suspected, you're done with 120 when the surface looks evenly ground and no 60 grit pits remain. Don't be fooled by some of the larger pits that 120 can make itself. These will come out in 220.

Going on to 220

As you begin 220, start to pay a little more attention to preventing astigmatism especially if the tool is thin. Be sure to rotate the mirror on a regular basis, and be sure you're grinding it on something soft. Also, keep mixing the abrasive between the mirror and the tool. In most respects, 220 is about the same as 120, except that this is your last chance to remove any large pits and the surface must be spherical when you finish 220.

To control pits, follow the progress of the ground surface with a loupe magnifier. If you've had your curve generated, watch the generator marks closely. They can fade into the ground surface and seem to be hidden - and you will not know it until there when you polish.

You should remember that 220 can leave some isolated pits a bit larger than the normal 220 pit size. However, you can tell these pits from leftover 120 pits because they will not stay in the same place after a spell of grinding. It is not uncommon for an ATM to grind extra hours trying to remove these pits when, in fact, they are caused by the abrasive and will be removed by the next abrasive. But don't ever let this be an excuse for falling to remove all the pits from the previous abrasive.

After a couple of hours of 220, you should be ready for the light test and 320 or 30 micron grit.

The light test is a very good test for the evenness of your ground surface. This test is described in detail in many telescope making books, and is very easy to apply.

Place a light several feet behind your face-up mirror. Stand back from the mirror a couple of feet and lower your until the angle between the light, the mirror, and your eye is so large that the surface takes on a shine. The finer-ground the surface, the less extreme the angle.

Study the surface It should stay evenly lit from edge to edge as you move from side to side. If the center of the mirror is hazy, it has not be fully ground by your latest abrasive. That also suggests that the mirror's curve is not spherical - so continue grinding until it is. This test will only give information on the overall smoothness of the ground surface, and is not a test for isolated pits.

Keeping the edge properly beveled becomes more important as fine grinding progresses. After finishing 220, I like to fine grinding the bevel through 12 micron grit. This helps prevent scratches at the edge in the finer stages of fine grinding and polishing. To fine-grind the bevel, obtain a small piece of sheet metal or brass 2" to 3" square. Tape the sheet to a block of wood the same size, leaving the face of the sheet to a block of wood the same size, leaving the face of the sheet exposed. Start grinding the bevel with 220 grit, rounding if off. When the bevel is round with 220, you can continue to line grind the same way through the finer abrasives, or wait and grind the bevel with smaller abrasives as you use them on the mirror.

Meanwhile, here is a good time to get a very accurate reading of your focal length. The 220 fine-ground and spherical surface, when wet, reflects an image of the Sun that can be accurately focused and measured.

The Fine Side of Fine Grinding

#320 and 30 micro aluminum oxide are about the same size, and they are your next abrasive. From now on, the precautions described in the "Preventing Astigmatism" section must be applied cleanliness is also an important factor. Use the normal precautions, wash up thoroughly so you don't carry grit in your clothes, and keep your work area clean.

I prefer to suspend fine abrasives in water, although sprinkling very small amounts of abrasive on, then smearing it around with your wet hand is acceptable. For suspending abrasives, I use 1 tablespoon of abrasive to 1/2 cup of water. This goes a long way when using a solid tool. More abrasive mixture may be needed with a segmented tool.

In the finer stages, you should grind at a slow, steady pace being very careful not be let the surfaces get dry. If they show a tendency to slick, or if it's hard to push the tool center over center, it's a sign the mirror surface is not spherical. Keep the abrasive stirred and use a shorter stroke for a while to remedy the situation.

If you're grinding with a solid tool, be careful not to let the tool and the mirror stick together. If they do get stuck tight, you must act quickly. Splash water on the exposed mirror, then place a 2x4 on the edge of the tool and hit it hard with another 2x4. Be careful the tool does not fly off and land on the floor. Do not use a hammer. I've seen it done: if you slip, you will break the mirror. If they refuse to separate, soak them in warm water.

Sticking is caused by vacuum between the tool and the mirror. Segmented tools will not stick unless you leave the tool and the mirror together until the water dries off.

Continue to keep track of pits as before. Apply the light test often - it is effective from here on out, so use it. Continue as described through your finest abrasive. The smaller the abrasive gets, the more danger of getting a scratch from the tool, You must be increasingly careful. In these finer stages the light test can be done without a light, because room light will be sufficient. With your eye at the correct angle, you'll see an evenly illuminated mirror surface. A note of caution: With the finest abrasives, rubbing the mirror with your hand will give it an extra shine in that spot and will reflect more light in the light test.

Next: Polishing

When your final abrasive is complete, your mirror is ready to polish. Don't discard the grinding tool or put it to other uses it may be required again if you find that you have astigmatism in the mirror after your first polishing period. Part two of this article will discuss pitch laps, polishing, figuring, testing, and most important for big mirrors, test interpretation.


Is it practical to hand grind a convex parabolic or hyperbolic mirror? - Astronomy

Parabolic Astronomical Telescope Mirrors 1/12 Wave are polished and figured to yield high-level performance. Each mirror is aluminized and hard overcoated with a protective overcoat, ready for placement in the telescope tube. All mirror surfaces are free of any defects which affect performances. Special types of equipment and techniques make the system mirror the least expensive to any other comparable coated mirror. Resolving power and reflective ability is the specialty of the GSO ASTRONOMICAL TELESCOPE MIRROR QUALITY.

GSO offers very HIGH-quality parabolic telescope mirrors for the people who want to build their telescopes or DIY project.

Our parabolic telescope mirror size ranges from 6" to 16", all of these mirrors are made from BK7 quality optical glass and all the mirror surface quality over 1/16 wave RMS at the least, typically better.

All telescope mirrors have an aluminum reflective coating, reflectivity is approximately 93%. The aluminum coating is protected by a properly applied protective coating (SiO2).

Secondary flat mirror 1/12 wave (DIAGONAL) are optically flat yield optimum performances when combined with above astronomical mirrors. Each mirror is aluminized and overcoated.

GSO offers secondary flat telescope mirrors to match the complete telescope set request. Our elliptic flat mirror has the same high optical quality as our parabolic primary mirrors using BK7 quality glass. All of the mirror surface quality over 1/12 wave RMS at the least, typically better.

All mirrors have an aluminum reflective coating of 93%. The aluminum coating is protected by a quartz overcoated to make the layer durable against aging effects


Where can I buy hyperbolic mirrors?

I would like to build a cassegrain–nasmyth telescope.

Could anybody please tell me where can I buy 1 hyperbolic mirror? what would it be the approx price?

I have searched them for several days and found nothing.

The primary ones would be 8''.

Also, I don't want to build the mirror by myself.

Edited by caballerodiez91, 18 July 2019 - 09:47 AM.

#2 steveastrouk

I would like to build a cassegrain–nasmyth telescope.

Could anybody please tell me where can I buy 1 hyperbolic mirror? what would it be the approx price?

I have searched them for several days and found nothing.

The primary ones would be 8''.

You'll need to specify the exact parameters for it to get a quote, but I am sure any of the pro-optics people here can help.

What material are you thinking of ?

#3 gregj888

For a Cassegrain you need a very specific hyperbolic mirror, focal length, conic and to some extent diameter. I don't know of any "off the shelf" hyperbolic mirrors, let alone a selection.

So this is a custom optic. Will likely cost more than a commercial OTA. a lot more if from a professional firm that can send you test data.

My only suggestion would be to take an existing Cass telescope (Orion has an f/12) and use the optics from it. You may need to add a relay lens for a nasmyth, but you'd have too some engineering to determine that.

#4 Mike I. Jones

I don't know your background, so I'll start with the easy question: why "hyperbolic"? (The proper term is actually "hyperboloidal", implying a figure of revolution.) Hyperboloidal primaries are used in coma-free photographic Ritchey-Chretien Cassegrains, Rosin astrographs and other compound systems. And the conic constant (the degree of conic strength) is design-specific, rather than one hyperboloid working for everything.

I'm guessing you mean paraboloidal rather than hyperboloidal.

If you're wanting to do an 8" Nasmyth-Cassegrain, but don't want to do the mirrors yourself, you'll need an optical design for it that states the distance of the tertiary fold flat in front of the primary, and how far you want the focal point to be to the side. Several of us here can easily do the design. Think about what you want and describe it here. There are several optical companies that can make the mirrors and certify their accuracy.

#5 Starman1

Lots of mirror companies sell hyperbolic mirrors.

Every time you see the specs as "0.997 Strehl", it is hyperbole.

Seriously, though, Mike's reply is apropos.

#6 gregj888

For a Classical Cass the paraboloidal primary is easy. The hyperboloidal secondary is generally the hard to make and find optic. Just my assumption.

""0.997 Strehl", it is hyperbole." ya, there are a lot of those mirrors -)

#7 Mike I. Jones

Lots of mirror companies sell hyperbolic mirrors.

Every time you see the specs as "0.997 Strehl", it is hyperbole.

#8 Stephen Kennedy

If you want to make a classic Cassegrain with a concave parabaloidal primary and a convex hyperparaboloidal secondary with a Naysmith focus you should get a copy of the classic book "How to Make a Telescope" by Jean Texereau which is available from Willman-Bell. It devotes several chapters to detailed instructions on how to make such a telescope. It includes how to make the mirrors. The primary can be made with average ATM skills with the only complication being it has to have a hole bored through the center of it. The secondary is very hard to make and test and is a project for an advanced ATMer. Even if you do not make the mirrors yourself, reading the book will give you a sense of why and how you need to be very specific about the conics you want the mirrors to be figured to by whoever makes them.

#9 caballerodiez91

I don't know your background, so I'll start with the easy question: why "hyperbolic"? (The proper term is actually "hyperboloidal", implying a figure of revolution.) Hyperboloidal primaries are used in coma-free photographic Ritchey-Chretien Cassegrains, Rosin astrographs and other compound systems. And the conic constant (the degree of conic strength) is design-specific, rather than one hyperboloid working for everything.

I'm guessing you mean paraboloidal rather than hyperboloidal.

If you're wanting to do an 8" Nasmyth-Cassegrain, but don't want to do the mirrors yourself, you'll need an optical design for it that states the distance of the tertiary fold flat in front of the primary, and how far you want the focal point to be to the side. Several of us here can easily do the design. Think about what you want and describe it here. There are several optical companies that can make the mirrors and certify their accuracy.

Yes, well, I want something like this:

I rather prefer to build a simple cassegrain telescope with 2 eight-inch primary mirrors.


How to make RC mirror?

Reason is because a Ritchey Chretien uses two hyperbolic surfaces and is a complicated optical design. Spacing is critical. A Newtonian is much simpler in optical design and uses only one parabolic surface and a flat secondary mirror. There is actually plenty of information on how to make a Ritchey Chretien. There may be no step-by-step procedures but there is plenty of optical knowledge floating around on the net.

Cassegrain Calculator gives you some idea if you know how to input correctly on what curves and conics to shape your mirror to: http://atm.zaciatok. ain_e_main.html

Also here is an ATMer who made his own RC. As you can tell it is a much more time consuming process for an ATMer to grind an RC mirror set. http://www.trivalley. hnik/rc_10.html

Also a quick search also found this homemade Ritchey Chretien: http://www.alessiopi. ritchey_ing.htm

The information is out there. You just need to search a bit more

#3 DigitalArtist

Reason is because a Ritchey Chretien uses two hyperbolic surfaces and is a complicated optical design. Spacing is critical. A Newtonian is much simpler in optical design and uses only one parabolic surface and a flat secondary mirror. There is actually plenty of information on how to make a Ritchey Chretien. There may be no step-by-step procedures but there is plenty of optical knowledge floating around on the net.

Cassegrain Calculator gives you some idea if you know how to input correctly on what curves and conics to shape your mirror to: http://atm.zaciatok. ain_e_main.html

Also here is an ATMer who made his own RC. As you can tell it is a much more time consuming process for an ATMer to grind an RC mirror set. http://www.trivalley. hnik/rc_10.html

Also a quick search also found this homemade Ritchey Chretien: http://www.alessiopi. ritchey_ing.htm

The information is out there. You just need to search a bit more

Thanks for your prompt reply. I know why it is difficult to make :-(. Yes you are right probably there is no STEP BY STEP instruction out there and that's why I ask the question. I have found some sites about this but none fully describe the process. How to test the mirror, what to do to make the correct shape etc. Do you know any book regarding this?

By the way how GSO is producing RC at such a low cost? As far as I know telescope mirror have to be hand polished to have correct shape. Have they developed any computerized machine?

#4 don clement

By the way how GSO is producing RC at such a low cost?

Doesn't GSO stand for Guan Sheng Optical?

#5 orlyandico

Yes.. it's a Taiwan company. Contrary to popular belief not all Chinese-sounding people are groveling in poverty. The per-capita income of Taiwan is at the level of the less-prosperous Western European countries, and higher than the Eastern European countries (or Russia).

So the question remains.. how does GSO do it, given that cheap labor is out?

#6 don clement

Yes.. it's a Taiwan company. So the question remains.. how does GSO do it, given that cheap labor is out?

Are the mirrors made in Taiwan or mainland China?

#7 DAVIDG

Making the hyberbolic primary uses the same technique as making a fast parabolic primary. The correct is usually about 1.2x more, but that depends on the exact optical configuration your making. I would recommend a combination of Foucault reading and also a null test method such as Ross Null as a double check on each other.
The secondary is a convex hyberbola, so it uses the same techniques used to make a hyberbolic secondary is classic cass. There are a couple of techniques one can use to test them and again I recommend that you use at least two of them as a cross check. One can make a concave hyberbolic test plate and test by interference and one can also use a Hindle sphere for example.
Finally the completed system should be assembled and test as an unit, again use two different test methods, such as double pass autocollimation and the star test. If the system needs a bit bit of fine tuning this usually done on the secondary to remove any residue spherical aberration.
So the techniques used the make a classic cassigrain are used to make a RC.

#8 Norm Meyer

The process of making a RC is the same as making a classical
Cassegrain. Jean Texereau explains how to do that in his book on telescope making. Granted the figures are different
but the process is the same.The same methods of testing and
figuring are the same it's that the RC has stronger curves.
If I were going to make one I would use one of the on-line
calculators to do the math for me and follow the proceedure
that Texereau describes. The primary would be the easiest
of the two mirrors although that wouldn't be a piece of cake. Usually the primary is quite fast F2 or 3. It would be a challenge for the average mirror maker. Then the secondary, I doubt the average TMer could do it.There are
a few out there that could. If you are really interested in
making one I would first make few fast Newts and when you
become accomplished at that then make a few convex spheres.
You could make a two mirror Schief or a Dall-Kirkham for
practise. That's what I would do.
Don is correct on GSO. How they do it is cheap labor for one thing. I have never used a GSO RC so I don't know how well they perform. My gut reaction would be "mediocre". There is a reason others get such a high price for one.
I keep thinking of the chapter title in ATM I "How to Make a
Cassegrain and Why Not To".
If you attempt one good luck to you it'll be a challenge.

#9 Norm Meyer

#10 orlyandico

GSO makes the Astro Tech RCs. And while they are not Paul Jones level, I don't think their users would characterize them as merely mediocre, focuser issues aside.

And I am fairly sure they are made in Taiwan proper, not main land China.

#11 don clement

And I am fairly sure they are made in Taiwan proper, not main land China.

I am fairly sure labor costs are lower if made on the mainland or not.

#12 orlyandico

#13 don clement

However we do see quality optics coming out of Russia. If your metric is bargain basement then.

#14 orlyandico

We also see quality optics coming out of Taiwan, e.g. all Televue optics.

This whole exchange is neither here nor there. The question is, how goes GSO make those RC's at the costs that they do. I personally don't have one, but my impression from the (many) users on this forum is that they are not bargain basement optically.

#15 don clement

We also see quality optics coming out of Taiwan, e.g. all Televue optics.

Not all. My Nagler 13mm was made in Japan.

#16 don clement

This whole exchange is neither here nor there. The question is, how goes GSO make those RC's at the costs that they do.

#17 a__l

#18 don clement

The subject was *how* to make RC optics, not Taiwan vs. China vs. Russia vs. Elbonia.

Yep that was the original question and one consistent with the ATM forum, however the anonymous OP quickly morphed the question into "By the way how GSO is producing RC at such a low cost?" Perhaps the original intent of the anonymous OP?

#19 don clement

Then there is the possibility of producing asphere optics by physically warping the optics, polishing a sphere and then releasing the physical warping to produce the desired asphere. It’s common practice to produce Schmidt correctors, using Schmidt’s original vacuum method. I have seen something similar done using an array of piezoelectric actuators used for warping instead of a vacuum. Also this technique would leave an extremely smooth surface as it was polished to a sphere, which can automatically produce a very smooth surface.

#20 DigitalArtist

The subject was *how* to make RC optics, not Taiwan vs. China vs. Russia vs. Elbonia.

Yep that was the original question and one consistent with the ATM forum, however the anonymous OP quickly morphed the question into "By the way how GSO is producing RC at such a low cost?" Perhaps the original intent of the anonymous OP?


Well, answering that question also shed some light on my first question. Anyway it would be nice if someone share his/her knowledge regarding making a RC mirror,I mean step by step process. Is there any expert reading this thread? Please share your knowledge. You will be blessed.

#21 orlyandico

#22 don clement

Well, answering that question also shed some light on my first question. Anyway it would be nice if someone share his/her knowledge regarding making a RC mirror,I mean step by step process. Is there any expert reading this thread? Please share your knowledge. You will be blessed.

The real experts are probably making RC optics for profit and wouldn't want to share their expertise so as to be "blessed", particularly by potential competitor.

#23 DAVIDG

I've made many optical surfaces, won a couple of awards for some of them, been teaching mirror making for about 30 years now and have consulted for Willmann Bell for a number of their publications on optics and telescope making, the latest being "Telescope, Eyepieces and Astrographs". Not bragging just trying to show that I know a little bit about making optics. The closest your going to find for a step by step method to make RC optics are in references such as the ATM series and Texereau's "How to Make a Telescope". Both have chapters on making classic cassegrains from scratch and 98% of this is exactly what you do to make RC optics. The difference is that the primary needs more corrections but the same methods used to parabolize a fast primary are the same as making a hyberbolic surface.
The only thing that I would do different is use additional test methods such as the Ross Null which wasn't available when these references were written.

#24 Mark Harry

Yes, all well and good Dave
But in making a hyperboloid from a CONCAVE surface as opposed to a CONVEX surface are the same.

One is definitely easier than the other.
M.

#25 DAVIDG

Yes, all well and good Dave
But in making a hyperboloid from a CONCAVE surface as opposed to a CONVEX surface are the same.


One is definitely easier than the other.
M.

Mark,
I agree that the convex hyberbolic surface is more difficult to make then the concave one, but in the case of a classic cassegrain which there have been instructions published on how to make them, it also uses a hyberbolic convex surface on the secondary as well. So the same techniques to grind, polish and test them apply to both making the secondary for a classic cass and also in RC.
The difference between a classic cassegrain and a RC is the fact that the RC uses a concave hyberbolic primary that has conic of greater then 1 but usually less then 1.5 vs a classical cass that uses a parabola with conic of exactly 1.0. Both systems use f-ratios or around f/3 to f/5 so again the techniques used to make the parabolic primary in the classic cass. are the same as to make the hyberbolic one in the RC system. One needs uses the same figuring and testing methods used to make the hyberbolic surface as you did in making a parabolic one.
Once you calculate the conic of the hyberbolic surface you can use that to calculate the knife edge readings and/or the spacing needed to set up the Ross Null lens. You can also use the Ross Null setup to make a concave hyberbolic test plate to use to test the convex surface of the secondary by interference just like testing a flat. As you know when the fringes are straight the two surface match and you now have the hyberbolic surface on the convex secondary.
So what I'm trying to point out is that the two systems,ie a Classic Cass with the parabolic primary and hyberbolic secondary are similar enough to an RC were both mirrors are hyberbolic that the instructions published in the literature will get you 98% of the way there.


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

08 Saturday Sep 2018

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:

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:

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?


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

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:

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:

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?


Parabolic or Spherical Mirror?

A: A Parabolic mirror is the ideal shape. See applet below.

#4 Joe Aguiar

#5 SpooPoker

Manufacturers typically supply parabolic mirrors for all Newtonians >= 6" unless the focal ratio of the smaller scope was below 8 (i.e. 114mm f/5).

Spherical mirrors usually pop up on smaller aperture Newtonians sold on the cheap - i.e. the many 4.5" f/8 incarnations out there.

The Spherical mirror does not have a true optical axis, but if we drew a line from the center of the mirror, we would notice that light rays are not all focussed to one point, rather the light will focus at different points. This is called spherical aberration and its effect may be significant for smaller focal ratio's (< f/7), distracting for medium focal ratio's (f/8 - f/9) and negligible for longer focal ratios. A Parabolic mirror does not have this particular problem although off axis aberrations will be its bugbear (albeit these are correctable with specially designed lenses that slip into the focusser).

A spherical mirror, in principle, should work within the diffraction limit of a 4.5" f/8 scope and thus be acceptable. However, in my experience, once one throws in other manufacturing errors / optical imprecision's, I have rarely found a spherical mirror primary Newtonian to work as well as its parabolic counterpart. Case in point, a C4.5 f/7.9 Vixen with parabolic mirror usually outperforms the typical 4.5" f/8 Newtonian with spherical mirror. I noticed this most on Venus during a thin crescent phase (5% illumination). The spherical mirror made Venus look 30% lit while the parabolic, Venus looked as it should have.

#6 BigC

Very little at high focal ratiosnote Herschell's 6" was about an f14 so the view is still diffraction limited.

Spherical surfaces are easier to make.

Using parabolic mirrors allows scopes to be more managable in physical length.

Probably the only Newtonian reflectors you should consider buying are ones with parabolic mirrors ,with the exceptions of the small 76mmF9 and 114F8.

#7 stargazer193857

A spherical mirror is very inexpensive to make, and can be done by machine. A parabolic mirror is polished from a similar sized sphere and is done by hand. Asymmetrical errors to its form can happen if not done right, and getting it right costs more money. I like my spherical mirror because I know that even if the manufacturer was incompetent, it is pretty hard to mess up a spherical mirror.

If the f# is at least 8, and the aperture 4.5" or less, you can probably get away with a spherical mirror and save money.

Like SpooPoker said, most large mirrors come parabolic standard. If they did not, you would see a fuzzy image at all but the lowest powers.

Binoculars have spherical surfaces. So do most eyepieces. Stars do get a little fuzzy towards the edge of the view, but this is not noticeable in my peripheral vision.

If you want larger aperture to see fainter stuff, you need to pay $$ for a parabolic mirror. By $$, I mean at least $300. Or you can get a small table top for $200. Low f# scopes require more accurate collimation, though. A parabola has an axis, whereas a sphere does not.

If you are happy with 4.5" and f8, you can get a good OTA on a cheap AZ mount for $70 shipped. It is called the Celestron Powerseeker.

#8 Jon Isaacs

What's the difference between a parabolic or spherical mirror in a reflector telescope? Which one is better?

As has been said, for a Newtonian, a parabolic mirror is the right shape and on axis, all the light is focused to a point. Your 4.5 inch F/4 Starblast definitely has a parabolic mirror.

Mirrors are ground to a sphere and then corrected to a parabola, it's a very small correction and with small, slower mirrors, the difference is small enough it can be ignored without out major consequences. With larger and faster scopes, a parabola is definitely a necessity. One hears of a scope being "over corrected" or "under corrected", that simply means that too much or too little correction from a sphere.

Most other common designs, refractors, SCTs and MAKs, are based on spherical optics. The SCTs and MAKs correct the spherical aberration/errors with corrector plates..

#9 BigC

#10 Geo31

A: A Parabolic mirror is the ideal shape.

#11 jrcrilly

A: A Parabolic mirror is the ideal shape.


Nor for anything else other than a Newtonian or a Classical Cassegrain.

#12 Geo31

A: A Parabolic mirror is the ideal shape.


Nor for anything else other than a Newtonian or a Classical Cassegrain.

#13 stargazer193857

Most other common designs, refractors, SCTs and MAKs, are based on spherical optics. The SCTs and MAKs correct the spherical aberration/errors with corrector plates..

#14 David Knisely

Manufacturers typically supply parabolic mirrors for all Newtonians >= 6" unless the focal ratio of the smaller scope was below 8 (i.e. 114mm f/5).

Spherical mirrors usually pop up on smaller aperture Newtonians sold on the cheap - i.e. the many 4.5" f/8 incarnations out there.

The Spherical mirror does not have a true optical axis, but if we drew a line from the center of the mirror, we would notice that light rays are not all focused to one point, rather the light will focus at different points. This is called spherical aberration and its effect may be significant for smaller focal ratio's (< f/7), distracting for medium focal ratio's (f/8 - f/9) and negligible for longer focal ratios. A Parabolic mirror does not have this particular problem although off axis aberrations will be its bugbear (albeit these are correctable with specially designed lenses that slip into the focuser).

A spherical mirror, in principle, should work within the diffraction limit of a 4.5" f/8 scope and thus be acceptable. However, in my experience, once one throws in other manufacturing errors / optical imprecision's, I have rarely found a spherical mirror primary Newtonian to work as well as its parabolic counterpart. Case in point, a C4.5 f/7.9 Vixen with parabolic mirror usually outperforms the typical 4.5" f/8 Newtonian with spherical mirror. I noticed this most on Venus during a thin crescent phase (5% illumination). The spherical mirror made Venus look 30% lit while the parabolic, Venus looked as it should have.

Actually, a spherical telescope mirror does have an optic axis. It runs along the radius of curvature of the mirror and intersects the mirror's center. Unfortunately, for light from infinity, the spherical mirror does not have a mathematically precise focal point. However, there is a point where for relatively small mirrors with a long enough f/ratio, a spherical mirror can be used instead of a paraboloidal one.

One way to rate telescope mirrors is by seeing how much their surfaces deviate from a perfect parabolic shape. One common rule of thumb states that the telescope's optics must not produce a wavefront error of more than 1/4 wave in order to prevent optical degradation. This requirement is sometimes extended somewhat to require that the mirror's surface must not deviate from a "perfect" paraboloidal surface by more than an eighth wave (approximately 2.71 millionths of an inch) in order for the mirror to be considered for astronomical use. By comparing the sagital depths of a sphere and a parabola of equal focal length, it can be seen that the difference between the two often exceeds the rule of thumb by quite a margin for short and moderate f/ratios. A spherical surface can be "fudged" into deviating less strongly from a parbolic shape by extending the focal length very slightly, such that its surface would "touch" a similar parabolic mirror's surface at its center and at its outside edges. This minimizes the surface difference between the two. Such spherical mirrors must have a minimum f/ratio in order to achieve this. According to Texereau (HOW TO MAKE A TELESCOPE, p.19) the formula is 88.6D**4 = f**3 (** means to the power of: ie: 2**3 = "two cubed" = 8), where f is the focal length and D is the aperture (in inches). Substituting F=f/D to get the f/ratio, we get: F = cube-root (88.6*D). The following minimums can just achieve the 1/8th wave surface rule of thumb:

APERTURE . . TEXEREAU MINIMUM F/RATIO
3 inch . . . . . . f/6.4
4 inch . . . . . . f/7.1
6 inch . . . . . . f/8.1
8 inch . . . . . . f/8.9
10 inch. . . . . . f/9.6
12 inch. . . . . . f/10.2

The above f/ratios might be fairly usable for an astronomical telescope's spherical primary mirror, as they do just barely satisfy the 1/4 wave "Rayleigh Limit" for wavefront error. However, amateurs looking for the best in high-power contrast and detail in telescopic images (especially those doing planetary observations) might be a little disappointed in the performance of spherical mirrors with the above f/ratios. Practical experience has shown that at high power, the images produced by spherical mirrors of the above f/ratios or less tend to lack a little of the image quality present in telescopes equipped with parabolic mirrors of the same f/ratios.

In reality, it is more important to consider what happens at the focus of telescope, rather than just how close the surface is to a parabolic shape. In general, spherical mirrors do not focus light from a star to a point. Their curves and slopes are not similar enough to a paraboloid to focus the light properly at short and moderate f/ratios. This effect is known as "Spherical Aberration" and causes the light to only roughly converge into what is known as "the Circle of Least Confusion", (see: ASTRONOMICAL OPTICS, by Daniel J. Schroeder, c. 1987, Academic Press, p.48-49). This "circle" is a blur the size of about (D**3)/(32R**3), where D is the diameter of the mirror and R is its radius of curvature. The larger the radius of curvature is, the smaller the circle of least confusion is. If the circle of least confusion is a good deal larger than the diffraction disk of a perfect imaging system of that aperture, the image may tend to look a little woolly, with slightly reduced high power contrast and detail. For example, for the Texereau use of a 6 inch f/8.1 spherical mirror, the circle of least confusion is nearly *1.7 times* the size of the diffraction disk produced by a perfect 6 inch aperture optical system.

For most spherical mirrors focusing light from infinity, the focal length is about half the mirror's radius of curvature. Thus, to improve the image, we can use f/ratios longer than Texereau's limits to reduce the size of the circle of least confusion to a point where it is equal to the size of a parabolic mirror's diffraction disk (one definition of "Diffraction-limited" optics). NOTE: the term "Diffraction-limited" has a variety of interpretations, such as the Marechal 1/14 wave RMS wavefront deviation, as well as the more commonly referred to 1/4 wave P-V "Rayleigh Limit". If we set the angle the confusion circle subtends at a point at the center of the mirror's surface equal to the resolution limit of the aperture of a "perfect" paraboloidal mirror (which is 1.22(Lambda)/D, where Lambda is the wavelength of light), we can come to a formula for the minimum f/ratio needed for a sphere to produce a more "diffraction-pattern limited" image. That relation is:

D = .00854(F**3) (for D in centimeters and F is the f/ratio), and for English units: D = .00336(F**3).

Thus, the minimum f/ratio goes as the cube root of the mirror diameter, or the "Diffraction Pattern-Limited" F/RATIO: F = 6.675(D**(1/3)).

For example, the typical "department store" 3 inch Newtonian frequently uses a spherical f/10 mirror, and should give reasonably good images as long as the figure is smooth and the secondary mirror isn't terribly big. For common apertures, the following approximate minimum f/ratios for Diffraction-pattern limited Newtonians using spherical primary mirrors can be found below:

APERTURE . . . F/RATIO FOR DIFF. PATTERN-LIMITED SPHERICAL MIRRORS
-----------------------------------------------------------------------------
3 inches . . . . . . f/9.6 (28.8 inch focal length)
4 inches . . . . . . f/10.6 (42.4 inch focal length)
6 inches . . . . . . f/12.1 (72.6 inch focal length)
8 inches . . . . . . f/13.4 (107.2 inch focal length)
10 inches. . . . . . f/14.4 (144 inch focal length)
12 inches. . . . . . f/15.3 (183.6 inch focal length)

Using f/ratios fairly close to those above for spherical mirrors in Newtonian telescopes should yield very good low and high power images. However, spherical mirrors with f/ratios significantly smaller than those listed above or given by our second formula can yield high power views which may be a bit lacking in sharpness, contrast, and detail. Indeed, a few commercial telescope manufacturers routinely use spherical mirrors at f/ratios even shorter than those given by Texereau, and these products should be avoided. An eight inch Newtonian using an f/13.4 spherical mirror could produce good images, but would also have a tube length of nearly 9 feet, making it harder to mount, use, store, and keep collimated. Thus, using spherical mirrors for diffraction pattern-limited Newtonians with the above f/ratios for apertures above 6 inches is probably somewhat impractical. The old argument about eyepieces performing better with long-focal length telescopes has been all but negated by the recent improvements in eyepiece design. Those who are grinding their own mirrors might wish to make spherical mirrors with f/ratios between the Texereau values and the fully diffraction pattern-limited numbers, as these could still yield fairly good performance without the need for parabolizing. In the long run, it is probably better to use a well-figured (1/8th wave wavefront error or less) parabolic primary mirror for moderate focal ratios and a small secondary mirror (obstructing 20 percent or less of the primary mirror diameter) rather than using a spherical mirror in moderate to large-sized Newtonians designed for planetary viewing.


Thursday, 13 March 2014

Galaxy - Distribution of Stars in Milky Way and globular cluster analogy

Particles in a gas approximate to point-like objects that interact roughly elastically through short-range forces when they collide, but are otherwise non-interacting.

Stars interact gravitationally over long ranges, occasionally with each other, but always with the overall gravitational potential of the system.

Sometimes people do talk thermodynamically about star clusters. You can discuss the "temperature" of stars when you are referring to the velocity dispersion in a cluster. The concept of heating or cooling a cluster also has some merit.

Gravity - Where does Jupiter's gravitational force come from? Why don't Jupiters gasses fly away?

You are confusing the "mass" with "solid". All matter has mass, and all mass produces a gravitational field. That includes gasses, liquids and plasmas.

Although gasses are much less dense than solids, gasses also have mass, and if you have enough gas it will have a measurable gravitational field.

Jupiter is big, it is composed of lots of Hydrogen and Helium (and some other gasses), and deep within the planet, the gasses are compressed into strange states. There may even be a rocky core, but it is under such extreme pressure that it is not much like "rock" as we understand it. But it is not necessary for a planet to have a solid core to produce a gravitational field, because all matter has mass not just solid matter.


Contents

Prehistory Edit

The first mirrors used by humans were most likely pools of dark, still water, or water collected in a primitive vessel of some sort. The requirements for making a good mirror are a surface with a very high degree of flatness (preferably but not necessarily with high reflectivity), and a surface roughness smaller than the wavelength of the light.

The earliest manufactured mirrors were pieces of polished stone such as obsidian, a naturally occurring volcanic glass. [4] Examples of obsidian mirrors found in Anatolia (modern-day Turkey) have been dated to around 6000 BC. [5] Mirrors of polished copper were crafted in Mesopotamia from 4000 BC, [5] and in ancient Egypt from around 3000 BC. [6] Polished stone mirrors from Central and South America date from around 2000 BC onwards. [5]

Bronze Age to Early Middle Ages Edit

By the Bronze Age most cultures were using mirrors made from polished discs of bronze, copper, silver, or other metals. [4] [7] The people of Kerma in Nubia were skilled in the manufacturing of mirrors. Remains of their bronze kilns have been found within the temple of Kerma. [8] In China, bronze mirrors were manufactured from around 2000 BC, [9] [ citation needed ] some of the earliest bronze and copper examples being produced by the Qijia culture. Such metal mirrors remained the norm through to Greco-Roman Antiquity and throughout the Middle Ages in Europe. [10] During the Roman Empire silver mirrors were in wide use even by maidservants. [11]

Speculum metal is a highly reflective alloy of copper and tin that was used for mirrors until a couple of centuries ago. Such mirrors may have originated in China and India. [12] Mirrors of speculum metal or any precious metal were hard to produce and were only owned by the wealthy. [13]

Common metal mirrors tarnished and required frequent polishing. Bronze mirrors had low reflectivity and poor color rendering, and stone mirrors were much worse in this regard. [14] : p.11 These defects explain the New Testament reference in 1 Corinthians 13 to seeing "as in a mirror, darkly."

The Greek philosopher Socrates, of "know thyself" fame, urged young people to look at themselves in mirrors so that, if they were beautiful, they would become worthy of their beauty, and if they were ugly, they would know how to hide their disgrace through learning. [14] : p.106

Glass began to be used for mirrors in the 1st century CE, with the development of soda-lime glass and glass blowing. [15] The Roman scholar Pliny the Elder claims that artisans in Sidon (modern-day Lebanon) were producing glass mirrors coated with lead or gold leaf in the back. The metal provided good reflectivity, and the glass provided a smooth surface and protected the metal from scratches and tarnishing. [16] [17] [18] [14] : p.12 [19] However, there is no archeological evidence of glass mirrors before the third century. [20]

These early glass mirrors were made by blowing a glass bubble, and then cutting off a small circular section from 10 to 20 cm in diameter. Their surface was either concave or convex, and imperfections tended to distort the image. Lead-coated mirrors were very thin to prevent cracking by the heat of the molten metal. [14] : p.10 Due to their poor quality, high cost, and small size, solid-metal mirrors, primarily of steel, remained in common use until the late nineteenth century. [14] : p.13

Silver-coated metal mirrors were developed in China as early as 500 CE. The bare metal was coated with an amalgam, then heated it until the mercury boiled away. [21]

Middle Ages and Renaissance Edit

The evolution of glass mirrors in the Middle Ages followed improvements in glassmaking technology. Glassmakers in France made flat glass plates by blowing glass bubbles, spinning them rapidly to flatten them, and cutting rectangles out of them. A better method, developed in Germany and perfected in Venice by the 16th century, was to blow a cylinder of glass, cut off the ends, slice it along its length, and unroll it onto a flat hot plate. [14] : p.11 Venetian glassmakers also adopted lead glass for mirrors, because of its crystal-clarity and its easier workability. By the 11th century, glass mirrors were being produced in Moorish Spain. [22]

During the early European Renaissance, a fire-gilding technique developed to produce an even and highly reflective tin coating for glass mirrors. The back of the glass was coated with a tin-mercury amalgam, and the mercury was then evaporated by heating the piece. This process caused less thermal shock to the glass than the older molten-lead method. [14] : p.16 The date and location of the discovery is unknown, but by the 16th century Venice was a center of mirror production using this technique. These Venetian mirrors were up to 40 inches (100 cm) square.

For a century, Venice retained the monopoly of the tin amalgam technique. Venetian mirrors in richly decorated frames served as luxury decorations for palaces throughout Europe, and were very expensive. For example, in the late seventeenth century, the Countess de Fiesque was reported to have traded an entire wheat farm for a mirror, considering it a bargain. [23] However, by the end of that century the secret was leaked through to industrial espionage. French workshops succeeded in large-scale industrialization of the process, eventually making mirrors affordable to the masses, in spite of the toxicity of mercury's vapor. [24]

Industrial Revolution Edit

The invention of the ribbon machine in the late Industrial Revolution allowed modern glass panes to be produced in bulk. [14] The Saint-Gobain factory, founded by royal initiative in France, was an important manufacturer, and Bohemian and German glass, often rather cheaper, was also important.

The invention of the silvered-glass mirror is credited to German chemist Justus von Liebig in 1835. [25] His wet deposition process involved the deposition of a thin layer of metallic silver onto glass through the chemical reduction of silver nitrate. This silvering process was adapted for mass manufacturing and led to the greater availability of affordable mirrors.

Contemporary technologies Edit

Currently mirrors are often produced by the wet deposition of silver, or sometimes nickel or chromium (the latter used most often in automotive mirrors) via electroplating directly onto the glass substrate. [26]

Glass mirrors for optical instruments are usually produced by vacuum deposition methods. These techniques can be traced to observations in the 1920s and 1930s that metal was being ejected from electrodes in gas discharge lamps and condensed on the glass walls forming a mirror-like coating. The phenomenon, called sputtering, was developed into an industrial metal-coating method with the development of semiconductor technology in the 1970s.

A similar phenomenon had been observed with incandescent light bulbs: the metal in the hot filament would slowly sublimate and condense on the bulb's walls. This phenomenon was developed into the method of evaporation coating by Pohl and Pringsheim in 1912. John D. Strong used evaporation coating to make the first aluminum-coated telescope mirrors in the 1930s. [27] The first dielectric mirror was created in 1937 by Auwarter using evaporated rhodium. [15]

The metal coating of glass mirrors is usually protected from abrasion and corrosion by a layer of paint applied over it. Mirrors for optical instruments often have the metal layer on the front face, so that the light does not have to cross the glass twice. In these mirrors, the metal may be protected by a thin transparent coating of a non-metallic (dielectric) material. The first metallic mirror to be enhanced with a dielectric coating of silicon dioxide was created by Hass in 1937. In 1939 at the Schott Glass company, Walter Geffcken invented the first dielectric mirrors to use multilayer coatings. [15]

Burning mirrors Edit

The Greek in Classical Antiquity were familiar with the use of mirrors to concentrate light. Parabolic mirrors were described and studied by the mathematician Diocles in his work On Burning Mirrors. [28] Ptolemy conducted a number of experiments with curved polished iron mirrors, [2] : p.64 and discussed plane, convex spherical, and concave spherical mirrors in his Optics. [29]

Parabolic mirrors were also described by the Caliphate mathematician Ibn Sahl in the tenth century. [30] The scholar Ibn al-Haytham discussed concave and convex mirrors in both cylindrical and spherical geometries, [31] carried out a number of experiments with mirrors, and solved the problem of finding the point on a convex mirror at which a ray coming from one point is reflected to another point. [32]

Mirrors can be classified in many ways including by shape, support and reflective materials, manufacturing methods, and intended application.

By shape Edit

Typical mirror shapes are planar, convex, and concave.

The surface of curved mirrors is often a part of a sphere. Mirrors that are meant to precisely concentrate parallel rays of light into a point are usually made in the shape of a paraboloid of revolution instead they are used in telescopes (from radio waves to X-rays), in antennas to communicate with broadcast satellites, and in solar furnaces. A segmented mirror, consisting of multiple flat or curved mirrors, properly placed and oriented, may be used instead.

Mirrors that are intended to concentrate sunlight onto a long pipe may be a circular cylinder or of a parabolic cylinder. [ citation needed ]

By structural material Edit

The most common structural material for mirrors is glass, due to its transparency, ease of fabrication, rigidity, hardness, and ability to take a smooth finish.

Back-silvered mirrors Edit

The most common mirrors consist of a plate of transparent glass, with a thin reflective layer on the back (the side opposite to the incident and reflected light) backed by a coating that protects that layer against abrasion, tarnishing, and corrosion. The glass is usually soda-lime glass, but lead glass may be used for decorative effects, and other transparent materials may be used for specific applications. [ citation needed ]

A plate of transparent plastic may be used instead of glass, for lighter weight or impact resistance. Alternatively, a flexible transparent plastic film may be bonded to the front and/or back surface of the mirror, to prevent injuries in case the mirror is broken. Lettering or decorative designs may be printed on the front face of the glass, or formed on the reflective layer. The front surface may have an anti-reflection coating. [ citation needed ]

Front-silvered mirrors Edit

Mirrors which are reflective on the front surface (the same side of the incident and reflected light) may be made of any rigid material. [33] The supporting material does not necessarily need to be transparent, but telescope mirrors often use glass anyway. Often a protective transparent coating is added on top of the reflecting layer, to protect it against abrasion, tarnishing, and corrosion, or to absorb certain wavelengths. [ citation needed ]

Flexible mirrors Edit

Thin flexible plastic mirrors are sometimes used for safety, since they cannot shatter or produce sharp flakes. Their flatness is achieved by stretching them on a rigid frame. These usually consist of a layer of evaporated aluminum between two thin layers of transparent plastic. [ citation needed ]

By reflective material Edit

In common mirrors, the reflective layer is usually some metal like silver, tin, nickel, or chromium, deposited by a wet process or aluminum, [26] [34] deposited by sputtering or evaporation in vacuum. The reflective layer may also be made of one or more layers of transparent materials with suitable indices of refraction.

The structural material may be a metal, in which case the reflecting layer may be just the surface of the same. Metal concave dishes are often used to reflect infrared light (such as in space heaters) or microwaves (as in satellite TV antennas). Liquid metal telescopes use a surface of liquid metal such as mercury.

Mirrors that reflect only part of the light, while transmitting some of the rest, can be made with very thin metal layers or suitable combinations of dielectric layers. They are typically used as beamsplitters. A dichroic mirror, in particular, has surface that reflects certain wavelengths of light, while letting other wavelengths pass through. A cold mirror is a dichroic mirror that efficiently reflects the entire visible light spectrum while transmitting infrared wavelengths. A hot mirror is the opposite: it reflects infrared light while transmitting visible light. Dichroic mirrors are often used as filters to remove undesired components of the light in cameras and measuring instruments.

In X-ray telescopes, the X-rays reflect off a highly precise metal surface at almost grazing angles, and only a small fraction of the rays are reflected. [35] In flying relativistic mirrors conceived for X-ray lasers, the reflecting surface is a spherical shockwave (wake wave) created in a low-density plasma by a very intense laser-pulse, and moving at an extremely high velocity. [36]

Nonlinear optical mirrors Edit

A phase-conjugating mirror uses nonlinear optics to reverse the phase difference between incident beams. Such mirrors may be used, for example, for coherent beam combination. The useful applications are self-guiding of laser beams and correction of atmospheric distortions in imaging systems. [37] [38] [39]

This property can be explained by the physics of an electromagnetic plane wave that is incident to a flat surface that is electrically conductive or where the speed of light changes abruptly, as between two materials with different indices of refraction.

  • When parallel beams of light are reflected on a plane surface, the reflected rays will be parallel too.
  • If the reflecting surface is concave, the reflected beams will be convergent, at least to some extent and for some distance from the surface.
  • A convex mirror, on the other hand, will reflect parallel rays towards divergent directions.

More specifically, a concave parabolic mirror (whose surface is a part of a paraboloid of revolution) will reflect rays that are parallel to its axis into rays that pass through its focus. Conversely, a parabolic concave mirror will reflect any ray that comes from its focus towards a direction parallel to its axis. If a concave mirror surface is a part of a prolate ellipsoid, it will reflect any ray coming from one focus toward the other focus. [40]

A convex parabolic mirror, on the other hand, will reflect rays that are parallel to its axis into rays that seem to emanate from the focus of the surface, behind the mirror. Conversely, it will reflect incoming rays that converge toward that point into rays that are parallel to the axis. A convex mirror that is part of a prolate ellipsoid will reflect rays that converge towards one focus into divergent rays that seem to emanate from the other focus. [40]

Spherical mirrors do not reflect parallel rays to rays that converge to or diverge from a single point, or vice versa, due to spherical aberration. However, a spherical mirror whose diameter is sufficiently small compared to the sphere's radius will behave very similarly to a parabolic mirror whose axis goes through the mirror's center and the center of that sphere so that spherical mirrors can substitute for parabolic ones in many applications. [40]

A similar aberration occurs with parabolic mirrors when the incident rays are parallel among themselves but not parallel to the mirror's axis, or are divergent from a point that is not the focus – as when trying to form an image of an objet that is near the mirror or spans a wide angle as seen from it. However, this aberration can be sufficiently small if the object image is sufficiently far from the mirror and spans a sufficiently small angle around its axis. [40]

Mirror images Edit

Mirrors reflect an image to the observer. However, unlike a projected image on a screen, an image does not actually exist on the surface of the mirror. For example, when two people look at each other in a mirror, both see different images on the same surface. When the light waves converge through the lens of the eye they interfere with each other to form the image on the surface of the retina, and since both viewers see waves coming from different directions, each sees a different image in the same mirror. Thus, the images observed in a mirror depends upon the angle of the mirror with respect to the eye. The angle between the object and the observer is always twice the angle between the eye and the normal, or the direction perpendicular to the surface. This allows animals with binocular vision to see the reflected image with depth perception and in three dimensions.

The mirror forms a virtual image of whatever is in the opposite angle from the viewer, meaning that objects in the image appear to exist in a direct line of sight—behind the surface of the mirror—at an equal distance from their position in front of the mirror. Objects behind the observer, or between the observer and the mirror, are reflected back to the observer without any actual change in orientation the light waves are simply reversed in a direction perpendicular to the mirror. However, when viewer is facing the object and the mirror is at an angle between them, the image appears inverted 180° along the direction of the angle. [41]

Objects viewed in a (plane) mirror will appear laterally inverted (e.g., if one raises one's right hand, the image's left hand will appear to go up in the mirror), but not vertically inverted (in the image a person's head still appears above their body). [42] However, a mirror does not usually "swap" left and right any more than it swaps top and bottom. A mirror typically reverses the forward-backward axis. To be precise, it reverses the object in the direction perpendicular to the mirror surface (the normal). Because left and right are defined relative to front-back and top-bottom, the "flipping" of front and back results in the perception of a left-right reversal in the image. (i.e.: When a person raises their left hand, the actual left hand raises in the mirror, but gives the illusion of a right hand raising because the image appears to be facing them. If they stand side-on to a mirror, the mirror really does reverse left and right, that is, objects that are physically closer to the mirror always appear closer in the virtual image, and objects farther from the surface always appear symmetrically farther away regardless of angle.)

Looking at an image of oneself with the front-back axis flipped results in the perception of an image with its left-right axis flipped. When reflected in the mirror, a person's right hand remains directly opposite their real right hand, but it is perceived by the mind as the left hand in the image. When a person looks into a mirror, the image is actually front-back reversed, which is an effect similar to the hollow-mask illusion. Notice that a mirror image is fundamentally different from the object and cannot be reproduced by simply rotating the object.

For things that may be considered as two-dimensional objects (like text), front-back reversal cannot usually explain the observed reversal. An image is a two-dimensional representation of a three-dimensional space, and because it exists in a two-dimensional plane, an image can be viewed from front or back. In the same way that text on a piece of paper appears reversed if held up to a light and viewed from behind, text held facing a mirror will appear reversed, because the image of the text is still facing away from the observer. Another way to understand the reversals observed in images of objects that are effectively two-dimensional is that the inversion of left and right in a mirror is due to the way human beings perceive their surroundings. A person's reflection in a mirror appears to be a real person facing them, but for that person to really face themselves (i.e.: twins) one would have to physically turn and face the other, causing an actual swapping of right and left. A mirror causes an illusion of left-right reversal because left and right were not swapped when the image appears to have turned around to face the viewer. The viewer's egocentric navigation (left and right with respect to the observer's point of view i.e.: "my left. ") is unconsciously replaced with their allocentric navigation (left and right as it relates another's point of view ". your right") when processing the virtual image of the apparent person behind the mirror. Likewise, text viewed in a mirror would have to be physically turned around, facing the observer and away from the surface, actually swapping left and right, to be read in the mirror. [41]

Reflectivity Edit

The reflectivity of a mirror is determined by the percentage of reflected light per the total of the incident light. The reflectivity may vary with wavelength. All or a portion of the light not reflected is absorbed by the mirror, while in some cases a portion may also transmit through. Although some small portion of the light will be absorbed by the coating, the reflectivity is usually higher for first-surface mirrors, eliminating both reflection and absorption losses from the substrate. The reflectivity is often determined by the type and thickness of the coating. When the thickness of the coating is sufficient to prevent transmission, all of the losses occur due to absorption. Aluminum is harder, less expensive, and more resistant to tarnishing than silver, and will reflect 85 to 90% of the light in the visible to near-ultraviolet range, but experiences a drop in its reflectance between 800 and 900 nm. Gold is very soft and easily scratched, costly, yet does not tarnish. Gold is greater than 96% reflective to near and far-infrared light between 800 and 12000 nm, but poorly reflects visible light with wavelengths shorter than 600 nm (yellow). Silver is expensive, soft, and quickly tarnishes, but has the highest reflectivity in the visual to near-infrared of any metal. Silver can reflect up to 98 or 99% of light to wavelengths as long as 2000 nm, but loses nearly all reflectivity at wavelengths shorter than 350 nm. Dielectric mirrors can reflect greater than 99.99% of light, but only for a narrow range of wavelengths, ranging from a bandwidth of only 10 nm to as wide as 100 nm for tunable lasers. However, dielectric coatings can also enhance the reflectivity of metallic coatings and protect them from scratching or tarnishing. Dielectric materials are typically very hard and relatively cheap, however the number of coats needed generally makes it an expensive process. In mirrors with low tolerances, the coating thickness may be reduced to save cost, and simply covered with paint to absorb transmission. [43]

Surface quality Edit

Surface quality, or surface accuracy, measures the deviations from a perfect, ideal surface shape. Increasing the surface quality reduces distortion, artifacts, and aberration in images, and helps increase coherence, collimation, and reduce unwanted divergence in beams. For plane mirrors, this is often described in terms of flatness, while other surface shapes are compared to an ideal shape. The surface quality is typically measured with items like interferometers or optical flats, and are usually measured in wavelengths of light (λ). These deviations can be much larger or much smaller than the surface roughness. A normal household-mirror made with float glass may have flatness tolerances as low as 9–14λ per inch (25.4 mm), equating to a deviation of 5600 through 8800 nanometers from perfect flatness. Precision ground and polished mirrors intended for lasers or telescopes may have tolerances as high as λ/50 (1/50 of the wavelength of the light, or around 12 nm) across the entire surface. [44] [43] The surface quality can be affected by factors such as temperature changes, internal stress in the substrate, or even bending effects that occur when combining materials with different coefficients of thermal expansion, similar to a bimetallic strip. [45]

Surface roughness Edit

Surface roughness describes the texture of the surface, often in terms of the depth of the microscopic scratches left by the polishing operations. Surface roughness determines how much of the reflection is specular and how much diffuses, controlling how sharp or blurry the image will be.

For perfectly specular reflection, the surface roughness must be kept smaller than the wavelength of the light. Microwaves, which sometimes have a wavelength greater than an inch (

25 mm) can reflect specularly off a metal screen-door, continental ice-sheets, or desert sand, while visible light, having wavelengths of only a few hundred nanometers (a few hundred-thousandths of an inch), must meet a very smooth surface to produce specular reflection. For wavelengths that are approaching or are even shorter than the diameter of the atoms, such as X-rays, specular reflection can only be produced by surfaces that are at a grazing incidence from the rays.

Surface roughness is typically measured in microns, wavelength, or grit size, with

Transmissivity Edit

Transmissivity is determined by the percentage of light transmitted per the incident light. Transmissivity is usually the same from both first and second surfaces. The combined transmitted and reflected light, subtracted from the incident light, measures the amount absorbed by both the coating and substrate. For transmissive mirrors, such as one-way mirrors, beam splitters, or laser output couplers, the transmissivity of the mirror is an important consideration. The transmissivity of metallic coatings are often determined by their thickness. For precision beam-splitters or output couplers, the thickness of the coating must be kept at very high tolerances to transmit the proper amount of light. For dielectric mirrors, the thickness of the coat must always be kept to high tolerances, but it is often more the number of individual coats that determine the transmissivity. For the substrate, the material used must also have good transmissivity to the chosen wavelengths. Glass is a suitable substrate for most visible-light applications, but other substrates such as zinc selenide or synthetic sapphire may be used for infrared or ultraviolet wavelengths. [48] : p.104–108

Wedge Edit

Wedge errors are caused by the deviation of the surfaces from perfect parallelism. An optical wedge is the angle formed between two plane-surfaces (or between the principle planes of curved surfaces) due to manufacturing errors or limitations, causing one edge of the mirror to be slightly thicker than the other. Nearly all mirrors and optics with parallel faces have some slight degree of wedge, which is usually measured in seconds or minutes of arc. For first-surface mirrors, wedges can introduce alignment deviations in mounting hardware. For second-surface or transmissive mirrors, wedges can have a prismatic effect on the light, deviating its trajectory or, to a very slight degree, its color, causing chromatic and other forms of aberration. In some instances, a slight wedge is desirable, such as in certain laser systems where stray reflections from the uncoated surface are better dispersed than reflected back through the medium. [43] [49]

Surface defects Edit

Surface defects are small-scale, discontinuous imperfections in the surface smoothness. Surface defects are larger (in some cases much larger) than the surface roughness, but only affect small, localized portions of the entire surface. These are typically found as scratches, digs, pits (often from bubbles in the glass), sleeks (scratches from prior, larger grit polishing operations that were not fully removed by subsequent polishing grits), edge chips, or blemishes in the coating. These defects are often an unavoidable side-effect of manufacturing limitations, both in cost and machine precision. If kept low enough, in most applications these defects will rarely have any adverse effect, unless the surface is located at an image plane where they will show up directly. For applications that require extremely low scattering of light, extremely high reflectance, or low absorption due to high energy-levels that could destroy the mirror, such as lasers or Fabry-Perot interferometers, the surface defects must be kept to a minimum. [50]

Mirrors are usually manufactured by either polishing a naturally reflective material, such as speculum metal, or by applying a reflective coating to a suitable polished substrate. [51]

In some applications, generally those that are cost-sensitive or that require great durability, such as for mounting in a prison cell, mirrors may be made from a single, bulk material such as polished metal. However, metals consist of small crystals (grains) separated by grain boundaries that may prevent the surface from attaining optical smoothness and uniform reflectivity. [15] : p.2,8

Coating Edit

Silvering Edit

The coating of glass with a reflective layer of a metal is generally called "silvering", even though the metal may not be silver. Currently the main processes are electroplating, "wet" chemical deposition, and vacuum deposition [15] Front-coated metal mirrors achieve reflectivities of 90–95% when new.

Dielectric coating Edit

Applications requiring higher reflectivity or greater durability, where wide bandwidth is not essential, use dielectric coatings, which can achieve reflectivities as high as 99.997% over a limited range of wavelengths. Because they are often chemically stable and do not conduct electricity, dielectric coatings are almost always applied by methods of vacuum deposition, and most commonly by evaporation deposition. Because the coatings are usually transparent, absorption losses are negligible. Unlike with metals, the reflectivity of the individual dielectric-coatings is a function of Snell's law known as the Fresnel equations, determined by the difference in refractive index between layers. Therefore, the thickness and index of the coatings can be adjusted to be centered on any wavelength. Vacuum deposition can be achieved in a number of ways, including sputtering, evaporation deposition, arc deposition, reactive-gas deposition, and ion plating, among many others. [15] : p.103,107

Shaping and polishing Edit

Tolerances Edit

Mirrors can be manufactured to a wide range of engineering tolerances, including reflectivity, surface quality, surface roughness, or transmissivity, depending on the desired application. These tolerances can range from wide, such as found in a normal household-mirror, to extremely narrow, like those used in lasers or telescopes. Tightening the tolerances allows better and more precise imaging or beam transmission over longer distances. In imaging systems this can help reduce anomalies (artifacts), distortion or blur, but at a much higher cost. Where viewing distances are relatively close or high precision is not a concern, wider tolerances can be used to make effective mirrors at affordable costs.