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How to Fabricate a Mirror
In this section you will find all of the information you need to grind, polish, and figure your mirror. You may use the following outline of contents to skip to a section. This page is perpetually under construction and in the near future will include photos, diagrams, and other improvements.
The spherical and parabolic telescope mirrors
Fabrication of spherical surfaces through abrasion
Defining your RoC and sagitta
Items you must have
Building the Tool
Damming the mirror
Preparing the tiles
Chamfering the Blank and Tool
Effects on Sagitta
When to move to the next grit
Moving from SiC to AlOx
Preparing the Lap
Preparing the Cerium Oxide slurry
Hot and cold pressing
Temperature and humidity
Avoidance of scratches
Avoiding edge defects
The Knife-Edge tester
Understanding the Foucault test
Constructing a Foucault Tester
Testing for sphericity
Figuring; Theory and Method
Parabolizing from a spherical surface
Distribution of work
Obtaining Data from the Foucault Test
Using strokes to correct the figure
How good should my mirror be?
Before we begin, Castle-Emerald would like to make the statement that there are many methods of fabricating a telescope mirror, all of which are valid. A particular approach may be less labor intensive while another may carry certain risks, like zonal defects. The methods presented here in this guide comprise, in our opinion, the best balance between speed and minimal risk. In other words, the inexperienced amateur will spend the fewest hours laboring while maintaining a very high chance of successfully fabricating a mirror of extraordinary quality.
Furthermore, Castle-Emerald would like to state, unequivocally, that anyone who has ever successfully produced a quality mirror is as much of an expert on the subject than anyone else who has ever done it. This is a process that has evolved over the course of centuries by the labors and ingenuity of amateurs, not professionals, to its present state; that inexperienced hands can create an object of such extremely high quality that it remains out of reach for commercial manufacturers to duplicate.
The Spherical and Parabolic Telescope Mirrors
The nature of reflection allows a parallel wave of light to be redirected and focused, simultaneously, to a focal point known as the Airy disk. Whether the focal ratio of a mirror requires a spherical or parabolic surface to accomplish this feat is irrelevant; a parabolic surface is very close to a spherical surface and the production of one is only different in that the final stage of figuring demands a specific type of stroke to produce a parabola. We will consider all work leading to this final step as perfectly equivalent; regardless of the final form, all steps leading up to and including the polish are exactly the same.
Imagine in your mind's eye that you have a huge sphere of glass, hollow on the inside (see fig. 1a).If a light source is placed at the center of this sphere (i.e. at the Radius of Curvature) it will travel outward as a wave and be reflected back upon the source of light. Now imagine that you cut a circle out of this sphere. This section will have a curve on the inside surface that is defined by the radius of the original sphere. This spherical section will also reflect a wave of light back upon its source if placed at the RoC (see fig. 1b).The entire process of grinding and polishing a spherical surface is to obtain in reality that section from your imaginary sphere. Before we begin, the characteristics of this sphere (its RoC) must be defined.
The important difference to understand at this point is how the focal length changes between a light source at RoC and waves arriving parallel, i.e. from a source at infinity. Imagine now that you have a spherical mirror and a light source at RoC, if you begin to move the light source away from the mirror, the rays of light forms a cone with a narrower angle and the end result is that the mirror will bring the light to focus at a point closer to the mirror than its RoC. Continue moving the light source further away and eventually, when it is so far away that there is no discernible angle to the waves upon arrival, the light will be brought to focus at one half the RoC (see fig. 1c).
In this configuration, a spherical mirror of short focal ratio is not going to be focusing the light from a source at infinity. At best, one zone (a ring) of the mirror will focus some of the light to a point - with the center bringing the light to focus at a distance greater than outer zone (the edge) does. To focus parallel waves, the sphere needs to be altered slightly; the center needs to be made deeper. When all portions of the mirror bring parallel waves to the same focal plane that the edge of the mirror does, it will be parabolic. This relationship between the angle of light waves and the focal point provides the basis for the operation of an incredibly simple testing apparatus that you will use to polish a parabola into your mirror; the Foucault or Knife-edge tester.
Fabrication of Spherical Surfaces through Abrasion
There are two types of surfaces which can maintain total contact when sliding past one another in any direction; the first is a flat plane and the other is two sections of a sphere with identical radii. We begin with two cylindrical pieces of glass and place one flat surface atop the other. When the top piece is moved with a stroking motion, the points of greatest friction will be the edge of the bottom piece (known as the "tool") and the center of the top piece (which becomes the mirror). Over time and many strokes with abrasive agents between the surfaces, the tool will gradually become convex and the mirror will become concave. A glass tool need not be used, not just because it costs more to use a glass tool, but because glass is too soft; nearly anything harder than glass can be used to fashion a better tool surface than glass, from nickels to diamond pellets. Castle-Emerald kits include high-durability porcelain tiles because it substantially reduces the labor required to complete a mirror and maintains the best chances for success.
Abrasive agents, like silicon-carbide, begin at a rather large grit size; #60 and #80 are typical. The particles roll around with the stroking action and at the points of greatest compression they remove tiny chips from the glass. The abrasive breaks down into ever smaller particles until it is no longer effective and at this point, fresh abrasive is applied to continue grinding. This cycle of grinding and recharging of abrasive is called a "wet".
To produce a sphere requires that a certain degree of randomness be involved. This is the reason that machines don't produce results of the same quality as human hands; every machine acts in a specific way that unfortunately leaves the marks of its personality on the glass. The human hand is indeed a machine, but it is one that possesses the very valuable trait of randomness for this type of work. Over thousands of strokes, no two are the same and naturally produce a spherical surface.
To exacerbate the randomness, we include a step that acts to ensure extra degrees of randomness while also distributing the work evenly. This is the counter-turn procedure. After a certain number of strokes, the mirror is turned once, roughly 30 degrees clockwise. The glass mirror is then left to rest on the tool and the stack is then turned roughly 60 degrees counter-clockwise. If the operator is using a drum type stand, he/she can walk around the work in a clock-wise fashion to accomplish the same rotation. This rotation/counter-rotation ensures that the surfaces are exposed to each other in an evenly distributed way which also compounds the level of randomness. When executed properly, this randomness piles up over time to produce an incredibly non-random surface; a section of a sphere. Once the desired curve is established in the mirror with a large grit size, the process continues with ever decreasing sizes of abrasive particles until the surface of the glass is smooth enough to be polished.
Polishing is accomplished with the same basic stroke using a pitch lap foundation instead of an abrasion tool. When the entire surface is polished, it can be tested with the knife-edge tester to determine sphericity and detect defects which might require work before parabolization can begin.
Defining your RoC and sagitta
In a nutshell, The focal length of a spherical mirror is half the RoC. So, if you wish to produce a mirror with a focal length of 50 inches, its spherical RoC will be 100 inches. Now that you know what RoC to produce, you need to figure out how deep the curve in the glass will be and that requires knowing the effective radius of the mirror's surface.
Your finished mirror will have a chamfer around the edge (you will learn why later on but right now you just need to know that it will be between 1/16th and 1/8th of an inch). Subtracting this value from your blank's radius, you can now figure out what your target sagitta will be using the following formulas. Both formulas will yield an approximate value for sagitta, either will work fine. (see fig. 2a).
Where "S" is sagitta, "r" is the effective radius, and "R" is the RoC:
S = R - √(R² – r²)
- S = r² / 2 * R
S = r² / 2 * R
For example, a mirror has an effective radius of 4.9 inches (a 10 inch blank) and a desired RoC of 120 inches (a focal length of 60 inches). The target sagitta would be 0.100 inches:
S = R - √(R² – r²) -OR- S = r² / 2 * R
S = 120 - √(120² – 4.9²) S = 4.9² / 2 * 120 S = 120 - √(14400 – 24.01) S = 4.9² / 240 S = 120 - √(14375.99) S = 24.01 / 240 S = 120 – 119.89991 S = 0.10004167 inches S = 0.10009 inches
S = 120 - √(120² – 4.9²) S = 4.9² / 2 * 120
S = 120 - √(14400 – 24.01) S = 4.9² / 240
S = 120 - √(14375.99) S = 24.01 / 240
S = 120 – 119.89991 S = 0.10004167 inches
S = 0.10009 inches
If you are replacing the mirror in an existing telescope (a very common occurrence), while grinding you should endeavor to keep tabs on the actual RoC by measuring the surface from one chamfer edge to the other. As you grind, the chamfer will narrow and your target sagitta should be defined by the desired RoC, which does not change. It is very useful to have a target sagitta as it makes things simple, but if you want to end up with a precise focal length, you should occasionally check the RoC with the following formula:
RoC = r² / 2 * S
Determining the actual RoC for your mirror while grinding allows you to know for certain if your curve is too shallow or too deep. Using this formula and adjusting your work, you can achieve a precise
focal length within millimeters of your target.
This concludes the introduction
"The cautious seldom err"
Let this be your mantra throughout this entire process
Preparatory Work for Grinding
The following are things you must have which are not included in the Castle-Emerald kit.
1) A clean workspace. Consider this critical; if you are unable to keep your work free of contaminants, you may spend many hours grinding that you wouldn't otherwise have to. You will also need to vacuum regularly and wipe surfaces clean.
2) A solid work stand. Whether you use your kitchen counter or a 55 gallon drum, your tool and mirror need to be steady. Scrap wood can be used to make a very simple yet effective stand.
3) A quality straight-edge and a set of feeler gauges to measure the sagitta during grinding.
4) A plastic pan or bucket of water large enough to accommodate your blank.
5) Containers for storing abrasives. Glass jars are fine, plastic is better, just make sure they have a screw-on lid which provides a good seal. For slurry mixes, empty soap bottles or barbeque sauce bottles work well.
6) Aluminum foil and plastic food wrap.
7) High quality epoxy.
8) Duck tape, packing tape, and/or masking tape.
9) A carborundum wet stone may be needed to maintain the chamfer on the blank.
10) An eye loupe or laser.
11) A Sharpie marker with a fresh tip.
12) A data sheet for recording your work and results.
Cleanliness supercedes other factors; hang plastic sheeting if you can't prevent dust or other debris falling from above. Carpet can be a good thing as it tends to trap dirt, abrasives, and debris. Avoid spaces that experience wild temperature fluctuations; this is less important during grinding than for polishing.
Before we get to work an extremely important word of caution should be conveyed regarding the handling of your abrasives. EXERCIZE EXTREME CARE TO AVOID CONTAMINATION. We recommend that you either leave the abrasives in their bags until you need to use it, or prepare the containers first (mark the container with the grit size and make sure it is clean) and transfer them to the containers in a methodical fashion starting with the finest particle size and working your way up to the largest. Getting some #500 grit SiC in your #220 grit is not a problem, but getting a few #220 particles in your #500 grit supply will ruin it.
Building the Tool
Damming the mirror and pouring the stone
The face of the mirror needs to separate easily from the dental stone once it has hardened. The stone is not likely to stick to the glass, but caution should prevail over expediency. Start by covering the face in plastic wrap (the wrap should make contact with the concave surface) and secure it with tape if necessary. A single layer is fine and it does not have to cover the entire surface. Don't worry if there are small wrinkles in the plastic; wrinkles increase the surface area of the tool and provide a better adhesion surface for epoxy.
Next, take a sheet of aluminum foil with a length greater than the circumference of your blank and fold it lengthwise into thirds (it needs to be 3-5 inches wide). Wrap this around the edge of the blank and secure it tightly to itself with tape. Finally, run tape around the blank along the seam to seal the foil dam against the edge of the blank. You should now have a suitable mold for the die stone.
Place the blank on a level surface (important) and prepare the dental stone. Once mixed, pour the mix into the mold. Don't dawdle during this phase; you have a limited amount of time to mix the dental stone and get it poured before it hardens. Once the stone has hardened, tear the foil away and separate the stone from the blank. The die stone should rest for a week to continue curing before going further. If you happen to be using plaster of paris, it should be cured for up to two weeks. If casting a portland cement tool, it should be wrapped in wet rags, placed into a sealed plastic bag, and then left in a refrigerator for 10-14 days to cure.
The edge of the tool needs to be reshaped slightly; you should have noticed the ridge left by the chamfer. Using a file or sandpaper, carefully reduce the edge until it more closely matches the curve of the tool face. The Idea here is to provide a flat surface to adhere the tiles to that is somewhat close to the convex curve that matches the concave curve of your mirror. Once you are satisfied with the condition of the tool foundation, it is time to adhere the tiles.
Preparing the tiles
It is important to have a strategy for placing the tiles very rapidly as most epoxies will only give you several minutes before hardening. There are some epoxies which are made specifically to set slower to give you extra time, you may find them more suitable for this application.
There are two types of tile tools; the channeled and non-channeled. A channeled tool's tiles are set apart with a gap of 1/8th to 1/4 inch between them. In the non-channeled tool, the tiles are set fairly close together (1/16th inch) and the gaps between them are filled with epoxy during construction. The advantage to a channeled tool is that because there are fewer tiles per area of surface, it is easier to mate with the mirror and hence, you will begin fine grinding sooner. The advantages to the non-channeled tool are that less grit will be required, fine grinding will likely require less labor, there is much less risk of tiles popping off, it is easier to clean between grit sizes, and it will leave you with a perfect surface for your pitch lap later. The non-channeled tool is what we recommend, but either will work.
Find the center of the tool face and mark it. To avoid the possibility of a zonal defect occurring, you will want to make sure that the tile placed on this spot is off-center (do not place a tile centered on this spot and do not have tiles meeting at this spot at their edges or corners).
While completely unnecessary, you may snap or cut spare tiles (be sure to wear eye protection) to place in the gaps at the edge of the surface, just keep in mind that the tool needs to be beveled, which is an aggressive procedure. Rule of thumb; if the space can accommodate more than half a tile, go ahead and place them but ignore any space smaller than a half-tile. If you are building a channeled tool, forget it completely; you will only lose those tiles fairly quickly and you might be running the risk of allowing water to enter under those spots which could cause delamination of your tiles. The negligible payoff is not worth the risk.
Applying epoxy to the center portion of the tool face, place your first tile (offset slightly from center) and work your way around, applying epoxy and tiles as you go. If using a quick-setting epoxy, be careful to mix only the amount of resin and hardener that you can adhere before it gets too tacky to apply. Do not worry if epoxy is on the outward face of the tiles as it will readily and quickly grind away.
Once all of the tiles are in place, continue to apply epoxy around the edge of the tool leaving extra epoxy on the outer edge of the tiles. This buffer will serve two purposes; 1) the tiles at the edge, being surrounded by epoxy, will resist popping off, and 2) the sharp edges of the outer tiles will be kept safely hidden from making contact with your mirror, which greatly reduces the risk of chipping and/or scratching your mirror.
If using a slower setting epoxy, you should at this point place your mirror blank face up on a level surface and place a layer of foil, paper, or plastic film on its face to protect the mirror from the epoxy. Flip the tool over and place it on the mirror to let it rest (this step allows the tiles to flatten forcing them to take the shape of your mirror's curve). This operation also allows you to continue to apply epoxy to the sides and bottom of the tool. This is mostly a precautionary step; while dental stone is a higher quality gypsum stone than plaster of paris, it is NOT waterproof. Dental stone will resist water damage to an extent, but five dollar's worth of epoxy is far less expensive than starting over and rebuilding your tool from scratch after having done any amount of grinding.
If you are worried about getting your tool right, for a nominal fee Castle-Emerald will build your tool for you and ship it with your kit.
Chamfering the Blank and Tool
The act of grinding brings certain forces to bear on the glass, which occasionally will naturally produce a disastrous result if steps are not taken to mitigate the risks. One such case is the tendency for the glass at the very edge of the blank to chip off in a large, clam-shell like flake, instead of the nice microscopic chips from the rest of the surface. This tendency most often arises when the angle of the edge is close to or less than 90°. Chamfering the edge of the mirror blank will greatly reduce the risk of large chips from occurring.
Like any grinding operation, this MUST BE DONE WET; Silicosis is a serious condition which is easily preventable. Use plenty of water and you'll be fine.
Using a carborundum (silicon-carbide) wet stone, rough side first, work the stone at 45° angle at the edge and slowly work your way around the blank. Try to apply more pressure as you stroke the stone away from the mirror face. This will reduce the chance that you might cause a chip to the mirror. While stroking, run the stone around the edge slightly. The combination of the stone's angle and direction of travel should feel natural and after a while, you will notice a groove start to appear in the stone. Once you have achieved a 1/8th inch bevel, flip the stone and use the finer grit to reduce the roughness of the bevel.
Now inspect the edge tiles of your tool. If you see any tiles whose edges are exposed (all of them if you are using a channeled tool) carefully take the corner off by grinding it with your wet stone in the same manner that you ground a bevel on your blank. Do not use too much pressure; having a tile pop off at this stage is the best case scenario if it happens at all, but you still don't want it to occur, so use care during this operation.
The process of rough-grinding to produce a curve is simple and straightforward. ATM's traditionally call this step "hogging" and accounts for about a third of the total labor involved in fabricating a mirror. It is purely muscle action over time. Castle-Emerald kits come with a pre-generated curve so the process of completing the rough grind described here will apply to a blank that has already been hogged.
The first part of rough grinding a pre-generated blank concerns the glass less than it does the tool. This is because rough grinding a hogged blank is all about getting your tool into the right shape for fine grinding. There are 3 objectives to meet during this stage, all of critical importance.
1) The tool must be mated to your mirror, i.e. you must achieve "good contact"
2) The glass must be ground with a curve all the way out to the bevel
3) You should be close to your target sagitta
The tile surface of your tool will slowly grind down (as does the mirror) and it will be the edge of the tool that needs the most work to achieve good contact. During this early stage it is very difficult to avoid deepening the curve in the mirror, which is why we recommend that when you place an order, you specify a RoC that is longer than your target; beginning with a shallow curve allows you to spend that extra glass to get your tool mated while hopefully reaching your target sagitta simultaneously.
The surface of the glass should look pretty rough, but don't fret because this will soon be smooth. You should also note that the curve ground into the glass does not reach the very edge of the blank. This is in the interest of preservation of the glass; while getting your tool into shape, you will necessarily lose a certain amount of glass to grind the tool. Not having the blank ground all the way out to the bevel actually requires less work and the mirror will be slightly thicker when you're all finished. The benefit of an extra few hundredths of an inch may be negligible, but you shouldn't remove more glass than you really have to.
While rough grinding, you should aim for achieving good contact while arriving at a slightly shallow curve. At this early stage, if you reach your target sagitta early you may find yourself fighting the tendency of the curve to deepen, which will force you to work with Tool-on-Top to bring the edge back down. This is not efficient. However, if your sagitta is slightly shallow, it will allow you to work with Mirror-on-Top for more wets which ultimately produces a mirror with less total labor. While this may seem confusing and complicated, it will become very clear once you have done the work and recorded the results of your actions.
How shy of your target sagitta should you be? It's mostly a matter of work habit and preference, but generally speaking, if you are about 5% shy you'll be in pretty good shape e.g. if you are making a 10 inch f/6 your target sag will be .100 inches and you should be at no more than .095 inches before moving on to fine grinding. This will allow you to let the mirror grind out from the center with each new grit size while avoiding extra work with ToT to reduce the sagitta. Additionally, you will get to clearly see what the total surface should look like before moving on to the next grit, you will have a much better understanding of what the rate of grind is for any grit size, and most importantly, you will be able to avoid working with Tool-on-Top during the last few grit sizes and this is paramount to avoiding turned-down-edge (the most dreaded defect to repair while figuring).
There are two stroke types; the Chordal stroke and the Normal stroke. In both cases the mirror is moved over the tool away from the operator and then back toward the operator. The mirror should reach a maximum displaced distance from center-over-center by 1/6th the diameter of the blank. So, if you have a 10 inch blank, the amount at which the glass will overhang the tool at the end of the stroke will be 1.67 inches. The maximum travel of the blank from the peak overhang of one side to the peak of the other will be 3.33 inches of total travel.
The Chordal stroke is used predominantly for hogging and you should not have to use it much with the Castle-Emerald kit. In this type of stroke, the center of the blank is placed off to one side as much as a third the diameter of the blank while stroking forward and back. This stroke forces the edge of the tool to grind against the center of the mirror and is the fastest way to increase the depth of the curve in the glass. Starting with a pre-generated blank, you should only allow a slight overhang when using the chordal stroke (perhaps 1/10th diameter).
In the Normal stroke, the mirror is placed centered over the tool and these center points cross over one another with each stroke. This is the stroke you will be using the most and the only thing to note is simply this; pay attention to the stroke length! Don't allow your stroke to become too long. The most common cause of grief for first time mirror maker is that the stroke is allowed to lengthen to a point where the operator is constantly losing good contact, and hence, grinding errors into the glass. This will also be the most common cause of chipping and scratches.
The grinding work occurs under two configurations; Mirror-on-Top (MoT) and Tool-on-Top (ToT). MoT is more efficient for two reasons; 1) the mirror blank is much heavier than the tool and the extra pressure equals faster grinding, and 2) there is a much greater volume of glass to remove from the edge to reduce the sagitta than there is at the center to increase it. Invariably, you will have to spend time working with ToT, but if you find yourself working more than a third of your wets with ToT, it is a sure sign that your habits need adjustment.
Only the Normal stroke should be employed when working with ToT; using the Chordal stroke in the ToT position is an invitation to disaster; it can easily produce non-symmetrical errors which can only be corrected through grinding, but you won't know the errors are there until you have polished out your mirror.
Begin by applying water to the surface of the tool or mirror (whichever is on bottom) using a spray bottle. Don't drench it, one or two squirts is enough. Next, using a spoon, apply a small amount of abrasive to the wet surface. A little bit goes a long way, so use it sparingly. If you find that unspent grit is being sloughed off the edge while grinding, you're probably applying too much. Now set your mirror on top of your tool with the wet abrasive between them to begin.
It is important to note here that whenever you bring anything into direct contact with your blank that you should exercise caution. Once you have gently brought anything into contact with your blank, the same care should be used to separate them.
As you stroke the blank, the abrasive will begin to break down into smaller and smaller particles until it no longer effectively grinds. At this point more abrasive is applied to recharge and the operation continues.
ALWAYS KEEP YOUR WORK WET!
If glass is ground under dry conditions, microscopic particles of glass can become airborne and subsequently inhaled. Once these particles become stuck in the lungs, they will be yours to keep for the rest of your life. If a person inhales enough glass particles it will result in a condition known as silicosis which can drastically reduce a person's lifespan. DON'T MESS AROUND! Keep your work wet and you will completely eliminate the risk of airborne silica. It only takes a little bit of water to achieve complete safety. Also, as a side note, it should be mentioned that you should never empty your pan down a drain; the "mud" left behind by spent abrasive and silicates will form concretions in drain pipes that may cause real damage. Dump it outside.
Rotation and number of strokes
At this point you are actively working and you need to understand the importance of randomness. There are certain things which should never be random, like stroke type, length, and position. Then there are things which need to be kept random to produce good results. We recommend that you count the number of strokes you make before executing a turn and alternate between three numbers. 8-9-10 works well because you can typically grind "once around the barrel" in an average wet, but it really doesn't matter. It works like this: Grind out 8 complete strokes then turn the blank 30° or so clockwise. Now walk clockwise around the stand roughly 60°. If you are using a work stand that does not allow you to walk around it, the same action can be achieved by rotating the stack 60° counter-clockwise. Now grind out 9 strokes and repeat the rotation. After the next series of 10 strokes, revert back to 8 strokes and continue the process.
Whether you choose counter-clockwise or clockwise rotations doesn't really matter - as long as it is consistent from start to finish. If you need to mark the back of your mirror with an arrow to remind yourself which direction to rotate, go ahead and use your Sharpie.
Effects on Sagitta
Different stroke types and work positions are going to have certain effects to the curve in your blank. Successfully grinding a mirror with a specific focal length requires that the operator makes the correct decisions at every step along the way. Each grind session begins with making a decision to work with MoT or ToT and what stroke type is to be used. The following is a generalized description of the effects that different strokes and positions will have on the mirror blank.
Chordal Stroke, MoT
The edge of the tool grinds against the inner portion of the blank and rapidly increases the sagitta. The greater the amount of off-center overhang, the faster the center of the mirror will grind out.
Normal Stroke, MoT
The zones of the mirror and tool are generally kept in close contact. Because the center of the mirror is always in contact while the edge spends time overhanging the tool, this configuration will result in a slow but steady increase in sagitta.
Normal Stroke, ToT
The points of greatest friction will occur away from the center of the mirror. Even though the edge of the blank spends time out of contact in this configuration, the blank's curve will be forced into a flatter shape, reducing the sagitta (albeit at a slower rate than MoT increases it).
Before executing this procedure, it is important to reiterate that you must exercise due caution. You will be bringing metal objects into contact with your blank in three places, two of which naturally chip easier than any other part of the glass - the very edge. Once you gently bring the straight-edge to rest, the weight of the ruler from gravity should be the only pressure exerted upon those points of contact.
Using your straight-edge ruler, place it across the mirror in such a way that it traverses the center of the blank. Next take your feeler gauges and find the combination of blades that fit under the gap. Take the values on the blades and add them up. This total is your sagitta. You might find it useful to rearrange the order of the blades because later on, you will be swapping them and it can reduce the time required for this measurement if you have a stack of known value and are able to swap a single blade for another.
This measurement should be repeated two more times with the straight-edge placed 60° to either side of the first measurement. If you find that one measurement is more than five thousandths different from the others, it may indicate that you have a non-symmetrical error in the glass. If this is the case, repeat the measurements to confirm your values. Now check the width of the chamfer in the places where the straight-edge sat during the measurement. If the bevel is not symmetrical, you probably have nothing to worry about (the spots where the bevel is widest will naturally reveal a sagitta value that is less than the value where the bevel width is thinnest). However, if your chamfer is very close to the same width the whole way around your blank, you need to indicate the measurements on your data sheet and continue grinding with the Normal stroke until the sagitta values measured are within a thousandth of an inch. This is purely a precautionary policy; it is better to spend an extra few wets at a heavy grit size early on than to waste many times that amount of labor later on when you discover you have no choice but to back up from a finer grit size.
Also of importance to note here is that your target sagitta value should be derived from the actual diameter of the mirror and not that of the blank. In other words, you must measure the diameter of the blank MINUS the chamfer. While maintaining the exact same RoC while grinding, the chamfer will slowly become narrower and the effective radius of the surface will increase. This means that your sagitta should increase as well. If you are aiming for a focal point range within several inches, this matters little, but if you are aiming for a precise focal length, you must be sure to use the correct value for effective radius in your calculations.
CONSIDER THIS OF CRITICAL IMPORTANCE. The process of making a mirror is absurdly simple, but you must make the correct decisions when grinding and figuring. There is simply no better guide to making the correct decisions than the knowledge of your past work results. The following is a simple chart which should be used religiously to record every single thing you do with your mirror. Printable data recording chart available here.
Download the printable Data Recording Chart
Reaching the rough grinding goals
The first phase of grinding occurs under work at the largest grit size and before you move on to fine grinding you must be certain that your tool and mirror are in the proper states. There are 3 conditions that must be met before you can begin fine grinding.
1) Achieving good contact
Most importantly, your tool needs to be in the right shape; it needs to have a nice smooth surface that matches the curve in your blank. To determine whether you have arrived at the proper state some simple tests can be administered.
The Sharpie test.
Using a Sharpie marker of dark color, draw a grid or an asterisk-like star pattern on the face of the blank and execute a wet. You will notice that the marks on the center will grind away quickly and the marks at the outer edge will take about twice the work remove. If you find that the lines vanish too quickly, you can reduce the number of strokes before executing turns. After a complete wet, carefully rinse the mud off of the mirror and inspect the grid marks. You should see that all of the lines have been ground away to the same extent out to the outer 1/6th diameter of the mirror. If you wish to test the contact all the way out to the edge, reduce the number of strokes per turn and spend half of the wet with ToT. Under this scenario the lines should all look evenly worn away. This is a very reliable test.
The ToT test
Pepare a wet with ToT; apply the water and evenly distribute a small amount of abrasive. Gently bring the tool to rest on the surface of the mirror as if you are about to grind and lightly move the tool to spread the abrasive around. If you are in good contact, the movement of the tool should feel smooth and silky like a ball bearing, i.e. it should move freely with only the slightest push and not experience any noticeable resistance in any direction. This procedure can quickly tell you if your tool isn't the correct shape; if the tool is too flat or not flat enough, the tool will not consistently "float" on the mirror, it will instead hang in certain spots. This test cannot tell you if the edge of your tool is not contacting the edge of your mirror so it shouldn't be relied upon if you've been using the chordal stroke.
Sticking and locking
If during grinding you happen to experience the tool and mirror sticking at certain spots in the stroke, or if they become locked, it is a sure sign that you are not in good contact. If the tool and mirror become locked, it is because to tool's center is too low or you have a "hole" in the center of your mirror and it is acting like a suction cup. If you are experiencing any amount of hitching, sticking, or locking when rough grinding, you do not have to bother with a contact test yet.
2) Grind the curve all the way out to the chamfer
This is simple enough, just inspect the area just inside the chamfer and make sure that the established curve (the ground surface) meets the bevel all the way around the blank.
3) Reaching your target sagitta
The important concept to understand here is that you are aiming for a specific RoC and the sagitta will change slightly as the effective radius of the mirror increases. The issue of discrepancy is due to the fact that you don't know exactly how wide the chamfer will be when you're finished. First determine what sagitta you should have for your current effective surface radius and you'll know where you stand. Be sure to measure the blank from the inside of one bevel to the other across the center of the disk and divide this quantity by 2 to find the value for the radius (r). Using your feeler gauges, determine the value of sagitta (S). You can now use the following formula to determine the radius of curvature (RoC):
RoC = r² / 2 * S
If your measured value for RoC is too short, you need to spend some time in this early stage working with ToT to bring the edge down and reduce the sagitta. As you move through finer grit sizes it is never very difficult to increase the sagitta if you need to, but it will become very difficult to decrease it. On the other hand, if your RoC is slightly long (slightly shallow sagitta) you can allow the curve to slowly deepen on its own. This is the reason you should order a RoC longer than your target; it is simply less work and offers a bit more control.
Once you have reached the goals of rough grinding (good contact, completely ground to the chamfer, and near your target RoC) you can begin the process of making the surface smooth enough that you can polish it. Of absolute importance is the cleaning of your workspace and tool. Use an old toothbrush to clean your tool under a running tap and be sure to get rid of every single abrasive particle. To clean your workspace, start from the top and wipe everything down to the floor. The more diligent you are bout keeping your workspace clean, the less chance you have of wasting many hours of work.
From this point on, you also need to be sure that the only abrasive container that is in your workspace is the grit size you are currently using. You should leave the abrasives in the bags they were shipped in until you have completely cleaned your workspace and you are ready to begin using it. If you decide to place abrasives in other containers before you need to use them, begin with the finest particle sizes and work your way up to the largest. It's fine if you contaminate the #220 grit with some #320 particles but if you get even a few #220 size particles in the #320 it will be ruined.
After a few wets of the grit of smaller particle size you should notice that, working first with MoT, the center of the mirror begins to change in appearance. The surface of the glass is becoming smoother as the finer particles take smaller chips of glass and when the center no longer changes in its appearance from one wet to the next, it is ground to your current particle size. Take a good look at the surface from the center outwards and notice the change in the appearance of the glass. The first objective is to get the entire surface ground to match the appearance of the center zone. When you have brought the edge to the same condition as the center, it is time for inspection for pits.
At this early stage of #120 grit, pits are obvious enough to be seen with the naked eye but you should endeavor to be more thorough. You can use an eye loupe and carefully inspect the entire surface, but using a small laser is much faster. In a fairly dark environment, hold the laser at an extreme oblique angle so the dot looks like a line across the surface and slowly scan back and forth. When the laser encounters a large pit it will scatter the light and become instantly visible. Circle every pit with your Sharpie and be sure to scan the entire surface thoroughly. Indicate the number of pits in your data chart.
Understanding and detection of pits is the most crucial aspect of fine grinding. Each particle of abrasive, as it rolls around, is removing microscopic bits of glass at the points of greatest compression (which is usually the microscopic "mountain peaks") but occasionally, the chip will be much larger than average. Some of these can be so large that they are measurably beyond the tolerance required to move on to the next particle size. Not grinding the glass surface down to eliminate these pits means that you will be left with a flawed surface after polishing and you cannot allow this.
Pits near the center aren't much of a problem, but pits near the edge must be removed. The edge of a mirror defines its performance so getting this portion right is your biggest concern throughout this entire process. At first, you may have 7-10 pits, but after several more wets, this should drop to 2-5. When you are nearing the point where the pits are almost gone, start filling the pits in with sharpie ink between each wet so you can more clearly see your progress. When you have eliminated the pits in the outer zone, you're probably ready to move on.
Also of importance to note here is a phenomenon referred to as "pit chasing". If you spend a little too much time on a particular grit size, you will notice that you always have roughly the same number of pits; no matter how much time you spend to eliminate them, they are always there. During grinding to remove the pits, you occasionally produce new ones. The important thing to know is that it is not the number of pits that matters; it's their size and location which is most important. Large pits near the edge must be taken care of! You will eventually hit a condition at the end of a wet when the pits in the outer zone are gone or almost gone and the remaining pits are minor - this is your cue to switch grit sizes.
A large pit near the very edge is likely going to be the unluckiest thing you encounter. If this happens, switch to ToT for at least 2 out of every 3 wets and keep tabs on your sag. If you are at the #120 or #220 grit and have a very large pit near the edge, don't be afraid to back up a grit size to eliminate it.
If you encounter a scratch, it is likely due to some form of contamination in your workspace. We have actually never encountered scratches but we do know that it happens. Be diligent in cleaning your workspace and this will likely not be an issue for you. Any deep scratch should be ground out before moving on to the next grit so you can just treat it like a long pit.
When to move to the next grit
If this is your first time grinding a mirror, this will be the trickiest aspect of the process; there is no other place where experience reduces total labor as moving to the next grit at the very earliest moment. Ask yourself these questions: have I ground out the entire surface to the current particle size?, and have I at least reduced the pits to the extent that they will be eliminated by the next particle size? The answer to the first question should be fairly obvious, but the second requires some guesswork. Be cautious and you will end up with the proper results.
If you have completely ground out your mirror with the current particle size and you seem to have a lot of nasty pits (more than 7-10) that never seem to be going away, with fresh ones replacing the eliminated ones, you may have a problem. First, are you using weights on your mirror or are you applying extra downward pressure while grinding? If so, knock it off. After reducing the pressure, you should soon see improvement. Using weights to hog a blank can be effective at reducing labor, but you shouldn't use them during fine grinding. Avoiding the extra pits is a better labor-saver than using weights or extra pressure. If you haven't been using weights or undue pressure, you may have a contamination problem. A couple of particles of the wrong grit size easily produce large pits. If it is possible that you did not clean sufficiently, stop and clean everything again. If this does not fix the situation, you might have contaminated your grit supply and you will likely have to replace it. As a last ditch effort, you can move to the next grit size and hope you have enough abrasive to last until the next size, but this is going to at least double the labor required during that stage.
On a related note, there is a phenomenon that seems to occur between #100 to #300 size particles; glass seems to prefer pitting at these sizes. It might have something to do with the chemical structure of glass at this level that lends its nature to pits, or it could be the particles themselves. Whatever the cause, just know that the #120 and #220 are probably going to produce more pits than you will encounter at #320 and beyond. Concentrate on the pits in the outer zone of your mirror and start to back off the pressure you exert during strokes until the pits are no longer very deep or gone completely.
As you grind you will notice the width of the chamfer shrinking. If your chamfer is 1/4 inches when you start, you can expect it to be less than 1/8 inches by the time you finish. If you spend more time grinding than necessary, perhaps you had to back up a grit size while fine grinding, you may need to increase the bevel slightly. Once you have gotten past #320 grit, you do not have to worry about maintaining the bevel, as long as there is some left, it will suffice.
If you wish, as you are fine grinding, you can take a spare tile and carefully grind the bevel with each new grit size. It will become progressively smoother and can serve as an excellent reference for what the mirror surface should look like after being completely ground out to that particle size.
Moving from SiC to AlOx
Starting with the #500 grit SiC or the tail end of #320, you should be working exclusively in the MoT position. Also, you should become obsessive about controlling the length of your strokes. Hopefully, you are exactly at or about 0.5% shy of your target RoC and you can allow the #500 grit to grind out from the center all the way out to the edge. If you have a Turned-Down-Edge defect, this action should repair it while you grind. This is completely precautionary; you can certainly grind a mirror free of edge defects while working with ToT, but it will only cost you 90 minutes to 2 hours extra work to ensure that after you have polished your mirror you do not have to go back and grind again, losing 10 to 20 hours of labor. If you notice that the very edge takes a long time to grind out, you may have indeed had TDE.
By now, you should have noticed from your record of data that each smaller particle size takes less total time and requires fewer wets, as well as the fact that less abrasive is needed for a single wet. These characteristics become amplified with AlOx.
At the end of #500 grit Silicon-Carbide you need to be completely pit-free before switching to Aluminum-Oxide. AlOx does not produce pits, but it is definitely not going to be able to grind enough glass to remove any remaining pits you may have, so take care of them now. AlOx particles look like disks, and they don't roll around as much as they do slide around. As they slide, they shear off the tiny peaks in the surface of the glass making it smoother.
Because AlOx particles are so tiny, it is more practical to prepare a slurry mix rather than apply water and powder separately. Take a portion of your AlOx and put it into an empty clean bottle. Plastic soap bottles and the like work very nicely, just don't use a pump or spray bottle; the particles are sure to destroy the mechanisms. We recommend a 1:1 ratio of AlOx to distilled water with a drop of dish soap for good measure (a glycerin based dish soap will ease the surface tension of water). A small amount of slurry can then be applied to your tool and watered down with your spray bottle after having spread it around a bit.
You will find that a single application of AlOx slurry will last a very long time. Instead of pausing to apply more slurry, you will likely only need to add a little water from time to time to prevent the tool and mirror from sticking. When the edge has been ground completely to 5 micron, you are ready to polish.
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