Mike's Mirror Making Musings

Copyright Michael E. Lockwood, 2005-2007.

0.0 - Introduction, disclaimer, random info

This document is intended to help mirror makers take some of the mystery out of figuring, and to make the process more tolerable.  After making a good number of mirrors, some techniques float to the surface and just seem to work better.  It is my goal to mention these here.  Some things just don't seem to work well.  I'll try to mention those too.

The advice given is intended to help those working on mirrors from 4" to 12" in diameter, with focal ratios between F/5 and F/8.  Faster or larger mirrors may require different techniques and often subdiameter laps.  Slower mirrors are ideally figured with very gentle techniques that remove glass very slowly, or they can be left spherical if that is desired.  Advice on topics other than figuring may be applicable to mirrors that don't fall in the range given above.

DISCLAIMER:  There are many, many ways to make a mirror.  What I'm describing here is my particular flavor.  There are no absolutes in such a bizarre undertaking that involves making one of the most precise surfaces ever crafted by a being on planet Earth.  I've taught mirror making classes, and these techniques worked well there.  The problem is there are so many variables involved that each person will have to control a slightly different set, depending on their work habits, environment, choice of materials and how they work their hands and arms.  So, to reduce the chances of missing some critical bit of information, I also expect that you've read at least two other pieces of literature on mirror making before you start relying on my instruction for making critical figuring decisions.

If you have any doubts about whether I'm right or not, remember one thing - it's MY web page and I'm always right here!  All temperatures are in degrees Fahrenheit, and all dimensions are in inches.

Now for some instruction to make the art of figuring a bit easier and hopefully faster, too.  First I'll lay a bit of ground work on fine grinding, polishing, and lap pressing.  Hopefully this will help the reader get successfully through polishing with a mirror that's more likely to be in a state that's ready for figuring.

0.1 - Fine Grinding

I recommend taking the time to fine-grind the backs of the mirror and tool.  It will make polishing easier later on.  What, you're ignoring that previous statement?!  DON'T!

If your mirror is at all thin for its size, grinding the back of the mirror is just as important as grinding the front!  If the back is not flat, the mirror will warp during grinding and polishing, and you will probably end up with ASTIGMATISM, and there is no reason for this, other than carelessness.  No matter how well you figure the mirror, if it has significant astigmatism you will never be happy with it, and it will not perform.  Also, a smooth mirror back will allow the mirror to slide around in the mirror cell more easily, which makes it less likely to "hang up" and get stuck in certain positions.  This can affect performance by pinching the mirror, and it can cause collimation to intermittently shift.  A smooth mirror back helps avoid these problems.  It also looks better!

Grind the back of the mirror agains the back of the tool or against something else (a piece of glass, or flat piece of metal) until you don't see much difference from GOOD straight edge.  Better yet, use a good spherometer to check the curvature.  Keep grinding the back up through at least 12 micron, making sure it stays flat.  You don't have to grind as long as the optical surface, but try to remove most of the pits of the previous grits.

Fine grinding is your last chance to get rid of pits from 220 grit (or worse), which will NOT polish out before your run out of time, patience, and cerium oxide.  My grinding sequence is typically 80, 120, 220, 320, and then I begin fine grinding with 25 micron.  I HIGHLY recommend MicroGrit aluminum oxide - it's really good stuff.  When you make the transition from 220 or 320 carbo to 25 micron aluminum oxide, spend extra time at 25 micron and make DAMN SURE that no 220 or 320 pits remain.  (You can use 40 micron instead of 25 micron, or use 40 micron and then 25 micron.)  There will always be some larger pits, but should change locations after each wet or two.  These come from the subsurface cracks produced by grinding with carbo, and must be removed with the aluminum oxide.  Spend at least an hour here if this is your first mirror, preferably more.  Use the time to tweak the sagitta and get the focal length closer to what you want.  I've spent several hours on 25 micron, because sometimes 220 pits can take a while to remove.

Carbo and aluminum oxide are different materials with different characteristics, after all.  So, I check carefully for pits after 320 grit (looking for generation marks or 220 pits) and then do a serious cleanup and grind with 25u for an extended period to remove subsurface fractures until the grind looks excellent.  Alternatively one could use 500 grit, but I prefer to save a carbo cleanup step and just run with 25u longer.  This also gives time to tweak the focal length a bit if necessary, and to get the blank nice and spherical before moving on..

When using fine abrasives, take several teaspoons and put it in a squirt bottle.  Add about 8 ounces of water.  The mixture should be like milk when shaken, containing a good amount of abrasive.  Shake up the mixture, and squirt on a small puddle about the size of a quarter, and gently set the mirror on the tool.  Watch the layer spread out between the two disks.  Take a few gentle strokes.  A little water/abrasive should ooze out the edges, but most should stay between the disks if you've used the right amount.  Start working, but with fingertip pressure.  In other words, don't push down on the top disk - merely let the weight of the mirror or tool do the work.  (This is your time to relax and rest your hands and arms before the labor of polishing.)  You'll start to hear the abrasive biting in after a minute or two - that's when the grinding begins.  Friction will be quite low.  At this point, note if there is any slip/grab tendency - if there is, there is more asphericity than there should be or a mismatch between the shape of the tool and mirror.  Keep going, but be gentle.

After 10-15 minutes of grinding there should be no bubble in the center (a sign that the tool and mirror do not mate yet), and the surfaces should thus be in full contact.  (If not, go back to the previous abrasive and get it spherical.)  Clean off the glass "sludge" every 15 minutes or so.  Add a little water if the mixture gets too dry.  You don't need too much abrasive - it doesn't wear out that quickly.  You will need less abrasive as you continue grinding, as the surfaces will mate closer and closer and you won't need as much to fill the gap.

The way I do it, fine grinding is a much wetter process than coarse (carbo) grinding.  With MicroGrit, this method works very well, and the grind is quite efficient.  Drying out the grind is asking for nonsphericity, in my experience.  (If you have your own techniques that involve very dry wets during fine grinding, that's fine, but I never do it that way.)

When there are no bubbles of air trapped between the blanks, you're probably removing pits on all of both surfaces.  You can verify this with the sharpie test - draw a grid of lines such that they create approximately 1" squares on the surface of the mirror.  Then grind for a bit - ideally the lines will go away uniformly if you do a few minutes of MOT and then a few minutes of TOT work (or TOT then MOT, it shouldn't matter).  You can usually go on to the next abrasive if the lines have been worn away a couple of times, provided you don't find abnormally large pits.  Looks very carefully at the edge and center of the blank with a loupe.  Try to find pits that are several times larger than the background small pits.  If you find these, chances a previous grit's grind wasn't quite complete.  If you find them only at the center or edge, then the radius of curvature of the mirror has changed a bit since that larger grit was used, and you should not start polishing until you're sure it is spherical.

After all big the pits from carbo are gone (and you've looked very hard for them!) due to 25u grinding, I usually go to 12 micron, and then 5 micron.  Each should take 1/2 to 1 hour if 25 micron was done correctly.  Do more if you have any question in your mind about remaining pits.  Use a 10X power eye loupe or magnifier to inspect the surface - it should be VERY uniform in pit size over the entire surface of both disks, and free of scratches.  If you finish 5 micron MicroGrit with an excellent uniform grind and no scratches, polishing will go much faster.  Be gentle in all fine grinding, but be very gentle at the end of 5 micron.  Add water only if you can get away with it during the last 15 minutes of 5 micron work.  Keep the work from drying out or there may be contact problems.  Use fingertip pressure to move the tool/mirror.  A good 5 micron grind will ensure fast polishing.  If you know what you're doing, you can use 3 micron.  I find that finishing with 3 micron abrasive speeds up polishing over 5 micron.  Just be careful and gentle with the grinding.

A few last tips about fine grinding:

1) Near the end of fine grinding, when using 9u or 5u, don't use too much ink for the sharpie test.  Opt for a thin line rather than a wide line produced by some permanent markers.  The ink itself can affect the contact between the tool and mirror, so keep it to a minimum.  The lines should grind away quickly and uniformly.  Be especially concerned if the lines near the edge of the mirror have a tendency to not go away as quickly as other areas of the mirror.  If you work both TOT and MOT and this happens, you need to looks for pits, grind longer, and check your grinding stroke for the proper length/technique.  Redraw the sharpie lines and grind gently until the lines near the edge of the mirorr disappear just as quickly as in other areas.  Then be grateful - you have just saved yourself many hours of polishing!

2) Clean off the sludge for the last 5-10 minutes of grinding with each fine grinding abrasive and randomize your stoke a bit to help get as spherical as possible before switching grits.  This will help avoid grinding in a low outer zone, which takes a LONG time to polish out (as mentioned in hint 1).  This is especially important for the last grit - you want a sphere accurate to 1u at the end of 5u grinding, which you will obtain automatically with proper technique.

0.11 Glass- and tool-specific advice

0.2 - Pitch and Lap Tips

I use Cerox 1670 from Salem Distributing.  It cuts fast and leaves a fairly smooth surface.  It can be used for figuring if you use a lot of water.  However, refined Cerium products are better for figuring - they leave a smoother surface, work slower (and therefore are easier to control), but cost more.  Other ceriums may work just as well as the one I recommended.  (However, I have heard of several people having some scratching problems with Cerium from Willmann-Bell, myself included.)

I recommend Gugolz 64 pitch for polishing at around 70 degrees Fahrenheit for moderate F/ratio mirrors (F/5-F/7).  For a Texereau-style pitch hardness tester, G64 has a fall rate in the range of 0.030" to 0.100" in five minutes (1 kg mass, point ground as described by Texereau in an appendix).

At this hardness (for Gugolz 64), the pitch channels will close up in a few hours of work.  I have found that one of the best indicators of the hardness of a pitch lap and how well it is working with the operator's tecnhique is the time it takes the channels in the lap to (nearly) close under normal hand polishing conditions.  For me, pitch that flows enough in 1 hour to nearly close the channels is quite soft (like Gugolz 55, mentioned below), and a lap with channels that close up only after 10 or more hours is really hard.  My preferred range for work with a full-size lap is a channel closing time of 1.5 to 4 hours.

I like Gugolz 55 for subdiameter figuring laps at this temperature, especially for use on mirrors faster than F/5 (which I am not discussing here).  G55 is also good for polishing in the winter, when I'm cheap and only heat the house up to 65 F.  Figuring an F/4 mirror larger than 8" with a full-sized lap requires using unconventional methods, so I use soft subdiameter laps for this.  Subdiameter laps are a whole other animal, and I'm not covering their use in this document.  The fall rate for a Texereau-style tester is closer to 0.080" or 0.100"+ for Gugolz 55.

Gugolz 73 works well for making optical flats because it's DAMN hard at 65-70 degrees.  The channels close up quite slowly, in 10+ hours of work.  Sometimes they never seem to close!

Note - the hardness of pitch can vary depending on how old it is, how it has been treated, and by who manufactured it and how well they control the hardness in their manufacturing process.  If you are having figuring problems and suspect the pitch, I encourage you to take a few hours and build a simple pitch tester - it will help you identify what hardness of pitch you are working with.

0.21 -  A few lap-making thoughts:

I make my mid-size laps by cleaning the mirror and placing a layer of tin foil over the mirror.  Wrap a wall of masking tape around the mirror, over the foil.  Pour the pitch on the mirror.  WARNING: if your mirror is plate glass, this may cause the glass to crack if you haven't warmed it up gradually to about the same temperature as the pitch!

After pouring, the pitch should flow out to be at least 1/4" thick at the edge of the mirror.  I like a lap thickness between 1/4" and 3/8".  Thicker is fine too, but it requires more pitch.  Before the pitch cools too much, set the tool on the pitch, making sure that one edge contacts before the other.  The tool will "float" on the pitch if it's not too hot.  (If it is too hot, some pitch may be forced upward between the masking tape and the tool.)  Make sure the tool gets into contact with the pitch over its entire surface - this may require you to press down the tool into the pitch using your hands or weights.  Once the tool is in full contact with the pitch, remove any weight you have placed on the tool.  Let the pitch cool, remove the masking tape, and slide the pitch lap off the mirror.  (That operation may NOT be easy, but it will eventually slide off.)

Once the mirror and lap are separated, the foil should peel right off the pitch.  If it doesn't, run some cold water over it for a few seconds and it will.  Voila, we have a lap that will be in full contact almost from the beginning, as long as there weren't too many wrinkles in it.  Channel it by your choice of methods.

0.3 - How to Press a Lap

My motto is "When it comes to pitch laps, contact is everything".  NOTHING will work as it should if you don't have contact.  Here's how I get it.

0.31 - Warm pressing

A warm press is done when a lap does not conform well to the mirror (facets off by 1/16" or more in height), or when you are pressing a very hard pitch lap.  Warm pressing involves heating BOTH the lap and mirror to about 90 degrees in a water bath.  Do it in a clean container, not in a dirty sink.  Use a thermometer or you can easily overheat the water.  If you're using plate glass for the mirror or tool, raise the temperature of the water gradually or you may fracture the glass - you have now been warned twice!  From here on, I'm assuming everything is Pyrex.   Once both pieces are heated, remove them from the water and apply polishing compound liberally to the pitch.  Don't be afraid to wet the pitch and then sprinkle on a little Cerium.  Be wary that a little goes a long way, and don't waste it.  Spread it out with your finger.

You want to get some Cerium pressed into the pitch right now.  Put the lap on top of the mirror, which has also been wetted with some polishing solution.  For an 8" lap, apply about 15 - 20 lbs. to the back of the tool.  After about 10 minutes, I usually remove the weight and separate the lap and mirror.  Then I set the lap back on and add the weight again.  This presses even more cerium into the pitch.  Press for a total of an hour and the lap should be in good contact.  Have a tasty beverage and relax while the weight does the work.  If the pitch is really soft and the channels close up a lot, you are probably done with pressing.  It should appear that some of the polishing compound has imbedded itself in the surface of the pitch over all of the lap.  For Gugolz pitch, which is black in color, this pitch will take on a grey, matte finish, rather than black and shiny.

I use warm pressing when I need to "move" the pitch around a lot.  This technique is dependable, controllable, and quite useful.  Once contact is estabished at the beginning, you shouldn't need to warm press unless you don't use the lap for a while (a week or more).  A lap that requires warm pressing every time you use it is probably TOO HARD.  (Again, that's my opinion, and this is my web page.)

0.32 - Cold Pressing

A cold press is NOT an option before ANY polishing or figuring session - you MUST do it.  Raise your right hand and swear an oath that you will not start polishing without a proper cold press.  Skipping the press is just asking for unpredictable figuring and worse.

Generally, I press with the mirror on the bottom, because the mirror acts like a bowl that retains liquid/moisture better.  Spread some polishing mixture on the mirror surface.  Spritz on some extra water with a spray bottle.  Set on the lap, and add weight.  You will have to learn to judge when the lap is in contact - for a medium softness lap 8" in diameter, intimate contact is obtained at the earliest after 1/2 hour.  Want a full hour if you have any question.

After time has passed, remove the weight and flip the mirror/lap over if you are going to polish mirror-on-top (MOT).  Do NOT separate the lap and mirror.  If the mirror/lap have dried out, decenter the lap or mirror slightly and spritz on the water or polishing mixture.  Gently rotate the mirror or lap to distribute it, and start polishing.

Important - you should feel even, significant drag when polishing.  It should be the same in all directions and parts of the stroke.  You should also feel drag if you spin the lap/mirror - it shoudn't spin like a top!  If it spins easily, that's a sign that the center of the lap is in contact, but not the edge, or that the polishing mixture is too thick.

If you have doubts on lap contact, stop and press, dammit!!  This is less critical during initial polishing when you're just removing pits, but SUPREMELY critical when your are spherizing or figuring.  NOTE:  For strongly aspheric surfaces (F/4 parabolas and faster), the lap drag will decrease as you decenter the lap during figuring.  For the mirrors I'm discussing here, the drag may vary a little during figuring, but not too much.  At any point, slipping/grabbing is a sign of problems, and pressing should be done immediately.  Stopping to press is encouraged - it gives you a break from the labor of polishing, and encourages the formation of spherical surfaces.  Press every 1/2 hour if you like, esepecially later in polishing.  Pressing is often overlooked by those seeking a spherical surface.  Without pressing, the lap shape can get out of control (especially with hard pitch) and the figure will follow!

0.4 - Polishing

For 4"-12" mirrors, I like to stick my palm to the back of the mirror, and push the mirror forward while applying lots of downward pressure through the center of the lap/mirror.  For larger mirrors, you can apply both palms.  A 4" is challenging for anyone with large hands.  Just a little moisture will allow your hands to adhere to the fine-ground back of the mirror (you did fine grind the back, right?).  Another option is to use some of the rubber material that you put in the bottom of drawers that is intended to keep things from sliding.  Try not to apply pressure with your finger tips or the back of the heels of your hands - make the pressure go through the center of the work through your palms.

I will note here that, especially later in polishing, you can often feel when the mirror isn't spherical if the lap is in good contact - the friction will change slightly during the polishing stroke, indicating that the lap and mirror don't mate perfectly for some position.  My most frequently obtained defect is high outer zones (also referred to as TUE, but more than the edge is turned up), and I can feel the just-pressed lap digging into it as the lap moves away from a centered position.  After polishing a bit, this sensation is gone.  This is because the pitch has been pushed up at and inside the edge of the lap, and the edge is not being worked as much.  This is a good time to stop and press, and then work on the TU zones some more.  (Texereau's method of TUE removal has been very effective for me for high outer zones.

Vary the length of your strokes, and the side swing.  The normal polishing stroke is a stroke with a slight W to it, averaging 1/3 the diameter of the mirror (1/3 D) in length total.  Do some longer, some shorter.  For some reason, I get my best spheres with softer pitch, polishing MOT.  If the edge is turned up at the end of polishing, I widen the W a bit to make the center deeper and head towards a sphere.

Trim the lap channels when they get narrower than 1/8" or so.  Keep the edge of the lap beveled.  Try to be neat with trimming.

After about 5-6 hours of polishing an 8" mirror, most of the pits should be gone.  Check the figure with a Foucault tester.  You should begin practicing your testing skills now, and take enough time to learn to take accurate readings.  Others have covered Foucault testing in excellent articles - I assume the reader has attained a reasonable degree of testing ability, and can repeat readings to within a few thousandths of an inch for a moving source tester.

If the edge is turned down (TDE), I encourage some tool-on-top (TOT) work.  Volumes have been written on TDE, and I will let you read them.  In my experience, TDE is from imperfect contact, which is often caused by the lap "riding" on top of a raised defect in the mirror, such as a turned up outer zone (see my oblate sphere page), or a layer of water and cerium oxide that is too thick.  The layer of polishing compound might be floating the mirror, causing the mirror to tip slightly, and planing off the edge.  If the polishing is done without enough water, the lap and mirror can dry at the edge and more wear then occurs there, causing a TDE.  If you press down on the edge of the lap without knowing it, or apply pressures that "tip" the lap or mirror slightly as you polish, this can cause TDE.  So, keep good contact, spray on water when needed, and press down in the center of the mirror.

TDE is different than a longer focus outer zone.  Technically, the edge of the mirror is the outer 1/8" or 1/16".  That does NOT include the outer zone!!!!!  The outer zones are the outer 1-2" of the mirror, and represent a large percentage of the surface area of the mirror.  Starting figuring with outer zones that have a longer ROC than the central zones can actually be beneficial, since some of the edge correction is already done.  If you don't see a diffraction ring all the way around the mirror, chances are you have a TDE.  It should be fixed before figuring.  If the outer zones have a longer ROC than the center, do a zonal Foucault test and evaluate the figure of the mirror.  You might be farther along than you think.  I have started figuring a few times with an outer zone that's on the order 20% corrected, while the edge of the mirror was good.

0.5 - Avoiding scratches

I have never strained pitch.  I reuse it many times until it becomes too hard and then it gets tossed.  Getting pitch hot enough to strain releases much of the volatile compounds that make it soft and useful.

Scratches are caused by:

1) Incomplete polish - particles catch in pits and cause scratches.  The solution is to polish longer and see further causes below.

2) Cleanliness issues - keep laps covered when not in use, and simply wipe the mirror with the edge of your hand before polishing.

3) Poor quality cerium - decant bad cerium or buy better quality cerium.  (I think this is the most common cause.)

4) Hard pitch or poor lap contact - use softer pitch and make sure laps are in full contact.

5) High polishing pressure - reduce polishing pressure.  Often hard pitch and heavy pressure make for lots of sleeks.

Dust falls constantly, but I have never, ever seen a scratch from it.  Laps just absorb it, or it gets carried away by the cerium slurry.  Most sleeks during polish are from poor cerium, I believe.

This assumes a reasonably clean environment.  What is clean to some is not clean to others.  If it doubt, just vacuum a lot and try to avoid having strong breezes blowing through kicking up dust.  Reasonable care must be used here.

You should worry more about the bigger particles that doesn't get airborne.  They have to get on the lap or mirror somehow.  So, just keep whatever is over the mirror clean.  For me that's the machine arm and tool, for polishing by hand that is the hands and arms and sleeves.

1.0 - Figuring a mirror with a full-size lap

In order to start figuring, the following conditions should be met:
1)  The mirror is polished out - no pits can be detected.
2)  You are comfortable with Foucault testing and can get reasonably accurate, repeatable readings.
3)  You know how to analyze data, or are comfortable using the excellent free software available.  (I use FigureXP.)
4)  The lap is in good condition, of acceptable hardness, and in good contact.  This is NOT the time to make a new lap.
5)  The edge of the mirror is not turned down, and the surface of the mirror appears smooth (not rough) under the Foucault test.
6)  There are no major raised areas or depressed areas on the mirror (zones).  A TUE or raised center are okay, in moderation.
Every figuring step starts with a cold press long enough to obtain full contact.  This is not negotiable.  Remember, contact is everything.

Figuring is the process of making a fairly spherical mirror into one that isn't a sphere.  The parabolic shape that we desire is either "deeper" than a sphere in the center, and matching at the outer edge, or "flatter" than a sphere at the edge, and matching at the center.

A non-spherical shape in the mirror implies that the pitch must flow in order to conform to the shape of the mirror once the mirror is decentered from the lap.  While centered, the lap and mirror mate.  As soon as a stroke starts, the pitch must flow to maintain contact, and the action of the lap is not nearly as predictable.  This is why figuring is so mysterious - it's tough to predict just where the contact between the pitch and mirror is the most intimate, and this is where the most action, or wear, is occurring.  Therein lies the art of making optics.

1.1 - Basic strokes - the normal stroke

Let's start with the basic strokes - 1/3 D, COC.  That's a stroke that's a total of 1/3 the diameter of the mirror long, and the centers of the mirror and lap coincide at some point during the stroke - COC = center-over-center.  Some side-to-side motion is fine, the stroke doesn't have to go exactly COC.  There are two varieties of this stroke - MOT (mirror on top) and TOT (tool on top).  Either stroke can be used to obtain a reasonably spherical mirror.

Figuring strokes are SLOW and deliberate, and gentle.  Start and stop the strokes smoothly.  Going too fast will cause the mirror/tool to slip and grab, indicating that you have lost contact.  Slow and smooth strokes are a necessity, and allow the lap to stay in contact and encourage smooth optical surfaces to form.  Smooth is important, particularly if you want to do demanding planetary observing.

When the pitch is reasonably soft and in good contact, and the two surfaces are fairly close to a sphere, the area worked by the lap can be assumed to be most of the mirror, with more wear occurring near the edge of the mirror when the lap is on top, and more wear occurring near the center when the mirror is on top.  Thus, a mirror with high outer zones (often called TUE) may be remedied by doing some MOT polishing to deepen the center, thus shortening its radius of curvature (ROC) to that of the outer zones.  This may be quicker than wearing down the outer zones, and less likely to turn the edge.

 However, when used on a non-spherical mirror, the results are not as predictable.  In general, the overall effect is similar, though.  After a good cold press, MOT normal strokes (not parabolizing strokes) will generally help remove defects near the center of the mirror.  High spots or low spots, such as a raised ring outside the center or even a central hole, can be "smoothed" using MOT normal strokes.  The overall correction of the mirror will DECREASE, though, but this is remedied by switching back to the parabolizing stroke.  Using the TOT normal stroke, defects in the outer zones can often be smoothed.  In general, MOT normal strokes will reduce correction near the center earlier (as the central area is more likely to spherize) than the edge, and TOT normal strokes will reduce correction in the outer zones more quickly than the inner zones.  This is not a hard and fast rule, but I have found it to be reasonably dependable.  So, overcorrecting the outer zones can be remedied by TOT normal strokes.  A hole in the center can be helped by MOT normal strokes.

With the purpose of normal strokes now understood a bit better, it's time to start figuring.  If have started figuring from spheres, from a shape with a raised center and partially corrected outer zone, and from variations of these.  So long as the deviations from a sphere are fairly smooth (no deep troughs) and are only 20% or 30% of those of the ideal parabola, figuring can generally begin, as long as the edge is good.

1.2 - Alternative parabolizing strokes

Below on the left is a picture of Texereau's recommended parabolizing stroke.  On the right is my recommend parabolizing stroke to start with.  Both are done MOT, with slow, smooth strokes.  The line depicts the travel of the center of the mirror over the lap.
Tex Mine

The most common error I see with parabolizing with a full-size tool is polishing a deep central hole into the mirror with little edge correction added.  So, until the worker knows how the lap is going to act, start with the stroke on the right.  This will add more correction in the outer zones of the mirror.  Hopefully, smooth correction will be added from the edge to center.  Center correction is EASY to add by decentering the mirror, and we can do that later, after the edge is in good shape.  I recommend working with the stroke to the right for about 10 minutes.  Keep the mirror/lap wet to slow down the polishing action, and keep the strokes slow and smooth.  The weight of the mirror is all the pressure that is used.  Towards the end of the 10-minute session, you may feel differring amounts of friction when the mirror is centered and when the mirror is offset.  This means the lap/mirror have changed shape, and a cold press will be useful soon.

So what is correction?  Correction is departure from a sphere.  In our case, while all of the mirror surface is being polished, the most glass is being removed near the center.  This means that the central zones will have shorter ROCs than the outer zones.  Starting with the central zone and moving out, each zone has a longer ROC than the one before.  I define the difference in ROC between two zones as the "difference" or "delta".

Example 1.1:
We are figuring an 8" mirror with a full-size lap.  It's of moderate focal ratio.
We are using a 4-zone Couder mask for the Foucault test.  The ideal readings for the Foucault test are:  0.000", 0.020", 0.040", 0.060".  

We note that the total correction is 0.060" - that is, the difference in ROC between the outermost and innermost zones is 0.060".  The difference between any two adjacent zones is 0.020".  (Getting the same "correction", "difference", or "delta" between each adjacent zone is possible by designing the mask openings such that each annulus (ring) has the same surface area.  The mask opening shows a part of this annulus.)

Let's say the stroke I described above works well.  We might see the following readings after doing the Foucault test:  0.000", 0.005", 0.015", 0.030"
Now we compare the differences between the zones (deltas) to the ideal deltas.  The measured deltas are:  0.005", 0.010", 0.015".
Divide each measured delta by the ideal delta (0.020") and multiply by 100 to get the percentage correction.  We get:  25%, 50%, 75%.

If the mirror tested perfect, we'd see 100% for all three.  These percentages represent how much the slopes of the two adjacent zones differ.  The Foucault test measures slope, and in figuring we make the zones have different slopes.  The slopes get shallower of "flatter" as we move out from the center.  As it is, the corrections we measured are higher as we move out   That means the slope differences are greater as we move out on the mirror, and closer to the ideal relationship.  We would say this mirror has more "outer (edge) correction" than "inner correction".  This would be the ideal outcome of using the stroke I described above.  The next step in figuring this particular mirror would be to adopt as stroke that introduced more center correction and less edge correction, and to sneak up on approximately 100% correction in each zone.

Example 1.2:
For the same 8" mirror mentioned above, we take the following measurements:  0.000", 0.015", 0.025" 0.030"
Calculating the corrections (find deltas, divide by ideal delta, multiply by 100), we get:  75%, 50%, 25%

We have a corollary to the case above (Example 1.1).  Now, the central zones have more correction in relation to each other than the outer zones.  (This is a similar to a central hole, but a central hole often occurs when the outer zone correction is near %0.)  In this case, we need to adopt a figuring stroke that corrects the edge more than the center, which has already been described.  Hopefully this can be done without overcorrecting the central zones.  If this occurred, some MOT normal stroke work might reduce it.  Okay, I'm getting ahead of myself.....

Okay, let's discuss the examples.  In Example 1.1, the mirror needs more correction in the center than in the outer zones.  In Example 1.2, the mirror needs more correction in the outer zones than the central zones.  These are two typical results after a couple figuring sessions.  

The goal of figuring is to bring the correction (differences in ROCs between the zones) to the ideal values at the same time.  This is a bit like herding cats, but it can be done, I assure.  The key is to SLOWLY add correction and CONTINUOUSLY adapt our technique.  We'll sneak up on a nice smooth parabola and surprise it by aluminizing it before it can get away!

So why do we use the strokes described above?  Here's the principle involved in parabolizing, and in lots of figuring:  The pitch lap can be visualized as doing most of its work at the edge.  For simplicity, I'll refer to the figure below.  So, when figuring, imagine the indicated parts of the lap working the most on the mirror.  When the mirror is offset to the side, the center of the mirror is nearly over the edge of the lap, where the action is.  Thus, the center is being worn down more than the rest of the mirror.  If the mirror is slightly decentered, the area worked most on the mirror is the area just inside the edge, like the outer zone or two. So, if we modify the parabolizing stroke to have more forward and back strokes when a certain part of the mirror is over the edge of the lap, then that part of the mirror will generally get more correction added than the other areas.  That's it in a nutshell - that is the one guideline that will let you figure a mirror!

Active zone

Now this part of the lap is not the only part that is active and polishing, but it can be a very powerful visualization tool.  If you mark the zones on the back of the mirror with marker, you can easily see when they are passing over the these areas of the lap and adjust your strokes.  This will take practice and adjustment depending on your lap and polishing style, and you will have to observe where the correction happens - it may happen just inside or just outside where you are visualizing it, and this is why figuring is an art, not a science.

Remember that to add correction, you must change the slope relationship between two zones - if you want to increase the correction between zones 1 and 2, then you can "wear away" zone 1.  Then zone 1 has a steeper slope than zone 2, and the correction increases.  If you wear away both zones a much smaller change or no change in correction may occur.

With this "active" lap area in mind, we now understand why the following strokes work to do what they do:

Center correction Correction outer zones

The stroke shown in the first figure may be effective in bringing the mirror in Example 1.1 closer to the ideal parabola.  With this technique, the center of the mirror is over the edge of the lap.  Most correction is added to the center.

The stroke shown in the second figure may be useful for Example 1.2.  Here, the edge of the mirror passes most often over the edge of the lap.  Correction is added in the outer zones, mainly.  Care should be used with this stroke, and a careful watch should be kept for signs of a turning edge.

Well, this may seem like a very short, fairly simple explanation of figuring, but the techniques described above are just about it.  Together with a good computer program to reduce the date, you can make an excellent mirror by following these guidelines:

1)  Try to add correction in the outer zones first.  Test often.
2)  Modify the polishing technique to add center correction once the outer zones are 50% corrected or so.
3)  Try to bring all zones to correction at the same point.  It is much easier to correct the center when the edge is done than to correct the edge when the center is done.  Try to get the edge right first, if possible.
4)  Use a computer program to find the "high spot" on the mirror, and (gently and slowly) wear it away using the "active lap area" visualization mentioned above.

1.3 - Computer analysis programs - A very good thing

Use software that you are comfortable with to produce an error profile of the mirror.  Try to make the outer zone flat - that is, adjust the ROC in the program until the outer zone has zero error.  For an undercorrected mirror, the central area of the mirror will appear high (possibly VERY high), indicating that more parabolization is needed overall to reduce the central error.  Once the corrections are within 30% or so of 100%, take a closer look at the error plot.  It may indicate the high areas are fairly specific - say a high center or a raised 80% zone.  If so, work these areas over the edge of the lap with some side-to-side blending motion to keep the surface smooth.

I have used FigureXP quite a bit and I like it.  The latest version lists % correction between adjacent zones, the same number I used in the examples.

1.4 - Some Final Tips

Don't forget the normal MOT and TOT strokes.  If you get in a situation where the correction is high, then low, then high as you go from the center of the mirror to the edge, you have a "kink", as Zambuto has called it.  A kink can also have low, then high, then low correction.  The first type (high-low-high) indicates a raised area.  The second (low-high-low) indicates a depressed zone.  These should show up on the error profile.  These kinks can be reduced by applying one of the normal strokes.  If the kink is near the outer edge, do TOT.  If it's near the inner edge, do MOT.  Overall correction will decrease, but you will have a smoother mirror, and you can just start back in with parabolizing.  The normal strokes are a "soft reset" or "undo" button.

Don't be afraid to go back towards a sphere - it will help you out.  Usually the tough problem that you're avoid will be replaced by a simpler problem, like a high center.  Also, you don't have to go all the way back to a sphere - you can just back off the correction (anywhere from 20% to 80%) until the problem is gone, and then start parabolizing with a MODIFIED technique, based on your figuring experience and how you think the lap and surface will react.  Continuous adjustment is the key.  Take it slow, back up if necessary, press often, and you will eventually progress to a good figure.

1.5 - Example mirror, 6" F/6 mirror figuring log

After this mirror was polished, high outer zones remained.  A good amount of TOT work was done to remove it.  When I started figuring, the outer zone had about 0.010" of correction in it already, and the edge was good.

For figuring, I use a slow-acting refined Cerium oxide.  Decanted Cerium or Rouge would work fine too.  Also, only very light pressure was applied to the lap.

The pitch lap was fairly soft - 0.086" of fall were measured for a 1 kg mass in 5 minutes.  Temperature was 68 degrees.  Pitch was Gugolz 55 and some harder pitch mixed in.

Step 1:  15 minutes of my standard parabolizing stroke (not Texereau's), with less center emphasis.  Also, shorter strokes when going COC to avoid further correcting edge at this point, since it already has some correction.  For the following Foucault readings, R = reading of KE position, R-R1 = reading minus first reading, and ideal is the ideal KE reading for a perfect parabola, all in thousandths of an inch.

Foucault readings:   Zone #    R     R-R1  Ideal   Correction
                       1       88      0      0      
                       2       92      4     17     Z1-Z2: 24%
                       3       99     11     32     Z2-Z3: 47%
                       4      109     21     46     Z3-Z4: 71%

So, we observe that the outer zones are more corrected than the inner zones.  This is fine, since the center is easier to correct.

Step 2:  10 minutes parabolizing stroke, with a bit of extra action for center of the mirror, that is, when the mirror overhangs most.

Foucault readings:   Zone #    R     R-R1  Ideal   Correction
                       1       65      0      0      
                       2       81     16     17     Z1-Z2: 94%
                       3       90     25     32     Z2-Z3: 60%
                       4      104     39     46     Z3-Z4:100%

This step produced full or nearly full currection between zones 1 and 2 and between zones 3 and 4.  The correction between zones 2 and 3 is lagging.

Step 3:  Go to short normal strokes to widen central hole and generally reduce correction, and even it out.  Do 1/6 D strokes with a little side swing for 6 minutes.  Do 5 minutes of parabolizing strokes afterward to add a little correction back..

Foucault readings:   Zone #    R     R-R1  Ideal   Correction
                       1       50      0      0      
                       2       63     13     17     Z1-Z2: 76%
                       3       72     22     32     Z2-Z3: 60%
                       4       85     35     46     Z3-Z4: 93%

All zones reduced, but this effect was the most pronounced in the center zones, since we did MOT.  Need to add correction outside of zone 1, in zones 2 and 3.

Step 4:  8 minutes of normal parabolizing strokes, with some emphasis on zones 2 and 3.  That is, when zones 2 and 3 are over the edge of the lap, more forward-and-back strokes were performed.

Foucault readings:   Zone #    R     R-R1  Ideal   Error  Correction
                       1       65      0      0      0 
                       2       81     16     17     -1    Z1-Z2:  94%
                       3       90     30     32     -2    Z2-Z3:  93%
                       4      104     45     46     -1    Z3-Z4: 107%

FigureXP shows ~1/30th wave P-V on the wavefront.  Surface is smooth, and edge is good.  Slight work on the transition between zones 3 and 4 could improve the figure, but at some risk.  Alternatively, the normal parabolizing stroke, avoiding working the center, could improve the numbers slightly.  Working time would be a minute or two.  This mirror is done.

Well, there's the process of figuring a moderate F-ratio mirror in 4 steps.  This mirror lives in my travel scope.  It is a good planetary performer.  F/6 is a good compromise for this size mirror if you want to observe planets and deep sky.

Hope this example was helpful.  Here's a link to the FigureXP file for this mirror.  Right click to download the file ("save link as").

            Clear skies and happy figuring,

            Michael Lockwood

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