Figuring a Fast Meniscus Mirror

In traditional ATM stages, figuring a sphere into a paraboloid is the last hurdle before having a completed mirror, and that hurdle is really just a speed bump. It is important, to be sure, but it usually only takes a modest amount of time to complete, and is well described online and in print. Figuring a fast meniscus mirror, on the other hand, is a completely different beast, and this post will discuss the issues related to it in depth.

It all leads to this. I was obsessed by process to get here, not fully appreciating how long I would be here.

The issue of a meniscus

Before getting too far into the details, let’s address the issue of figuring a meniscus vs. a traditional blank. If you have been following along, you have thin, polished out, nearly spherical meniscus that you are going to figure to your target focal ratio. Regardless of figuring technique, the key considerations introduced by the thin meniscus are:

1. The thin mirror allows you to easily work with the mirror on top of your figuring lap, giving you very fine control of pressure. But also, having the mirror on top means you don’t need to worry about adequately supporting the mirror to prevent flex while figuring with a heavier tool on top.
2. The thin mirror heats and cools rapidly. That means that you need to allow for a bit of time after a figuring session, and handling the mirror on your test stand, before doing figuring tests to allow time to cool. But it also means that the time is very short (minutes), because it cools very quickly.
3. Care must be taken testing a meniscus because it is less stable due to the curved back and can easily tip off a test stand or rig.

Beyond these considerations, a meniscus is not that much different from a traditional mirror. The real issues come from the fast focal ratio that typically comes hand-in-hand with the meniscus.

The issue of focal ratio

Figuring a mirror that is f/3 or faster is at least an order of magnitude harder than figuring an f/6 mirror, because the amount of correction needed to be put into the glass is roughly 10 times as much, and the precision of that correction over the entire face of the glass is also correspondingly higher.

Using Mel Bartels’ online Ronchi calculator, one can readily see the amount of work required to figure a mirror at different focal ratios, measured in “waves of correction”. For a 12″ mirror at f/6, 2.5 waves of correction must be applied to a spherical mirror to properly parabolize it. For that same diameter at f/3, 19.7 waves of correction must be applied. At f/2.6, 31 waves of correction are needed, or 12.4 times more correction than f/6! This assumes ideal polishing conditions, and does not account for the human factor where mistakes can lead to even more effort.

Testing correction at faster mirror speeds also presents problems, since the curvature is much more pronounced and, consequently, it is much harder to read shadows precisely using the traditional ATM technique of Foucault testing. Fortunately, Mel Bartels has found that using the Matching Ronchi (described below) test is much more amenable to fast mirrors, with the happy side effect that it is much easier to perform than the Foucault test.

To be fair, recent advancements suggest two alternate tests that would be equally favourable to fast mirrors, although neither were used for this project. The first is the Unmasked Foucault test, which takes the guesswork out of determining zones on a standard Foucault test and puts that work into software. I found it challenging to take sufficiently clear images for that test to work, but others have been more successful. The other test, probably the best choice moving forward, is the Bath interferometer test. This test allows for a precise profiling of the mirror face using reasonably inexpensive test equipment. While the testing is more involved than a Ronchi test, the output is much deeper and can be more useful for corrective action.

As a final note here, I should also mention that the Foucault test does provide some very useful output, even for fast mirrors. The shadows produced in that test give an excellent indication of surface roughness, indicating when a figuring technique is “digging”, or your lap is producing very uneven wear, or you have an unnoticed scratch.

The figuring process (a)

The figuring process, in a nutshell, is designed to selectively modify a spherical surface so that it becomes a paraboloid. There are a number of techniques for doing this that, in my mind, boil down to two approaches:

1. Modifying the mirror centre and then pushing that correction out to the edge of the mirror.
2. Modifying the edge and work it inwards to the centre.

At the risk of oversimplifying, approach 1 can be called the “Mel Bartels” approach, and approach 2 can be called the “Carl Zambuto” approach.

The following graphic illustrates the parabolization options:

As has been the case throughout this project, I followed approach 1, which I will detail below. In broad terms, however, the figuring process involves many sessions using modified polishing strokes to selectively remove glass, and, between those sessions, taking Ronchi images that are compared to theoretical results to qualitatively measure progress. In some cases, polishing may be further modified by changing the lap itself, pressing out regions to force the action to selected locations, to fine tune the correction. When the matching test is virtually undistinguishable from perfect, star testing is then used to put finishing touches on the figure, and then the mirror is done.

In broad terms.

The Matching Ronchi test

As noted above, the Matching Ronchi test is a fast and accurate way to assess progress during figuring. It involves taking a Ronchi image and matching it to a theoretical result to determine how much correction has been put in, and how much still needs to be done (and where).

It may sound complicated, but it is actually surprisingly easy to do. A Ronchi tester is not any more complex than a Foucault tester, merely replacing the knife edge with a “screen” of tightly spaced lines. The screen generates an interference pattern on the mirror face, which is then photographed and the image overlaid with predictions. Because the patterns are very distinct, and the eye is very sensitive to deviations, it allows high degrees of correction to be empirically measured.

In the image above, you can see the actual results “behind” the sharp, partially transparent, lines of the theoretical result. Where the lines don’t match up exactly, more correction may be needed. What is particularly nice is that Mel Bartels Ronchi calculator does the overlay automatically, including zonal guide lines, so testing and evaluating is very, very efficient.

A key to using the Matching Ronchi test accurately is to have a very accurate measurements of your mirror parameters, including diameter and focal length, as well as a reasonably precise measure of the “offset” for the Ronchi image. Like Foucault, Ronchi images are taken at various offsets from the radius of curvature (RoC) of the mirror. The further away you are from RoC, the more lines are produced on the Ronchi image. The goal is to have approximately 8-10 lines to match against, so the offset should be picked accordingly and then input into the calculator. You can also use the calculator to dynamically adjust the offset and find a “best fit” for your results, in effect having a floating RoC that best matches your current correction. While not always appropriate, it can be useful at the end of the figuring process.

The figuring process (b)

With the basics out of the way, let’s dig into the actual figuring process that was used. Recall that the “Mel Bartels” approach is to work from the centre of the mirror, outward. So the technique is to “dig a hole” in the middle of the mirror, and then push that correction outward.

The digging is done using a variation of the classic mirror-on-top “W” stroke used to parabolize traditional mirrors, but making the strokes very wide. In fact, you want the middle of the mirror at the edge of the lap at either side of the stroke. And, because the stroke is so wide, a simple “W” is not enough, so I would characterize it as “vVv”. Note that the middle part of the stroke is longer (a capital “V”) as compared to either side. Doing this “vVv” in combination with the traditional “spin and walk the barrel” will dig a hole in the middle of the mirror pretty quickly (an hour or two).

The goal at this first stage is to generate a “pinch” in the Ronchi lines, indicating the middle is deeper than spherical, like this:

It will take several hours of the “vVv” to get a sufficiently deep hole (depending on your mirror size, of course). As with all figuring, you MUST break your work up into small sessions of, initially 30 minutes or so, to allow the effects of the session to be assessed. Towards the end of the figuring process, each session could be as short as 1 minute.

Once there is a decent “pinch” to the Ronchi lines, the stroke then changes to a long centre-over-center (CoC). Ordinarily, a CoC stroke tends to make a mirror spherical but, in this case with a depression in the centre, it has the effect of “pushing out” the correction to the edges of the mirror. Note that by “long”, I mean 50-60% (so a 14” mirror should move forward and back 7-8”). While doing this long CoC, sometimes the centre will flatten out too much. To counteract this, you could introduce a slight “W” to the stroke (or more if it is very flat). The ultimate goal here, though, is to get the entire surface roughly parabolized, meaning a reasonable qualitative match to the Ronchi from centre to edge. Here is an image in the early stages of this, showing nice smooth lines:

It is important to note that breaking up your work into sessions is not only necessary to monitor progress. It is also necessary to allow you to regularly press your lap: warming it and using your mirror to adjust its curve. This is because fast mirrors are highly aspheric, and you want your lap to follow along as its curve changes, or you will get unpredictable results. Because this is done so often, I wanted an efficient way to heat my lap, and so invested in a heat gun. Once you get the hang of how to not completely melt your lap, it becomes an indispensable tool.

With rough parabolization in place, the process unfortunately becomes more ad hoc, as corrective action will depend on exactly what remains to be done and so cannot be easily written down. However, in general the process involves:

1. Identifying the most significant deviation from perfect using the Matching Ronchi test.
2. Perform targeted corrective action at that deviation, using very short sessions to ensure that the intended effect is being done.
3. Measure, and repeat (2) until the deviation is corrected.
4. Go back to step (1) until the mirror is as near perfect as possible, keeping in mind that at some point, correcting a deviation is more likely to introduce more side effects than the correction warrants.

Mel Bartels also has a very useful “pitch lap calculator” that allows you to predict where the most action is for a given stroke size, shape, and pitch lap configuration. This is particular helpful if you take the advanced approach of “shaping” your lap.

Keep in mind that CoC strokes will tend to flatten correction, and “W” strokes will tend to put correction into the surface roughly the width of the “W”. It is around this time that you need to be particularly mindful of a turned-down edge, which is overcorrection at the edge of the mirror. This is notoriously hard to correct but has, in practice, not been an issue for me. Lastly, you need to strive for keeping the Ronchi bands smooth at all times. A “kink” in a band, aside from being an obvious defect, is equally notoriously hard to correct, and THAT is speaking from experience.

Lap shaping is a technique where you cut a shape out of paper or Bristol board, and press it into the surface of your warmed lap. The effect of this is to contour the surface so that it deliberately wears against the glass unevenly. This enables you to correct some parts while leaving others untouched. Note that in most cases, the impact of a lap shape is not at all obvious when coupled with a particular stroke, which is why the calculator is so helpful. Also, shaping laps can dig unwanted features into your glass very, very quickly, so you must use these with short sessions and look at your glass carefully after each session. This is one case where using Foucault to assess surface roughness becomes particularly useful. The image shown above was the direct result of a shaped lap that had sharp points near the centre, causing a horrible rippling effect.

As a final point, you should note that parabolization is reversible. If you mess up (and you probably will, at least once) you can revert to a spherical surface by simply doing 30% CoC strokes. It will probably take about 10 hours or so, depending on how much correction you had, but it allows you to “undo” and try again. Speaking from experience, it works, and allows you to fine tune your parabolization process, whether you want to or not. For this mirror, initial parabolization attempts took a very long time but by the end I could figure the mirror in about 15 hours.

Star testing

While the matching Ronchi test is a highly sensitive and simple test to administer to assess your figure, the “gold standard” for measuring mirror performance is the star test. As with much of what I have described, there are plenty of online and print resources that discuss star testing. The essential points for this project are:

1. Subtle issues not easily seen in the matching Ronchi test are more obvious in a star test.
2. Fast mirrors require a star test rig that is sturdy enough to hold collimation precisely.

The latter point is particular significant because fast mirrors are notoriously sensitive to collimation errors and if your test rig is a quick-and-dirty type that doesn’t hold collimation particularly well, then it will be hard to assess whether a particular defect you are seeing is related to the mirror or the rig.

In the end, my collimation test rig was my final optical tube assembly. I tried making several rigs but could not eliminate collimation errors to my satisfaction and then decided that rather than spend more time engineering a better rig, I would just build the OTA and test there. That was not before a disastrous result that I will now share.

The final mirror for this project is a v2 mirror. The v1 mirror was completed right to star testing, but the test rig I had fashioned was missing a vital element: a tip clip. During star testing the rig was accidentally moved in such a way as to allow the mirror to tip out, fall to the ground, and break in two:

It was a tragic end to, at that point, 18 months of work and 150 hours on the glass alone. After a few weeks of recovery, I decided to glue the pieces together to use as mould for a new slumping form, and in less than six months had a new glass slumped, ground, polished, and figured.

In my estimation, the v2 mirror is not quite as good as the v1 from a matching Ronchi perspective, but nonetheless is giving really good results. Here is a sample star test image, to conclude this section:

While a proper star test involves actively comparing images while focusing in and out, the image above shows a number of desirable features, such as a nice round image and diagonal shadow with no obvious signs of pinching. The linked video shows good symmetry moving in and out of focus, with no sign of astigmatism, and reasonably good “diagonal breakout”. The bright ring in the image at about 80% seems to map to a non-smooth bend in the Ronchi image, but in practice that does not seem to have affected mirror performance, being one of those cases where trying to fix a defect could lead to greater defects.