From: "Herb Kasler" 
To: "Jerry B. Hillman" ,
        
Reply-To: "Herb Kasler" 



Jerry,

Although I can't say with certainty, since you did not post (at least as
far as I can tell) the line frequency of your Ronchi grating, I would say
that your mirror is unfortunately still not on the road to parabolization,
and that there's as yet little point in spending hours trying to get good
Focault numbers on it, unless you just want to learn how to use your
tester. What I see when I look at your ronchigram is a flat center and an
overcorrected  (i.e. turned-down) edge. The Ronchi lines should not hook
inwards like that as you approach the edge of your mirror. That is, the
degree of inward slant of the lines should not increase towards the edge.
In fact, for a short focal-length, large mirror like yours, the lines
should actually become more parallel as you approach the extreme edge. It
also looks like the center of your mirror is undercorrected, as the line on
the right, which crosses the mirror closer to the center, looks pretty
straight in the middle to me, but that is a very minor problem. Having been
in a similar situation myself, I would have to say that your best bet is
probably to go back to a sphere and start over, because you will likely end
up with a bad 85-95% zone if you proceed from from where you are now, and
that is maddeningly difficult to fix. I wasted a great deal of time trying
to do it before giving up. Once your edge is overcorrected, getting a
zone-free figure back is really, really hard.

 In general, it will also be much easier for people to give you a more
precise evaluation of your surface if you

    1) post the line frequency of your grating along with the other data,
and

    2) post pictures in which there are a total of 6 dark bands on the
mirror surface. That will
        allow evaluation of the whole surface.

My guess as to why you might think what you've got now is good enough to
start taking zonal measurements would be that either:

1) After looking at all those earlier, grossly zony, "peanut"
ronchgrams, you (understandably) feel that any apparently smooth figure is
better than that. Unfortunately, that is not true. If your edge is severely
overcorrected, you would be better off with a sphere.

or

2) You don't have a picture of exactly what your ronchigram for a
well-parabolized mirror should look like, so
    anything with lines that curve in the right direction looks good.

If it's the latter reason, don't do another thing before you go here:
http://members.aol.com/RonWin20/  and download Ronwin 2.0. It is an
excellent utility for generating pictures of what your mirror should look
like on the Ronchi tester when its finished, overcorrected, or
undercorrected. You don't actually need to worry about exactly where your
ROC is when you compare the picture at different offsets. Just get it to
where it looks as close as possible to one of the pictures, and then assume
that is the right offset. Then move back and forth from there and evaluate
how close to the pictures from those offsets you mirror looks. If it stays
really close, than you're in good shape. If it changes too quickly or too
slowly, then your mirror is either over- or undercorrected.

As to evaluating zonal errors, the point is that the shape of the lines
must be *exactly* what the picture looks like. There is no fudging the
details here. For a mirror of the size and focal length or your mirror,
there is no point in starting to generate numbers before you really, really
can't tell the difference between the computer program output and your
mirror. For smaller, longer mirrors, a good Ronchi test might be enough,
but for bigger, faster mirrors, you could easily be as much as a wave off
and still not be readily able to see any difference. With the Focault
tester, after some practice, you should be able to get this down to 1/4
wave or better, which will allow you to make a decent mirror.


And on the subject of star laps, perhaps a little bit of clarification
would be helpful. When you parabolize with a star lap, you don't use it the
same way you use a normal lap. The classic "Texereau"  method of
parabolization with a full-sized lap involves taking the shortest route to
a parabola from a sphere by both digging out the center and planing down
the edge. This is illustrated by figure 2-2b in Texereau. You do this by
using short strokes out to the side and long strokes in the middle, with
large overhangs of the tool. This way,  you do it with the removal of the
least amount of glass possible. You also stay at exactly the same ROC. But
(especially for big, fast mirrors) it is very hard to control this method
of parabolization. It is really easy to turn your edge in the process of
trying to reduce it. Just a little too much overhang, or hand pressure on
the wrong part of the tool, and you're sunk. For that reason, most people
working on larger mirrors use a slower, but much surer way of approaching a
parabola. In fact, it is almost never really slower, because the time and
effort required to remove the glass is practically never the limiting
factor. It is the number of times you have to start over because it went
wrong. What you do is rather than trying to keep the ROC the same and
remove as little glass as possible, you try to remove the glass in the
best-controllable way possible, and that means you take it all out of the
center. This is illustrated by figure 2-2a of Texereau. It is MUCH easier
to control how you remove glass from the center than how you remove it from
the edge. This is because you never have to work with large overhangs, and
so there is no danger of inadvertantly leaning on your tool the wrong way
and shaving 9 waves of glass off of the outer edge of your mirror. This
will slightly shorten the ROC of the final product, but not enough to make
a difference in the design of the OTA. It will also require the removal of
roughly 4 times more glass, but that is really not a big consideration. For
my 16" f/4 (BVC-so a little softer and quicker) mirror, using a
10" tool with rouge, I got the figuring done this way in a little
under 40 minutes of total work on the mirror. This was done in quite a few
progressively shorter steps, starting with around 20 minutes, and going
down to about 1 minute at the end.

So basically with center-parabolization, the idea is to dig the most glass
out of the very middle, and take out progressively less glass towards the
edge, tapering down to nothing at the very edge. Of course in reality, you
don't actually remove no glass from the very edge, but you remove the
least, and so you never have to monkey around with big overhangs, which is
where you usually get into trouble. This is where the star lap comes in.
The idea of the star lap is that by tapering down the surface of the tool
that is in contact with the mirror into several points, you create a tool
that removes progressively less glass from the outer part of the mirror
than from the center. By controlling the degree of taper of the points of
the star, you can precisely control how much the rate of glass removal
tapers towards the edge. A blunt star will remove more glass from the edge,
and a very pointy one will remove less. For a 10" tool, you would do
this with an overhang that never exceeds 2.5-3" inches, so as long as
you keep your hands off the outer edge of the tool, you will never send
your edge into oblivion. It is also very unlikely that you will generate
"wavy" zonal errors, since the taper of the star points naturally
generates a smooth figure. It is possible to dig a hole in the center this
way, but that can be fixed easily.

This converts the process of parabolization from a very tricky motor skill
which takes everyone a long time to learn into an intellectual excercise
that a reasonably smart person can grasp very quickly. I have not used the
program that Jim Burrows pointed you to myself, but have rather determined
how to taper the points empirically. If the edge is going down too fast,
make the star pointier and use less overhang. If the center is reducing too
quickly, make the star blunter, avoid the center and overhang a little more
(but not too much!). If you are still digging out the center too much, you
can even put  an inverse star into the center of your lap so as to create
an annular zone of contact that will leave the center untouched. Also, you
don't care about the middle 3-4" of your mirror, since they will be
behind the secondary, and contribute very little to the RMS error besides.

So how do you make all these star laps? You just cut the pattern you want
out of some thick plastic sheeting ( I used several layers of Ziploc
freezer bag), and then warm-press it into your lap against the mirror
surface. This will allow you to rapidly generate as many different patterns
as you will need from the same tool. I must have used at least half a dozen
patterns in the final, successful figuring of my mirror. You can verify
that the zone of contact is the right shape by applying the tool to your
mirror with some rouge, swishing it around a little, and then pulling it
straight off. You should see your star on the mirror surface, painted in
rouge. Depending on the hardness of your pitch, the star pattern will only
last 10-20 minutes, but you should never go longer than that in one step
anyway.

There you have it. I have spent the better part of my morning spelling out
for you a methodical strategy for parabolizing your 16" mirror. If you
take the time to fully understand what I have told you, you will be able to
succeed despite your relative inexperience. My 16" mirror was the
first one I made, and it's pretty decent as far as I can tell. Someday, I
will be able to do a real star test on it.... The 3-4 mm of TDE that it
still has are residual from my earlier, botched figuring attempts. They are
still there because I didn't have the willpower to spend another sweaty
hour polishing them out before my final figuring. It's too bad, I kind of
wish that I had now. If I had either done that, or had started out doing
what I did in the end, which is what I described to you above, I would be
the proud owner of a mirror with a nearly perfect edge, and I wouldn't now
have to take a Sharpie marker to its beautiful, shiny surface after I clean
it.


Good luck,


Herb.

--- BBBS/NT v4.00 MP