ATM 'Frozen' liquid mirrors

[CHEN@uit.gsfc.nasa.gov]

Hi folks:

         Thanks, everyone, for the comments and suggestions.  As
I expected all along, the ATM community has enough experience and
ingenuity to tackle just about any problem.  I am optimistic that
we will soon be able to lick the problems of spincasting
astronomical quality epoxy mirrors. 

Mr. Augello, I like your tennis ball idea.  I'll give it a try. 
I am also very envious of your Maplenoll air bearing.  You don't
happen to live within a day's driving distance to Baltimore, do
you?

Mr. Pfaff, your comment is thought provoking.  I wonder why I
haven't come across any publication on making epoxy optical flats
this way.  I looked over my samples carefully.  The flats are
smooth with millimeter scale bumps.  The spincast samples are 
smoother, no bumps, except for the tiny ripples spiralling out
from the center in a regular pattern.  I can think of two
possible explanations. The first is that the spinning gives a
smooth airflow over the top surface and maybe more even cooling. 
The second is that a particle in a spinning fluid is held in
dynamiical equilibrium.  No matter where a small disturbance
occurs, the centrifugal, viscuous and gravity forces will try to
push it back into position.  A  particle in a flat liquid, on the
other hand, is only in static equilibrium.  The restoring forces
are much weaker, especially in the horizontal direction.  As the
epoxy cures and generates localized heating, the heat is smoothed
out over a spinning surface but causes bumps in a static flat. 

     Another observation is that the bottom of the epoxy, where
it contacts the container, is very much smoother than the top. 
This is of course a no-brainer - that is how replica gratings
have been  made for several decades.  As an aside and for those
not familiar with this subject, it is very difficult to make
machines that can rule very closely packed, very straight lines
in a diffraction grating.  Gratings had therefore been very
expensive. It was discovered early in this century (I think) that
copies of a master grating could be made by laying epoxy on it,
cure, and then separate and put on a glass support substrate.  A
single master can in this way be used to make many high quality
replicas, thereby reducing the cost of spectrographs. 
Incidentally, the availability of affordable replica gratings
made possible widespread observation and analysis of stellar
lines.  Analysing line profiles and strengths in stars forms the
basis of the field known as astrophysics. 
  
   I have come across literature where epoxy was used to
replicate ultrasmooth (about 3 angstroms rms, if I recall
correctly) surfaces.  So the bottom line is, if you already have
a flat smooth surface, it is not difficult to produce an epoxy
replica. But if you want to make a flat with epoxy in a dish,
then it will be necessary to attack the problems of vibration and
even cooling.  


      Just out of curiosity, I set up a couple of 8" glass dishes 
atop a sandbox supported by some partially inflated bicycle inner
tubes from K Mart.  I put water in the dishes and watched the
reflection of overhead lights on the surface.  The images move,
despite my best efforts at vibration reduction.  I cured some
epoxy overnight.  The surfaces are definitely better (fewer bumps
and ripples) than previous samples done without damping.  However
they are not perfect flats.  I take this to mean that making
static epoxy flats will really require very precise vibration
isolation and even cooling, more so than spincasting.    

      Regarding your comments about large spincast glass mirrors
have ripples on the surface.  As you correctly point out, the
ripples are caused by uneven cooling and surface tension.  This
effect is unavoidable in any type of phase transition where
typically the cooling occurs at the surface and propagates into
the bulk of the material. Freezing water, for instance, would not
give a smooth surface.  (Same goes for aluminum, Mr. Gwinner, by
the way).  Spincasting epoxy circumvents this problem by using a
chemical reaction that causes solidification at a uniform slow
pace throughout the material.  This is achieved by appropriate
choice of curing agent, temperature, and by doing it in small
batches. 

      Another point.  Spincast glass can be non-smooth because it
can be polished after cooling.  Epoxy on the other hand is a
softer surface that, as far as I know, does not take a polish. 
The effort is therefore to make the epoxy  mirror as perfect as
possible coming off the mold.  As I mentioned in an earlier post,
previous workers came close to it but could not lick the problem
of a vibration free turntable. Nowadays, as the liquid mercury
folks have shown, the problem can be solved.

    Mr. Cooper, I would very much appreciate a reference for that
Home Shop Machinist article detailing how to make an air bearing. 
I am not much of a machinist, but perhaps some of my more capable
fellow amateurs can make use of it.

    Mr. Foster, I like your (and Bryan Leenheer's) idea of a
container floating in a liquid and driven by magnetic coupling. 
That sounds like a good way to do spincasting if an air bearing
is not available.  Based on my experience, the container will
need to have fins on the bottom to couple to the fluid motion (as
Ken has also pointed out).  Otherwise, since the rotation is so
slow (a few rpm), the centering forces are very weak and
disturbances will cause the container to oscillate about the
center of the rotating fluid. 

    Do you have any suggestions on implementing the magnetic
coupling?  (Question to Andy also). I had thought of using a
magnetic stirrer but they are usually made for higher speed.  I
may be able to use a slow rpm motor turning a bar magnet outside
the vessel, with another bar magnet inside churning the liquid. 
(Maybe one of those cow magnetc from Edmund Scientific, coated in
epoxy or teflon).  A more elegant way would be to use a magnet
inside the liquid and an external set of induction coils to turn
it.  I wonder if anyone know of any plans for a setup like that.

    Ric, thanks for that post about an electrical fluid shock
absorber.  It sounds like an interesting subject.  Can you find
the reference?  The subject also jogs my memory about electro-
and magneto-rheological fluids.  NASA has used a technique to
move fluid in zero g in space for many years.  Some very fine
magnetic particles (iron, usually) several tens or hundreds of
angstroms in diameter are dispersed in a non-conducting fluid. 
The particles are specially coated so that they do not coagulate
and precipitate out, but stay in the fluid and participate in the
Brownian motion. Application of an electrical or magnetic field
to this 'ferro-fluid' then causes it  to move back and forth
under control.

    Some astronomers in Italy suggested using s similar technique
to control the surface of an electrically conducting fluid such
as mercury.  By passing a current through the mercury and then
applying a magnetic field, it is possible to cause local bumps
and depressions in the surface.  In other words, making an
adaptive mirror that can compensate for phase changes in
starlight caused by passage through the atmosphere.  They have
demonstrated the principle in a laboratory setup, but no actual
observations that I am aware of.  I had pondered at various times 
whether the same technique can be used to make axis-symmetric
changes in a rotating liquid epoxy surface.  One should be able,
for example, to rotate a liquid mercury into a parabolic surface. 
One can then apply a current and a magnetic field to modify the
parabola into a hyperbola, for instance.  A layer of epoxy on top
of the mercury can then be cured to take the shape.  The result
would be spincast Ritchey-Chretien telescope secondaries
(directly) and primaries (by replication).   Well, it's a
thought.      

    Mr. Schwartz, your suggestion of a photocell bridge circuit
for speed control is interesting.  It certainly seems more
elegant than my current system of reflective object sensor +
pulse counter + microcontroller.  However I have trouble
visualizing the setup.  Can you please give more details?  I am
thinking of a motor driven platter containing a fluid.  Where do
the sensors go?  Are you looking at the vessel horizontally or
vertically?  Please comment.

    Andy, you mentioned that your company makes ceramic bearings
of extraordinary roundness.  Can you tell me where to get them? 
They may be useful for spincasting.  Do they have enough
reflectivity to serve as reference surfaces in interferometers ?

    Your post also suggested using boron nitride to promote
conduction and even curing.  Can you give us some info on the
advantages of boron nitride?  I am aware that glass microspheres
are usually used to reduce shrinking in epoxies, and powdered
silver for electrical or thermal conduction.  The use of
additives, of course, usually adds texture to the epoxy surface
and gives it a rougher appearance.  On the other hand, since
epoxies are usually cured in thin layers, maybe only the topmost
surface needs to be additive free.

    Once again, thanks again everyone for your input.  Happy
spinning.


Peter C. Chen,
chen@uit.gsfc.nasa.gov
homepage http://snoopy.gsfc.nasa.gov/~lunartel/lunar1.html