Oblate Spheres - Why do they form and how to get rid of them

Copyright Michael E. Lockwood, 2006-present

When polishing out a mirror a common shape to arrive at is an oblate spheroid, which is basically a figure that has a longer radius of curvature (ROC) at the center of the mirror and shorter ROC as you move toward the edge.  The shape is kind of like a dinner plate - shallow curve or fairly flat in the center, and curving upwards at the edge.  This is due to polishing techniques that are not quite correct.

There is no problem with having an oblate sphere - the real problem lies with the turned-down edge (TDE) that often accompanies the oblate sphere and which will not go away until the oblate condition is fixed!  The TDE is caused by the pitch lap riding up the "rim" of the oblate sphere, and knocking off the edge.  This TDE is strictly a function of the shape of the mirror - there is nothing wrong with the pitch.  Fix the mirror's shape and the TDE will go away naturally with normal polishing, provided the polishing technique is modified a bit to keep the mirror spherical and keep from forming another oblate sphere.

Below is a picture of what is going on.  Working tool-on-top, if we imagine pushing the lap to the right, the leading edge is the right edge, and it digs into the surface of the mirror, polishing away the mirror to the lower line (scale greatly exaggerated).  After the edge of the mirror passes the edge of the tool, we see why the TDE is generated.  This is illustrated on the left side of the figure.  If the stroke is going ot the left, the lap is resting on the central portion of the mirror and the edge.

off center

The surface area of the edge of the mirror is FAR less than the area of the center.  Both support the weight of the lap, and the polishing pressure applied by the operator.  The result is that the edge wears away MUCH master than the center, leading to a TDE.  Why does this condition form?  Because many mirror makers (myself included) realize that the contact of the lap feels better if we push down on the leading edge of the lap a bit as we move it away from us.  This causes the lap to dig in, and creates a low spot inside the edge of the mirror.  This condition is self-perpetuating, and pretty soon a bad case of oblate sphere has developed.  If the mirror maker has listened to the advice of those who say "don't test until it's polished" then he/she may be in for a nasty surprise in the form of an oblate sphere and bad TDE.  Therefore, I recommend testing throughout polishing to see what is happenning.  If an oblate is forming, take steps to remedy it.

So how do we correct the condition?  The tendency of the lap to dig in must be stopped.

Working TOT, usually I just try to apply slightly more pressure to the trailing edge of the lap (not the leading edge).  That is, while pushing the lap away from me, I apply a little more pressure with the heel of my hand.  When pulling the lap back towards me, I apply a little more pressure with my fingers.  With pressing and polishing time, this will help.  You may need to stop and press the lap every 5 or 10 minutes, and your hands may get tired from this technique, but it works.  This method also should naturally remove the TDE since the outer area of the mirror is being worked - the TDE should be polished away along with the raised rim of the mirror.

Working mirror-on-top (MOT) with uniform pressure and possibly strokes a little longer than 1/3 D will also generally help.  (You would think that applying slightly more pressure on the leading edge of the mirror while working MOT would help, but this can be a dangerous habit that can lead to a turned edge, so I don't recommend it.)  More side-to-side motion in the stroke may also be necessary.  The thought here is to deepen the center and help blend the zones into a sphere.  If you think this is similar to parabolizing, you're right!  However, working MOT will generally not remove the TDE nearly as fast as working tool-on-top (TOT).  More polishing will be necessary afterward to polish the TDE away.  However, I have found that polishing MOT will cause oblate spheres less often than working TOT.

Alternating between the MOT and TOT techniques described above is another good way to remedy the condition.  What technique works best will depend on your polishing technique and experience.

I will note that I have had more problems with oblates when working with harder pitch, probably because once the lap is deformed to have a low edge, the process that creates the oblate sphere becomes self-perpetuating and creates a worse oblate sphere if the stroke pressure/shape is not changed significantly.  Soft pitch is less likely to have this problem, but it is still possible!

It is my opinion that the majority of turned-down edges produced by amateurs (provided the pitch is approximately the right hardness) are produced by causing an oblate spheroid condition on the mirror's surface.

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