ATM "1/100th wave optics"

[Roger Ceragioli <rogerc@dakotacom.net>]

Hi Clive and All,

Clive Milne writes:

>    On the Subject of Wilson,
> He devotes a chapter to computer controlled figuring
>machines. The quality of the optics produced by these
>critters would make you drool. Quote: "The surface
>accuracy is commonly 1/100th wave, mostly limited by
>the ability to measure the wavefront". Obviously the
>issues are non trivial, but I was set to wondering,
>"If REOSC can do it, why can't we?"
>     None the less, Wilson is worth a read.
>   Clive.

A cautionary note.  I haven't looked at Wilson in a while, but it could
well be that his "1/100th wave" figure is an RMS figure error, not a peak
to valley.  Very likely, I would think.  1/100 of even 500 nm (his "wave
number" could be for a HeNe laser or a YAG or something else; but I'll
assume 500nm for the sake of illustration) is 5nm.  This is a surface
error, not a wavefront error.  So double it for the wavefront and you get
10nm.  40nm of pure spherical (all optics contain spherical, coma, and
astigmatism errors in fact) = approximately a 1/4 wave wavefront (see
Suiter for this equivalence).  So then 10nm would be about 1/16th wave PV.
Many amateurs can reach this figure with slow optics, rouge, and careful
work.  

But there's another catch.  The big mirrors are commonly rated with the
"Bending Modes" taken out.  I believe that means that various orders (i.e.
3rd, 5th, 7th, etc.) of spherical aberration, coma, and astigmatism are
mathematically subtracted from the actual interferometric data before the
final wavefront error is categorized.  This is legitimate because the big
mirrors are typically flexed in their cells slightly to improve the
wavefront (See! It's o.k. for ATMs to flex mirrors to make parabolas.  The
big boys do it too!).  I'm told that on the VLT mirrors, 20 bending modes
were removed from the data to get the wavefront error figure.

So all in all, 1/100th wave RMS optics may already be in many amateur
telescopes.

Roger Ceragioli