[ATM] How many zones

[mdholm at telerama.com (Mark Holm)]

Either my program CouderMask   
http://www.atmsite.org/contrib/Holm/coudermask/couderma.html

or Nils Olof Carlin's web calculator 
http://www.atmsite.org/contrib/Holm/coudermask/couderma.html

will give you an optimum number according to Nils' rather careful 
analysis.  My program will also print the mask pattern.

To save you the trouble, I have run it, and it says 4.3.  So, either 4 
or 5 would be good.  When doing my 8 inch f5.8, I thought that perhaps 
with only 4 zones, the individual zones were a little wide.  I thought 
there was perhaps a bit too much asymmetry between the  zone appearance 
(according to Nils, this is due to a third order term in the math.)  
Making the zones a little narrower would make this effect less 
pronounced.  As the curve gets steeper (lower f-number) the asymmetry in 
the zone appearance should increase, favoring narrower zones.  That is 
what Nils' equations show.

Also, If you are of the sort to believe quantitative measurement rather 
than trying to go more by appearance, you may want to try increasing the 
number of zones as you get close to a good figure.  The way to do this 
is to make a second mask with zones located between those of your 
primary mask.  Such a mask is called an "Intermediate" mask in my 
program, and the program will be happy to calculate and print it for you.

The way you use a second mask is:  Make a set of Foucault readings using 
your "normal" or main mask, then, without bumping either your tester, or 
mirror, get up and change masks to the "intermediate" one.  Then make a 
second set of readings, again without disturbing the location of the 
tester, so that the new readings can be referenced to the same starting 
point as those for the main mask.  It sounds tricky, but isn't really..

Yes it takes twice as long, but you get twice as many data points across 
the mirror.  That helps a lot in firming up the picture and helping you 
decide whether some zonal irregularity that you may see is really worth 
worrying about.  It is also good to make more than one set of 
measurements.  The power of averaging to reduce the risk of "outliers" 
in the data is even more than it's power to reduce the standard deviation.

I use Sixtests, by Jim Burrows as my Foucault data reduction program and 
strongly recommend it.  Others prefer other programs.  They all work, 
but in my opinion, Sixtests has the best math behind it, and does the 
best job of presenting a useful and easily interpreted picture of what 
the data is telling you about your mirror.  Sixtests is at  
http://home.earthlink.net/~burrjaw/atm/atm_math.lwp/atm_math.htm

If you do as I (and others) suggest, and take multiple sets of Foucault 
readings between polishing sessions as you get close to a good 
paraboloid, you may find my program FrontSix useful.   FrontSix is at  
http://www.atmsite.org/contrib/Holm/frontsix/frontsix.html
(I start taking at least two sets per figuring session as I cross the 
Strehl = 0.8 border and at least four sets per session when Strehl is 
over 0.9.)

FrontSix does the arithmetic to prepare multiple set Foucault data for 
Sixtests.  On its own, Sixtests only accepts data for one set of 
readings, or the average of several sets.  FrontSix does the averaging 
and a few other things, and lets you review your data better than a 
simple calculator would.

There are those atm's who think I rely too much on multiple zone 
Foucault testing.  They prefer to test in only a few zones, and use the 
appearance of the shadows, or Ronchi bands to tell them the curve is 
good otherwise.  I certainly don't want to suggest that one should 
ignore qualitative interpretation.  It is the best way to see narrow 
zones, turned edges,  "dog biscuit" and the like.  But I think when 
trying to decide if a curve is really a paraboloid, there is nothing 
like numbers.  It is a quantitative question, and quantitative questions 
are not answered without data.

Mark Holm
mdholm@telerama.com