Re: ATM P-V vs. RMS

[Aplanatic@aol.com]

Scott,

> What does it mean if the FIGURE program analyzes my Foucault 
>  data and reports that the mirror is 1/50th wave RMS?  I am afraid 
>  that all it means to me is that the mirror is better than when I 
>  tested it before the last figuring session and it only came out 1/20 
>  wave RMS.

Yes, I understand your point.  In fact, I don't personally believe that the 
measurement accuracy, even with repeated and averaged measurements, is much 
better than, say, 1/30 wave RMS for an f/4.5 mirror under the Foucault test.  
However, I do believe that the Foucault test is good enough, at this f/ratio, 
to figure a mirror that is essentially indistinguishable from perfection as 
long as my other criteria are satisfied, and the person testing the mirror 
has enough experience to null the outer zones with reasonable accuracy.  
Below f/4, for paraboloidal mirrors, I think the Foucault test starts to have 
some difficulties in this regard.

>  I would use these RMS numbers exactly the same way I use 
>  the P-V numbers--smaller is better.  However, I have no confidence 
>  that the RMS numbers derived from this analysis are any more 
>  meaningful than the P-V numbers derived from the same analysis.  If 
>  you believe they are more meaningful please explain it to me.

As Bratislav points out, you can have a rather poor mirror that satisfies the 
P-V criteria.  This poor mirror will not pass the Strehl test.  To see this, 
cook up an example where all of the surface error is at the edge of the 
mirror.  I think such an example is quite telling.
  
>  A number of people have discounted the transverse aberration value as 
>  not meaningful.  I have now prepared  number of mirrors using both a 
>  Foucault test and a null test.  What I find is that large TA values 
>  translate as zones in the null test.  Small TA values translate as 
>  fewer or more minor zones.  To me this information appears as useful 
>  as the calculated RMS rating. (At this point I have not compared RMS 
>  ratings with null tests enough to see if it also reveals the presence 
>  of zones or other measurable errors.)

Yes, the transverse aberration can tell us certain things about the defects 
in the mirror.  But as a single measure of the mirror's quality, it's not 
very meaningful.  On the other hand, if the mirror is reasonably smooth and 
shows a good Strehl ratio, you can have some confidence that it will star 
test, and ultimately perform, very well.  At least that's been my experience.

In the end, an experienced mirror maker like yourself can use a combination 
of P-V and TA to arrive at a good mirror.  But the first time mirror maker 
should probably use RMS or Strehl and not just P-V to decide when to quit 
figuring because of the small but nonzero chance that his or her mirror has a 
defect that passes P-V but produces poor images.

Dave Rowe.