Re: [ATM] PLOP Figures

[Mark Holm <mdholm@telerama.com>]

Hi Matt,

First thing: in Plop, you have to pay attention to the numbers.  It is a 
quantitative problem you are trying to answer, so there is no getting 
around working with the numbers.  Looking at the plots is interesting, 
but many Plop beginners get mesmerized by that color plot and start 
making incorrect conclusions.  The thing about the color plot is that 
David has it change its scale on the fly to fit the P-V error into the 
available color space.  This is a reasonable programming decision (and 
there is an option to override it) but it does lead people into 
incorrect thinking.  To demonstrate this, run Plop to calculate a 3 
point cell for your mirror.  The 3-point cell will have more residual 
deformation, both P-V and RMS than either the 6- point or 9-point.  BUT, 
the color range, from red to blue, will be exactly the same for the 
3-point as for the 6 and 9.

The most important numbers to use in order to decide whether a cell 
design produces low enough deformation are the RMS and P-V errors.  
These values are reported in millimeters.  In order to put them in 
perspective, you need to compare them to the wavelength of light.  (This 
is what the light does, so we have to "think" the same way light does.)

There is a slightly arbitrary decision to make:  what reference 
wavelength to use?  Light comes in a nearly infinite range of 
wavelengths.  For visual observing, the most popular choice of reference 
wavelengths is 550 nM  (nanometers).  This is equal to 550 x 10^-9 
meters or 550 x 10^-6 millimeters.

Let's take the worst number you quoted in your message,  1.76221e-06  
this is 1.76221 x 10^-6 millimeters.  In order to compare it to the 
reference wavelength, do the following calculation:

          Reference Wavelength / Error value = 1 /  Wavelength Error

I write it this way for a practical reason that I will now demonstrate.

Using the values above:    550 x 10^-6 / 1.76221 x 10^-6 = 312

So, the error represents 1/312 wavelength of light.
   (1/312 = 0.0032 but most of us think more readily with fractions than 
with decimals.)

For very good performance, you want the total error in your optical 
system to be no more than about 1/28 wavelength RMS at the final focus.  
(This is roughly half the Raleigh criterion translated to RMS numbers.  
You can get good performance up to about twice this amount, but most 
experienced visual observers say you can tell the difference between a 
system that just meets the Raleigh criterion and one with half as much 
error.  Below that, the improvements are subtle, if at all noticeable.)

An error of 1/312 wavelength at the mirror surface will be doubled at 
the focus, so 1/312 turns into 1/156.  1/156 is way less than 1/28, so 
we can conclude that the worst case number for the cells you analyzed is 
plenty small enough.  Either of these cells will cause so little 
deformation that you will not be able to detect it.  (Neither will 
anybody else.)

I recommend the 6-point cell to you (as Plop originally optimized it).  
The numbers are good (better than the 9-point cell) and you are more 
likely to be able to make the six point cell work well, especially if 
you are going to use wooden construction.

A couple of well done 6 point cells are linked to on the Links page of 
my mirror cell web site  
http://pong.telerama.com/~mdholm/atm/cells/index.html  Scroll down to 
the bottom of the table of contents on the right hand side to find the 
Links page.

P.S.  It may seem odd that the 6-point cell gave better results than the 
9-point cell.  I haven't time to go into the reasons here, but it is 
real and you can trust it.  It is not a general result.  Some 9-point 
cells will give better results than 6-point cells, you have to know how 
to set up Plop to let it get there.  Thing is, the 9-point cells that 
perform better in Plop's abstract analysis are likely to be difficult to 
build well.  The ones that are easier to build, don't do as well as 
6-point cells.

Mark Holm
mdholm@telerama.com
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