ATM [Fwd: Re: Mirror Cells for Amateur Telescope Makers]

[Mark Holm <mdholm@telerama.com>]

Hello fellow TN's,

Jonathan Dietch and I have been having an off list exchange on mirror cell 
designs using Plop.  I was pointing out cell designs using fewer points that 
have good, less than 1/40 wave P-V, deformations and correspondingly low RMS 
deformations.  Jonathan has brought up the term "maximum tolerable contour slope 
deviation" (see below).  He thinks that, though deformations may be small in P-V 
amplitude, that if they are close together, they contribute higher slope errors, 
and thus are objectionable.  I wrote a reply (see below), but am not absolutely 
certain of my ground.  We both would appreciate informed comments on this subject.

Mark Holm
mdholm@telerama.com

> Hi Mark,

 >

> Correct me if I'm wrong but to me P-V error is not the key factor in cell

> design.  It's the maximum tolerable contour slope deviation that is the

> issue.  What I am looking for is a contour that does not cause the reflect

> ray to deviate from focus by more than a small fraction of a wavelength.

> You can have a 1/60 P-V surface that gives horrible images because the

> surface is very wavy and not smooth.  I am not a math or engineering guy.

> Perhaps you can run some numbers on this?
>

> Thanks
> Jonathan 



> Hi Jonathan,
> 
> This ground has been gone over many times by people who are much better at the 
> theory and math than I.  I will try to explain.
> 
> 1. The ray theory of light is not sufficient when you get down to the level of 
> forming good images with resolution near the theoretical best.  Slopes only

> work with ray theory.
> 
> 2.  In wave theory, it is path length that matters.  In particular, for a good 
> image, it is the difference in path length between the "rays" that traverse

> one part of the mirror and another.  The Raleigh criterion says that for a

> good image, the difference in path length from one part of the mirror to

> another, as measured at the final image, should not exceed 1/4 wave.  Now the

> choice of 1/4 wave was somewhat arbitrary.  Over the decades (almost centuries

> now) since, experienced astronomers and opticians have found that it is

> possible to detect improvements in image quality due to smaller deviations,

> when those deviations are eliminated.  1/8 wave at the image is much closer to

> the real limit where getting any better is not going to help much.  Seeing good

> enough to make use of a better optical system doesn't happen too often in all

> but a few locations.  1/10 of a wave at the image is a good shooting point for

> perfectionist ATMs.  I think Mel Bartels has a discussion of this at his web

> site.
> 
> 3.  The theoretically astute say that RMS is a better measure than P-V because 
> RMS weights the deviations by the amount of light that is affected by a 
> particular surface defect.  Values for "good" RMS surfaces start around 1/100 
> wave and go down.  For smooth figure errors, RMS and P-V usually change pretty 
> much together, though it is possible to find examples of shapes where the 
> difference between the two is fairly significant.
> 
> 4.  ATM's discussing mirror figure usually assume a smooth figure.  What happens 
> if the surface is wavy?  Theoretical and practical work shows that small scale 
> irregularities, waviness, scatter light at larger angles outside the principal 
> diffraction peak than smooth errors.  So, a smooth 1/20 wave (surface) error 
> will scatter light from the principle diffraction peak a little to the side, 
> effectively widening and lowering the peak just a little.  1/20 wave ripple will 
> send the light more broadly over a larger area.  The central peak will be 
> lowered about the same, but not widened so much.  The light will show up farther 
> out in a wide blur.  The amount of light scattered is roughly proportional to 
> the area that is high or low.
> 
> 5.  The standards I state on my mirror cell web site are actually pretty 
> conservative.  In his Sky & Telescope article introducing Plop, David Lewis used 
> a criterion of 1/120 wave RMS at the surface as about equivalent to 1/20 wave 
> P-V at the surface, or 1/10 wave P-V at the image.  This was the maximum error 
> he was willing to let a cell introduce.  I usually use 1/40 wave P-V at the 
> surface or 1/20 wave at the image, roughly twice as rigorous.  My thought is 
> that cell design is usually easier to control than mirror figure.  Adopting a 
> more complex flotation design is less difficult than polishing a good figure. 
> One might as well do something that is reasonably easy to preserve image quality 
> in the hope that one will be able to make or buy optics good enough to warrant 
> it and enjoy seeing good enough to make use of it.  A good flotation system 
> can't make a poor figure better (Well except for the special case of deliberate 
> mirror flexing.) but a poor flotation can make a good mirror perform poorly.
> 
> Requiring that your cell introduce less than 1/40 wave P-V error is almost 
> certainly fooling yourself.  A. The cell probably won't work that well anyhow. 
> You get into construction tolerances and the approximations in Plop's analysis. 
>   B. Not many opticians can make mirrors better than 1/20 wave (1/10 wave 
> image).  And that 1/10 wave has to be made at the sum of the primary, secondary 
> and eyepiece errors.  C. Tube currents and atmospheric seeing will limit you to 
> this level or worse a lot of the time, unless you have access to a specially 
> good observing site.  To deal with tube currents, you really need to put a fan 
> blowing across the front of the mirror.  There are a couple of good Sky & 
> Telescope articles about this.
> 
> That is the reasoning as I know it.
> 
> Mark Holm
> mdholm@telerama.com
>