To: "James Lerch" ,"ATM
List" 
From: Mark Suchting 
Reply-To: Mark Suchting 


At 10:27 AM 8/11/2003 -0400, James Lerch wrote:


>  Having translated a Foucault data
>reduction program (I won't say I wrote it, as I didn't!) when I read
>"refocuses
>at best fit" I think along the lines of finding a best fit Radius
of Curvature
>for the reference parabola.

Thats it.

>Once the best fit RoC for the reference parabola has been found, and the
>Strehl
>reported, "Refocusing" to a different reference parabola has
never made the
>Strehl and RMS values improve (else the code should have used that one to
>start
>with..)

Thats because a `best fit ' result is already inherent in every mirror,
jsut by tweaking the focus.  In effect, we choose a best fit reference
parabola every time we rack an eyepiece in and out and choose the focus
position that gives us the most intense star image.


>Once the best fit RoC has been found, if the optic shows 15%
>overcorrected, the
>only 'trick' I've found to make the Strehl and RMS improve is to select a
>different, non parabolic reference surface (ie changing the Conic Constant,
>Deformation Constant, "little b", what ever we want to call
that term that
>describes on optical surface as spherical = 0, ellipsoid < 0 &
> -1, parabolic
>= -1, hyperbolic = <-1)


You can't change the Conic constant when evaluating a parabaloid. It always
must be -1. There is merit though in finding the best fit Conic constant as
the mirror progresses as it will show you if the relative removal rate
across the mirror is progressing in a smooth aspheric manner that will land
you at -1 if you keep polishing with the same stroke.

Actually I made an error in evaluating John Sherman's mirror data, the best
focus surface  error is  0.2 waves or 0.8 waves total path difference
between the  paraxial ( centre) and marginal  (edge) rays which means a
7.5% error in overall correction.



>I ask all this as I was once told the following:
>
>"... the mirror is indeed undercorrected. I have as much as 1/3 wave total
>aperical aberration, which can refocus to about 1/16 wave by my worst axis
>measurement (not the two combined)."



If you were referring to your interferometric measures done by Royce, that
wavefront ( showing a high at the 70% zone ) with low centre and edge, was
allready a best fit , meaning a total wavefront error ( measured from the
paraxial to the marginal ray ) of 4 times that figure, and a surface error
of half that  or 2/3 wave.


>Based on my limited experience, and your writings Mike, I wonder if in certain
>circles "Refocusing" really means changing the Conic Constant?  In your
>case the
>optic could be advertised as having a 0.859 Strehl, but it would be false to
>claim that Strehl AND say it is a parabolic mirror....

No, I don't believe anybody would do a best fit and advertise a Strehl
using a different Conic Constant than -1 .



>Current efforts to image the star test results for Charlie's mirror are to be
>done on an Equatorial Dob platform and a real star such as Vega. Currently
>were
>just waiting for a clear night. (apologies to Central Florida observers, the
>monsoon like rains of late may be our fault )


Why not image a star with the camera using a Ronchi grating and try to
simulate the Ronchi band bending ( if any ) using WinRonchi 2.0 ( which
allows you to simulate errors on spherical wavefronts) . If you pick a star
close to the North celestial pole, like Polaris , you won't have any
trailing problems.  Just remember to divide the pure spherical abberation
fed into the simulation by a factor of 4 to get the best fit PV wavefront
of your mirror , assuming you have simple third order spherical aberration.

~Mark Suchting

--- BBBS/NT v4.01 Flag-5