From: "James Lerch" 
To: "ATM List" 
Reply-To: "James Lerch" 


Mike and the List,

I'm going to top post my genuine appreciation for Mike's thorough, critical, and
independent evaluation of my raw data!  Thank you Mike!

I've also bottom posted some comments and questions below.

----- Original Message -----
From: "Michael Peck" 

>Out of the 264 images I found nulls in 263 - my algorithm failed to find a
>null in one of the central zone images. That data point was discarded in
>the rest of the analysis. For Vladimir's benefit, here is a plot of my
>estimated nulls plotted against James' adopted zone radii:
http://home.netcom.com/~mpeck1/astro/null%20vs%20zone.png> (plotted >points
are
fractional zone radius, with James' zones on the horizontal axis).

>For those who don't feel like examining the graph I get generally good
>agreement between my zone radii and James', with a slight tendency for my
>nulls to be farther out than his zones. The dispersion generally decreases
>with increasing zone radius. I've seen the same trends in a couple other
>data sets of his that I've looked at - in this case I think the large
>dispersion in the central zones is partly because the mirror is a bit rough
>(especially near the center). Our methods of sampling the surface are
>enough different to account for the dispersion. I'm not sure why my
>estimated nulls tend to be farther out than James'. One possibility is I'm
>locating the edge a little closer to the center than he is. In any case
>these differences have little effect on estimated surface error profiles.

I take comfort in knowing that these difference have little effect on the
estimated surface error profiles, however I feel I can get Robo to better.

After reviewing my 'Flip and Diff animations"
(http://lerch.no-ip.com/atm/2ndtry) its obvious Robo needs some help with
the central zones.  I think I can address this issue in two areas.

#1 Zone null search tweaks
    Fortunately the ability to do this is already built into the software.
Doing this will increase the test accuracy at the expensive of test time.
However, since a single diameter 15 zone, 4x KE readings per zone test only
takes ~11 mins, I don't believe a few extra minutes of unattended testing
is going to be a problem!

#2 Zone Intensity pixel layout.
    This will take a small amount of code change, but its a fairly simple
change.  Currently Robo evaluates 11 pixels in a vertical column for each
side of a zone to find the intensity.  The current pixel layout puts one
pixel on the
diameter tested at the calculated zone radius, and an additional 10 pixels
(5 above and 5 below) the single pixel at the intersection of the zone
radius / mirror test diameter.

    This vertical column of pixels, when used to test zones of short radius,
may
well tend to produce the dispersion Mike demonstrated for the inner zones. The
fix is to convert from a vertical column of pixels to an approximated curve
of pixels matching the zone radius.  (Simple enough)




>It appeared to me that the individual test runs were not significantly
>different from each other, so I combined the data into one large test. Here
>are my estimates of the Zernike coefficients from a 4 component model with
>spherical aberration terms only:
>
>Z coefficient   Value   standard error
>
>Z9 (3rd)        - 9.1   1.2
>Z16 (5th)       -14.9   0.9
>Z25 (7th)       -13.2   0.7
>Z36 (9th)       - 9.2   0.6
>
>Residual standard error 0.093 mm on 253 degrees of freedom
>
>Estimated surface RMS: 23.8 nm
>Estimated uncertainty in RMS estimate: 3.4 nm
>
>Estimated surface MSE: 565 nm^2
>Estimated uncertainty in MSE: 33 nm^2



> Unfortunately primary astigmatism can't be estimated from
>his data.
>
>I want to call attention to one final number - that residual standard error
>of 0.093 mm. That's my estimate of the repeatability of a single
>measurement. That's about 3 times higher than James estimates from the
>variance in his Foucault readings. Why the difference? I'm not completely
>sure, but I think it's mostly because his "true" null zone is shifting
>around randomly from one test run to another.
>
>In my opinion this is just barely adequate repeatability, and clearly well
>short of what expert testers are supposed to be able to obtain. In this
>case James made up for lack of repeatability of individual measurements
>with a hugely larger sample than most people would collect. Good for him. I
>think he needs to do that routinely if he wants to compete with more
>traditional methods.

Mike, "IF" the optic has astigmatism, would this account for the
residual standard error when all three axes are combined?



Thanks again for your hard work!

James

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