From: dan otto 
To: atm{at}shore.net
Reply-To: dan otto 


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 Note: forwarded message attached.



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Dec 2002 10:55:45 PST
Date: Sun, 22 Dec 2002 10:55:45 -0800 (PST)
From: dan otto 
Subject: Re: ATM Perfect zonal reading reference number generation
To: James Lerch 
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 James Lerch  wrote:

Greetings All,

I'm looking for a formula for generating perfect longitudinal knife edge
readings for Foucault tests.

Parabolic mirrors are easy enough (I've got that working already) What I'm
looking for is complete formula that will calculate the longitudal readings
for mirror have a non-parabolic conic constant.

BTW, when I say 'Perfect' numbers, I don't actually mean
"Perfect" :) Longitudal zonal readings that will spit out
"2-9s" for a strehl ratio would be fine!

For reference, I'm currently using the following formula to calculate
perfect longitudinal zonal readings

For each zone radius, (moving source tester) longitudinal reading = Z^2 / 4F

Where Z = center radius of Zone & F = Focal Length

For a fixed source tester, I just multiply above results by two. So far
this works out good enough for the intended purpose, but only for parabolic
mirrors.

Thanks in advance,
James Lerch
http://lerch.no-ip.com/atm




From Texereau's book Sedond Edition  Page 77



deltap = b ( Z^2/R + Z^4/ 2 * R^3)

Z is the zonal radisu  R is the radius of curvature

b is a coefficient of deformation b

"For the parabola b assumes the value -1 (the sign indicating that in
this case the marginal rays intersect farther from the mirror than axial
rays).If b is a number more negative tha -1, the surface is hyperbolic.  If
it is between -1 and 0, the figure is an ellipsoid of revolution about a
major ellipse axis; if between 0 and 1, it is an ellipsoid of revolution
about a minor ellipse axis. At b = 0 the figure is, of course, a
sphere."

You can see that for all but very fast mirrors the second term is not needed.

Dale Eason





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 James Lerch
<jlerch1{at}tampabay.rr.com> wrote:

Greetings All,I'm looking for a
formula for generating perfect
longitudinal knife edgereadings for Foucault
tests.Parabolic mirrors are easy enough (I've got that
working already) What I'mlooking for is complete formula that
will calculate the longitudal readingsfor mirror have a
non-parabolic conic constant.BTW, when I say 'Perfect'
numbers, I don't actually mean "Perfect" :)Longitudal
zonal readings that will spit out "2-9s" for a strehl ratio
wouldbe fine!For reference, I'm currently
using the following formula to calculateperfect longitudinal
zonal readingsFor each zone radius, (moving source
tester)longitudinal reading = Z^2 / 4FWhere Z
= center radius of Zone & F = Focal LengthFor a
fixed source tester, I just multiply above results by two. So
farthis works out good enough for the intended purpose, but only
for parabolicmirrors.Thanks in
advance,James Lerchhttp://lerch.no-ip.com/atm">http://lerch.no-ip.com/atmhttp://lerch.no-ip.com/atm">http://lerch.no-ip.com/atm
>
From Texereau's book Sedond Edition  Page 77
 
deltap = b ( Z^2/R + Z^4/ 2 * R^3)
Z is the zonal radisu  R is the radius of curvature
b is a coefficient of deformation b
"For the parabola b assumes the value -1 (the sign indicating
that in this
case the marginal rays intersect farther from the mirror than axial
rays).If b is a number more negative tha -1, the surface is
hyperbolic.  If it is between -1 and 0, the figure is an ellipsoid
of revolution about a major ellipse axis; if between 0 and 1, it is an
ellipsoid of revolution about a minor ellipse axis.  At b = 0 the
figure is, of course, a sphere."
You can see that for all but very fast mirrors the second term is not
needed.
Dale Eason
 
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Mail Plus - Powerful. Affordable. http://rd.yahoo.com/mail/mailsig
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