From: "Frank Q" 
To: "CSC" , "Atm" 
Reply-To: "Frank Q" 


Hi All

Regarding artificial star -> mirror distance, I crunched some numbers
and came up with the following for a 8" F/5 mirror:

Mirror/"star" distance       KE-Difference

2 * FL                             5.006 mm
10*FL                             0.555 mm
20*FL                             0.263 mm
40*FL                             0.128 mm
80*FL                             0.063 mm
160*FL                           0.031 mm

Where:

* The "star" is the ball-bearing illuminated by the sun.

* The 2*FL, 10*FL etc represent a slit(star) to mirror distance
of 2 x Focal-Length, 10 x Focal-Length etc

* The "KE-Difference" is the difference between where the rays from
the outermost and innermost zones are focussed. Note that for a stationary
"star" and moving knife edge, the difference is (r^2) / R = 5.006
mm which corresponds to the 2 * FL entry in the above table (2 * FL =
Radius of Curvature) as expected.

* The above results were obtained using a ray-tracing algorithm

So, from the above numbers, it appears that for a **perfectly** corrected
parabolic mirror, the KE-Difference is zero if the "star" is at
infinity - in other words, a Focault knife edge test will be a null test.
But if the "star" is 10 focal lengths away, you will observe the
characteristic dough-nut shadows consistent with an 11% corrected mirror
and 1.3% corrected at 80 focal lengths.

Cheers
Frank Q

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