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


"Dwight K. Elvey"  wrote:

> One thing to consider is that the center of the secondary
>is not on the axis of HYPERBOLOID. In fact, it is quite
>far from the axis of the correct HYPERBOLOID shape. You
>need to consisder this when comparing to a spherical shape.
>the minor and major axis would be quite different in
>curvature for a large axis offset.
>Dwight
>
>
>>From: MLThiebaux 
>---snip----
>>
>>2. The slightly spherical diagonal should be compared to the nearest
>HYPERBOLOID, not to the perfect plane.  The required hyperboloid has two
>principal curvatures differing by a factor of 2, say k and 2k.  One minimax
>solution (hard to explain without a picture) for fitting such a hyperboloid to
>the sphere is found to have the following properties:
>>

Dwight,   exactly so -- with the axis of the hyperboloid being the line joining
the virtual and real on-axis star images.  The offset would be
9/sqrt(2)" in my numerical example.  The offset is related to the
difference in curvatures which would always be in the ratio of 2:1 at the
center of the diagonal.

Martial Thiebaux
Rawdon Hills, Nova Scotia

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