Re: [ATM] Foucault test : DP=-H2/R or DP=-H2/R+H4/2R3 ??

[Jim Burrows <burrjaw@earthlink.net>]

At 2004-05-28 23:13 +0200, Raphaël Guinamard wrote:

>the general formula (for any type of curve) of the
>longetudinal aberation DeltaP is given as DP=-H2/R+H4/2R3, where H is the
>radius of the zone and R the curvature radius of the miror.
>For the parabola, the formula is given as DP= -H2/R, but without saying if
>the H4/2R3 is neglicted or if simply doesnt exist.

After nearly exhausting my supply of scrap paper, I agree (down to a sign) 
that DP (position of the KE) = H²(1/R + H²/2R²) is exact for fixed-source 
at the paraxial CoC and a parabola.  As I said before, H²/2R is exact for 
moving-source and a parabola, so the (small) fourth-order term is the error 
in the usual assumption that fixed-source readings are twice moving-source.

Note that the formula doesn't work for "any type of curve" - only a parabola.

         -- Jim Burrows
         -- mailto://burrjaw@earthlink.net
         -- http://home.earthlink.net/~burrjaw
         -- Seattle N47.4723 W122.3662 (WGS84)  

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