Re: ATM An efficint algorithm for robotic Foucault testing

[Jim Burrows <burrjaw@earthlink.net>]

At 11:03 2003-10-04 -0700, Dale Eason wrote:

>The part I am having trouble with is converting the
>results into a mirror profile.  Can one of you
>Foucault analysis authors or anyone help with that?

For moving-source, the calculation of the mirror surface height x involves 
the numerical solution of a differential equation:

         x' = dx/dy = y/(f -x)

with zone radius y and Foucault reading f (longitudinal distance from 
mirror vertex).  If we're talking really small, pixel-sized steps in y, 
probably you could get away with the simple Euler formula.  For a smoother 
solution or for larger steps, the ever-popular Runge-Kutta formula is 
suggested.  The fixed-source model is more complicated.  For that, take a 
look at Eq. (2.4) in my (long) article:

         http://home.earthlink.net/~burrjaw/atm/atm_math.lwp/atm_math.htm

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