XPost: sci.math   
   From: invlaid@invalid.com   
      
   On 1/10/2017 7:36 AM, Anton Shepelev wrote:   
   > Hello, all   
   >   
   > Is there a symbolic method to calculate the intensi-   
   > ty distribution on a flat screen from a  flat  wave-   
   > front  after it reflected from a curved mirror whose   
   > surface is described by an equation?   
   >   
   > The normal of the wavefront, and the relative  posi-   
   > tion of screen and mirror are known.   
   >   
   > I know of two ways to solve it:   
   >   
   >   1.  numerically,  by  tracing  the  rays reflected   
   >       from tiny sections of the mirror, and   
   >   
   >   2.  approximately, via the first N moments of  the   
   >       distribution,  which  can be found by integra-   
   >       tion over the mirror surface.   
   >   
   > Is there a method that will give an  exact  symbolic   
   > equation?   
   >   
   > P.S.: I  have  crossposted  the question to sci.math   
   >       because it is essentially a mathematical prob-   
   >       lem with a thin physical coating.   
   >   
      
   interesting problem, I have worked with non imaging optics using   
   reflective surfaces, and the exact solution can become very difficult   
   for a simple curve.  One problem was reflecting from a sectional   
   paraboloid with axis tilted, truncated, rotated in 3D.  I ended up using   
   your #1 above.  There were a few exact soultions that hold at certian   
   points only.   
      
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