Re: optics

[Bob Sciamanda <sciamanda@worldnet.att.net>]

Gary Karshner wrote:
> > The matrix-based ray tracing is based on paraxial approximation. The
> > results are not better than by old methods. But all can be comuterized.
>
> Ludwik,
>         I hate to disagree with you, but the advantage of the matrix method
> in optical design is not only that you can "easily" computerize it, but that
> you can abandon the paraxial assumption, and follow "individual" rays
> through the lens system. This has made possible the rapid advances that have
> occurred in optical systems in this half of the century. An optical designer
> used to measure the number of rays he could trace through a system per day,
> now it is measured in microseconds.
>
> Gary Karshner

I think Ludwig is correct.
I have written a ray tracing program (in Visual Basic) which relaxes the
paraxial condition and did not find matrices to be a useful tool.  The
matrix transformation effects a linear transformation among the vector
components.  The elevation angle and y coordinate relations connecting
two points on a refracted ray are linear only in the paraxial
approximation:

y' = {1}*y            +   {0}*A

A' = {(n/n'-1)/R}*y   +   {n/n'}*A

The exact (non-paraxial) equations would be non-linear.

-Bob

-- 
Bob Sciamanda				sciamanda@edinboro.edu
Dept of Physics				sciamanda@worldnet.att.net
Edinboro Univ of PA			http://www.edinboro.edu/~sciamanda/home.html
Edinboro, PA				(814)838-7185

St. Augustine (354-430):
  The good Christian should beware of mathematicians,
  and all those who make empty prophecies. The danger
  already exists that the mathematicians have made a
  covenant with the devil to darken the spirit and to
  confine man in the bonds of Hell.