From: derijken@mailcity.com (Dany)
Subject: The interpretation of the ETC equations.
Date: Wed, 29 Sep 1999 13:40:17 GMT
Newsgroups: sci.physics.electromag,sci.physics,sci.optics,comp.graphics.algorithms,sci.math.num-analysis
Keywords: Eikonal Equation in geometrical optics

Dear all Tutors and experts,

The ETC equations ( the Eikonal, the Transport, 
the Condition equation) are fundamentals in the 
study of geometrical optics (GO) and wave optics (WO).

The Eikonal Equation (EE):
( Del s )^2 =n^2,
The Transport Equation (TE):
( Del f . Del ) V + 0.5( Del . Del s) V=0
The Condition Equation (CE):
(Del . Del)V = 0

Where 
s is a scalar function of position,
V is a vector function of position.
n is the refractice index,
Del (or nable) is the patial differential operator
. is the dot product



These equations can be found in any GO/WO textbooks.
We have learnt by heart and known how to derive them.

However what we are still not completely understand are 
the interpretations ( or physical meaning) of these three
equations.

We have searched all the related books in our university
library.. these books gave well the derivation but not explain
what these really mean. or what are the consequences or
properties of them.

The only things we know sofar are:

For the EE:
 s is constant (scalar) function of position and called the
Eikonal ( or wave front).
and ???

For the TE:
the TE describes how energy is transported
and...???

For the CE:
???? we do not know !!!

Dear all Tutors and experts,

I you know what are the physical meanings of these equations
please let us know (we means TEACH us).

We  are very appreciated for any of you help.

Sometime things are easy and obviously for you..
but not for  newbies like us ( students)

So, please give us a hand ?

Thank you in advance for your time !. and.. help ?.


Dany and other students,

==============================================================================

From: Matthew Lybanon <lybanon@snaps.nrlssc.navy.mil>
Subject: Re: The interpretation of the ETC equations.
Date: Thu, 30 Sep 1999 15:59:07 -0500
Newsgroups: sci.physics.electromag,sci.physics,sci.optics,comp.graphics.algorithms,sci.math.num-analysis

A start, perhaps.  The eikonal (from the Greek "eikon," which means
"image") is the phase function in a situation for which the phase and
amplitude are slowly varying functions of position.  Constant values of
the eikonal represent surfaces of constant phase, or wavefronts.  The
normals to these surfaces are rays, the paths of energy flux.  Thus the
eikonal equation gives a method for "ray tracing" in a medium of slowly
varying index of refraction (or the equivalent for other kinds of
waves).
-- 
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| Matthew Lybanon                    | lybanon@snaps.nrlssc.navy.mil |
| Remote Sensing Applications Branch |                               |
| Naval Research Laboratory          | (228) 688-5263                |
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| U.S.A.                             |                               |
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