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Re: [TowerTalk] Takeoff Angles and Non-Reciprocal Propagation

To: David Gilbert <xdavid@cis-broadband.com>
Subject: Re: [TowerTalk] Takeoff Angles and Non-Reciprocal Propagation
From: Michael Keane K1MK <k1mk@alum.mit.edu>
Date: Sat, 03 Nov 2007 13:56:58 -0400
List-post: <mailto:towertalk@contesting.com>
At 01:34 PM 11/3/2007, David Gilbert wrote:

>Yes, the single ray (for the sake of argument) that travels from A to B
>is monochromatic, but it isn't infinitely thin in terms of it's
>interaction with surroundings.

Ahhh, there's a conceptual issue. In terms of geometric optics and 
ray tracing, a ray is assumed to be infinitely thin

>  That single "ray" is energy traveling
>with a spatial density (in terms of it's interaction with surroundings)
>that is a function of it's wavelength.

That's a ray bundle or a wave.

>  A "ray" passing within a
>wavelength or few of a physical feature is going to be influenced by
>that feature in a manner that is a function of its conductivity,
>dielectric constant, physical shape, and the incident angle.

That's physical (or wave) optics.

>  My
>proposition is that since the shape of a feature (relative to a
>wavelength) as seen by the ray isn't necessarily the same going in both
>directions, the paths taken aren't necessarily the same.

HFTA is based upon a computational method known as the Geometrical 
Theory of Diffraction (GTD) which attempts to combines geometrical 
optics (ray tracing) with diffraction at surfaces (wave optics).

This is done by shooting out lots of individual rays and then uses a 
diffraction kernel (mathematical prescription) that describes how a 
single incident ray reflects/diffracts into arbitrarily many 
(depending on the resolution) diffracted rays at each 
interface/boundary. HFTA then sums up all the refracted and 
diffracted rays going in a certain direction at infinity to compute 
the gain/loss in that direction.

In the GTD, a ray is unaffected by an obstacle that it passes near, 
only by obstacles that the ray intersects.

73,
Mike K1MK

Michael Keane K1MK
k1mk@alum.mit.edu

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