Extract from correspondence:

From demerson@nrao.edu Tue Oct  3 09:31:36 2000
Date: Thu, 07 Sep 2000 13:01:28 -0700
From: Darrel Emerson 
To: morris@iraux2.iram.fr, lucas@iraux2.iram.fr
Cc: richard@mrao.cam.ac.uk, ldaddari@nrao.edu, aperfett@nrao.edu,
    bshillue@nrao.edu, avaccari@nrao.edu
Subject: Holography polarization.

Hi Dave & Robert:

This is a rather hand-waving argument that claims to suggest that, as far as rejecting the reflection of the holography transmitter from the ground is concerned, vertical polarization is indeed a little better than circular. Have I got this right?

For the sake of this argument I'll assume the ground is perfectly flat. I believe real, rough ground will simply blurr the difference there might have been between different polarizations.

For a perfectly conducting ground, RH circularly waves either at normal incidence or at near-grazing incidence will be reflected predominantly as LH circular. At low elevation angles, horizontally polarized rays are reflected with a pi-radians phase change, while vertically polarized rays are reflected without the phase change.

With a REAL ground, Brewster's angle comes into it, because of the finite dielectric constant. For typical values of real ground electrical constants, Brewster's angle is around 20 degrees elevation angle, although of course it does vary with different ground properties.

AT Brewster's angle, incident vertical polarization is not reflected at all. At that angle, incident circularly polarized radiation of either sense will be reflected as 100% horizontally polarized.

ABOVE Brewster's angle (i.e. nearer to normal incidence), the phase changes of reflected horizontal and vertical components are the same as for a perfectly conducting ground. Depending on the angle, the reflected vertical component is reduced in amplitude more than is the horizontal component.

BELOW Brewster's angle (i.e. nearer to grazing incidence), the vertical component is reflected with a phase change pi radians different from the reflection above Brewster's angle. I.e. below Brewster's angle, both horizontally and vertically polarized rays are reflected with a pi-radians phase change. (This is responsible for the well known problem for communications in the HF band; for greater ranges, lower angles (i.e. nearer to grazing incidence) of radiation are desirable. You can't do this easily over normal ground, because both vertical and horizontal components are reflected such as to cancel the direct wave. All you can do is to increase the antenna height, to try to bring the first peak in the interference pattern, between the antenna and its reflection in the ground, down closer to the horizon.)

This relative phase change of the vertical component, as you go through Brewster's angle, means that although at high elevation angles a RH circularly polarized wave is reflected as LH circular, but at low elevation angles a RH circularly polarized wave is reflected as RH. (Because of the higher attenuation of the vertical component than the horizontal, the reflected wave is really elliptically polarized, but the circular component of this will remain RH.)

For our holography measurements, the transmitter has an elevation angle of about 8 degrees as seen from the receiving antenna - for all values of electrical properties of the ground likely to be encountered, this will be lower than the Brewster's angle. So, there is no change in sense of the circular component of the incident and reflected wave, and so using circular polarization will not help reduce ground reflections. Vertical polarization will be reflected more poorly than horizontal polarization, with more attenuation the closer you get to Brewster's angle.

Of course, if reflections from, say, the transmitter tower or other metallic conductors become an issue, then circular polarization would help. But I'm assuming that the transmitting antenna will have sufficient directivity to avoid most such problems, and that the main problem will be ground reflection.

With more hand waving, I claim that rough ground will just reduce any polarization discrimination between direct and reflected rays that there might have been, so qualitatively my argument is unchanged.

Does this sound reasonable? We should use vertical polarizaton. A couple of equations would have replaced a thousand words.

		Cheers,
			Darrel.