Zone Plate (reflecting) Fresnel Antennas for Amateur SETI -- Part Two

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Zone Plate (reflecting) Fresnel Antennas
for Amateur SETI -- Part 2
by Henry Wallace (ultrasonic@worldnet.att.net)

(see also Part 1)

Augustin Fresnel ( French engineer, 1788-1827 ) in 1814 gave the first satisfactory explanation of interference and diffraction of light by the wave theory. One of his contributions was the Zone Plate, which can be made of metal, is flat, and focuses electromagnetic radiation much as a lens or concave mirror.

This paper adds a ground plane to the conventional Zone Plate. This ground plane adds two important features advantageous to the SETI community. First, it doubles the energy-collecting ability of the conventional design, bringing the Zone Plate into competition with dishes of similar diameter. Secondly, it prevents the feedhorn from seeing the RF noise from the hot Earth: the groundplane blocks the energy from the Earth which otherwise would pass through the vacant spaces of the conventional design to the feedhorn. The expected advantages to SETI are simplicity of layout and the availability of much larger apertures.

Figure 1
Figure 2
Figure 3

Attached is a BASIC computer program which simulates the Zone Plate performance. First, this program assumes a "specular" surface ( not a perfect mirror surface ) for all metallic surfaces used in production. If perfect mirror surfaces were used, the simulation would have to be changed to obey Snell's Law ( the angle of incidence is equal to the angle of reflection ). This would require that obliquity factors be included. While neither of these changes are particularly difficult to add to the simulation, they will slow down the computer and probably are not required anyway. Others may not agree that these terms are not required.

The Computer Program

This BASIC program runs well on a Pentium 166 MHz computer under PowerBasic's 32-Bit Console Compiler for Windows. It is important that your computer have the math co-processor, which I believe all Pentiums above 150 MHz do. It runs fine with 32 megabyte of "core" memory.

The program generates four output files: DEGREEAXIS, BEAMPATTERN, BOUNDNUMBER, and BOUNDLOCATION. These files can be copied into Excel, and plotted using Chart Wizard. BOUNDNUMBER is just the number, from one to twenty, identifying the boundaries between the zones of the zone plate. BOUNDLOCATION is the radius, in meters, of each of these zone boundaries.

Lines 20-70. Sets up the electromagnetic parameters of the RF energy being expected. Line 25 puts an arbitrary amplitude Am into the program. This is to "bias" the program into the proper range of values for most accurate computations on your computer. It is arbitrary because it is effectively eliminated when the dB output is "normalized" to zero dB at top-dead-center of the beampattern, line 1750. The term dla, line 70, is the resolution of the simulation, in both x and y. For more resolution, increase the number in line 70, but machine operation will slow. Line 30 sets the frequency, in Hertz, and line 40 sets the RF wave velocity between here and ET, which is assumed to be constant.

Line 100-190 Computes the zone boundaries. Line 110 sets R, the height of the feedhorn above the bullseye. This sets the scale of the entire Zone Plate: the diameter of the bullseye increases linearly with R. Line 105 puts a small dead spot at the very center of the zone plate, to allow for a mast to be installed to hold up the feedhorn. Up to 20 zones are allowed, but you can increase this ( line 7, line 120 ). If you want to preview how big your zone plate is, you can insert a line 195 GOTO 1946 which will cause the computer to only generate the files BOUNDNUMBER and BOUNDLOCATION. Line 200. Sets the angle scan of the beampattern. It must start on zero in order that the dB normalization will work properly.

Lines 241-600 Computes the contributions from all the bullseye rings chosen in line 241. The following two figures are intended to help those who are interested in the geometry of the model see how it works.

Lines 630-1704 Computes the contributions from all the "shadows" of the bullseye rings which fall on the groundplane. The groundplane is separated from the bullseye plane by a distance d, which line 650 sets to one quarter of a wavelength. Line 630 allows you to make the groundplane optional. Line 741 lets you choose the size of the groundplane, ie, one ring larger or one ring smaller than the bullseye.

Frequency Sensitivity

All Zone Plates are frequency selective, and have a built-in preselector filter. You can, with a little effort, change this program to scan frequency instead of beampatterns. These changes are:

Line 200: change to read
200 FOR f=0.500000*f0 to 1.5000000*f0 step f0/100.000000000
Lines 218-227: Remove "REM" from first of each.
Line 1705: Substitute "f" for "deg".
Line 1750: change to read
1750 WRITE#2, SQR(ut*ut+vt*vt)
Line 1800: Substitute "f" for "deg"

The Program

There is a single beampattern attached, as a benchmark for this program. When you run this program, it should produce the data shown. Run time is 5 minutes, 50 seconds on a Pentium 166 MHz under PowerBasic's Console Compiler.

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