The 430 MHz line feed on the carriage house illuminates the 1000 foot dish when the ch is at za=0. As the ch goes up in za, the illumination on the dish spills over onto the ground/ground screen. Since the gain is proportional to the illuminated area (assuming uniform illumination) the gain will also go down. To figure out how the spillover increases with za, a simulation was done. This simulation used:

- compute rgrid which is a 600x600 grid of points spaced by 1 meter.
- Fill rgrid with the distance from each point to the center.

- Generate a aperture plane agrid(600x600) for za = 0

- use rgrid to find all of the points in agrid that have a radius between 305/2 meters and 91/2 meters (300 foot diameter).
- This is the part of the aperture plane illuminated by the
linefeed when za=0.

- Fill these points with unity.
- integrate over the entire agrid0
- Figure out how much the aperture plane moves in the x direction when the feed moves to a non zero zenith angle.
- Approximate this by looking at the triangle :
- angleEdge=asin(305/2 / radiusCurvature) = 35.0795 degrees
.. angle to edge of dish.

- r1=radiusCurvature*cos(angleEdge) .. height edge of dish to center of curvature
- r2=305/2 : radius of dish
- th=angleEdge + za
- solve tan(th)=(r2+dx)/r1 this give the x shift of the aperture plane.
- compute rgrid1(600,600). this has the radius for each point to the center of the dish, with the x coordinate shifted by dx.
- Find all of the points in rgrid1 within 305/2 meters of the center.
- Use these indices to integrate over agrid0 (the aperture plane at za=00
- The normalized gain(za)= total(aperature plane at za)/total(aperture plane za=0).

- Page 1: Illuminated area (gain) vs za.
- The black line is the simulated data. The red line is a linear fit to the data.
- The slope of the fit is -.0326 per deg za.
- Page 2: Measured gain vs za for linefeed.
- Data is from 20050301 thru 20120229
- black is the measured gain. The red line is a linear fit to the data: gain= C0 + C1*za
- The data is centered at 430 MHz.
- Each frame is a different bandwidth: 12.5,6.25,3.125,1.5625 MHz.
- the fractional slope : C1/C0 should match the slope of the line from the simulation:
- simulation: -.0326
- measured data:-.0288 to -.0295 ..

- so the match is pretty good.
- The gain increases as the bandwidth narrows since the linefeed has a fwhm response of about 9.5 MHz. centered close to 430MHz.

- simulation shows that the fractional change in gain with za for the line feed is:
- -.0326 *zaDeg

- Using the measured gain from the carriage house we get a normalized slope of:
- -.0288 to -.0295 * zaDeg. This agrees pretty well with the simulation
- The measured gain of the linefeed has a fwhm of about 9.5 MHz (centered at 429.5 MHz).
- What was not included in the simulation.
- The true illumination patter probably has a taper. This would weight the area spilling over at the edge with a smaller value
- So the simulation would come closer to the measured value.