One of the goals of the GBT development effort is to determine the primary beam pointing solely from measurements of the antenna structure with respect to the ground. The laser ranging system will measure the orientation of the edge of the main reflector with respect to the ground, the feed support arm with respect to the reflector, the secondary reflector with respect to the fed support arm, and the location of the secondary feeds with respect to the feed arm. To close the metrology loop between the ground and the beam position we need to know the position of the feed phase center with respect to its mechanical structure.
This report is a brief description of the process of determining the location of a feed's phase center from antenna range measurements. To some extent the phase center is an ill-defined concept because the feed's phase front over the reflector's aperture is never perfectly spherical. The phase center determined here will be an approximation. A complete analysis of the GBT's beam direction will require a physical optics calculation that takes into account the feed's phase pattern across the aperture. For most cases the primary beam direction error due to the phase center approximation will be much less than a tenth of a beamwidth.
The Green Bank antenna range produces an ASCII data file that contains a measurement parameters header and a list of amplitude and phase values as a function of azimuth on a single-axis rotating mount. The exact format of the file may be seen in the Appendix.
Figures 1 and 2 show the amplitude and phase of the antenna range measurement in the E-plane of the 1070 MHz GBT prime focus feed at 1.23 GHz. For the purposes of the note we are interest only in the phase behavior of the feed within the subtended angle of the main GBT reflector as noted by the vertical hash marks in Figures 1 and 2.
The phase pattern measured on the antenna range provides information on the location of the feed's phase center with respect to the rotation axis of the antenna range turret. We can break the phase center location into two components, one parallel to the feed axis and the other normal to the plane defined by the turret rotation and feed axes.
If the feed's wavefront is spherical, the measured phase will have components which are functions of sin(azimuth) for the phase center offset normal to the feed axis and (1 - cos(azimuth)) for the offset parallel to the feed axis.
In general, the feed's wavefront is not spherical, particularly near the edges of the feed's useful pattern. We can finesse this problem for the sin(azimuth) component of the measured phase by assuming that the phase pattern is symmetric and using the difference between the two halves of the pattern as shown in Figure 3. This figure shows the phase difference plotted as a function of sin(azimuth). The data should lie on a straight line through (0,0), but there appears to be a slight asymmetry in the pattern of a couple of degrees. The slope of the best-fit straight line in Figure 3 is twice the phase center offset normal to the feed axis. In this case it is only 9.5 degrees. This is equivalent to an offset of 0.013 wavelengths. At the frequency of 1.23 GHz one wavelength is 24.4 cm so the measured phase center offset is 0.32 cm.
If the feed's wavefront were spherical and the phase center displaced along the feed axis from the rotation axis, its measured phase should fall on a straight line when plotted as a function of (1 - cos(azimuth)). Figure 4 shows such a plot of the phase within the subtended angle of the GBT for our example feed. The two halves of the phase pattern have been folded about azimuth=0 and averaged to remove any effect of a lateral phase center offset.
The measured phase plotted in Figure 4 is not a straight line, but the maximum deviation is only about 10 degrees. If we define the phase center by the best-fit straight line to the data, we see that the offset between the phase center and the axis of feed rotation is -231.5 degrees (0.643 wavelengths) as given by the slope of the line. This offset is in the sense that the phase center is closer to the transmitter than the center of rotation. As a check on this calculation, a second phase pattern was measured under the same conditions except that the feed was moved 8.88 cm further away from the transmitter when pointed at azimuth=0. The best-fit straight line to this phase plot had a slope of -98.0 degrees (0.272 wavelengths). This gives a difference in phase center positions of 24.4 * (0.643 - 0.272) = 9.05 cm, which agrees well with the physically measured change in position of 8.88 cm.
The data analysis routines were written in glish using the AIPS++ mathematics module. I will be glad to supply the source code upon request.
This is the ASCII data file format from the Green Bank antenna range. Annotations following the # mark do not appear in the file.
06/01/99 # Date, month/day/year 14:24 # Local time 1070 MHz FEED # Measurement title -170 # Start azimuth in degrees 170 # Stop azimuth in degrees 1.2300000000E+00 # Frequency in GHz 100 # undocumented quantity E # Plane of pattern measurement PRIME # Type of feed # blank line E # undocumented quantity V # undocumented quantity X-Axis position = +0.000 inches # note 1 Y-Axis position = +0.000 inches # note 2 -1.7000000000E+02 # azimuth in degrees, measurement 1 -4.2087912088E+01 # amplitude in dB, measurement 1 -1.9247186538E+02 # phase in degrees, measurement 1 -1.6900000000E+02 # azimuth in degrees, measurement 2 -4.6172161172E+01 # amplitude in dB, measurement 2 -1.9533651923E+02 # phase in degrees, measurement 2 etc.
Note 1: Horizontal translation of turret normal to feed-transmitter line.
Note 2: Horizontal translation of turret along feed-transmitter line
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