A comparison of s11 measurements, autocorrelations, and electromagnetic models of the hera dish+feed: the height of the feed above the dish

We compare measurements of the S11 scattering parameter to electromagnetic models of the HERA antenna element. We consider three antenna models that vary in the degree to which they conform to the as-built configuration of the antenna, and we find that the predictions of S11 vs. frequency for the three models are significantly different. We further consider models in which we vary the height of the feed above the dish. We develop a goodness-of-fit metric for comparing the measurements to the models. We find that of the three different models for the antenna element, the one that most closely conforms to the construction of the antenna is clearly the best fit to the data, suggesting that S11 measurements are a good discriminator between models. We further find that the goodnessof-fit metric differentiates between models of the feed at different heights, and we find the best-fit height for each model. The best-fit heights agree with those measured in the field, except for a consistent offset of a few centimeters. This offset may be due to a bias caused by inaccuracies in the antenna model, errors in the zero point of the field measurements, or unmodeled motions of the feed (such as horizontal motion or tilt). The internal consistency of the fitted heights suggests that in principle S11 measurements could be used to measure feed heights in the field to a precision of about 2cm, if the source of bias could be understood and corrected. However, S11 measurements may not be practical during operations. We show that the frequency dependence of antenna autocorrelations on feed height is systematic and predictable, and thus might be used instead to infer feed height.