INTRODUCTION

This research was conducted under the guidance and mentorship of Dr. Alan E. E. Rogers during the 2000 REU program at Haystack Observatory. Radio telescopes have problems that are unparalleled in optical telescopes. These include side lobes, interference and spillover temperature. Side lobes and interference have been studied and exhaustive efforts have been applied to attempt to minimize their effects. However, throughout this quest for optimum receiving, the effects of spillover have often been overlooked. The small radio telescope (SRT) exhibits the effects of spillover.

WHAT CAUSES SPILLOVER?

Radio telescopes are designed to detect signals from sources. The dish collects the signal and brings it to a focus at the focal point where a feed detects and deciphers the signal. The angle that the feed subtends is usually larger than the angle the dish subtends. As a result, the feed will detect signal from the area behind the dish. This signal is the spillover.

WHY MODEL SPILLOVER?

When the elevation angle of the radio telescope changes, the region of spillover also changes. Sometimes spillover is solely from the ground, particularly when the radio telescope is pointed at the zenith. At other times, spillover is composed of ground and sky. The temperature of the ground is higher than that of the sky. Therefore, the spillover temperature will vary depending on how much sky and ground radiation contribute. The data the radio telescope collects will have the spillover contributions added into the signal. Calibration usually compensates for contributions like these. However, the calibrating method considers the spillover temperature a constant. As a result, for a data set taken over a wide range of elevations, the temperatures at lower elevations are lower than those at higher elevations. The goal of the model is to eliminate this trend in the data and give correct values of the temperature at all elevations.

THE DATA

The data sets for this report are created using the electronic noise calibrator as a source. This gives a constant T_source in the equation below, thus, any change in T_receiver is largely due to T_spillover . P_s and P_o are the power measurements from the SRT with a source and without a source, respectively.

MODELING THE SPILLOVER

To model the spillover, the angle of the dish that receives signal from the ground and the angle that receives signal from the sky must each be known. From figure 3 the relationship for the angle receiving signal from the sky can be acquired.


The value of a is half the diameter of the dish and b can be found by investigating the circular plane of the dish.


The angle c is equal to the elevation angle; d is equal to the focal length, f, minus the distance, z.


From the equation for a parabola, z can be evaluated.



Half the angle the dish subtends, e, is given by the dish's radius, a, and the distance, d.


A crucial factor in the model is the elevation that the sky begins to contribute to the spillover. The elevation angle that this happens at is simply e, the angle the dish subtends. All elevations above e have no contributions from the sky and those below have an increasing contribution from the sky. The ratios of sky and ground follow these equations:

CONCLUSION

For the SRT, f = 80.9cm and r = 105cm, thus e = 67^o. The value of 36.33 K for the spillover temperature gives the best result. This value is more realistic than the 20 K constant value. Uncertainty enters from the value of T_source, objects emitting near the radio telescope, and the receiver used for the data sets. The effects of the earth's curvature are minimal and not taken into account. Results can be improved with a radio telescope isolated in a flat, grassy field. When the model is applied, the trend seen in the original data set is eliminated. The model can be applied to whole data sets, or integrated into the SRT software, to compensate for the spillover.