  Image quality in mosaicked observations from interferometric radio telescopes
is strongly dependent on the accuracy with which the antenna primary beam is
calibrated. The next generation of radio telescope arrays such as the Allen
Telescope Array (ATA) and the Square Kilometer Array (SKA) have key science
goals that involve making large mosaicked observations filled with bright point
sources. We present a new method for calibrating the shape of the telescope's
mean primary beam that uses the multiple redundant observations of these bright
sources in the mosaic. The method has an analytical solution for simple
Gaussian beam shapes but can also be applied to more complex beam shapes
through $\chi^2$ minimization. One major benefit of this simple, conceptually
clean method is that it makes use of the science data for calibration purposes,
thus saving telescope time and improving accuracy through simultaneous
calibration and observation. We apply the method both to 1.43 GHz data taken
during the ATA Twenty Centimeter Survey (ATATS) and to 3.14 GHz data taken
during the ATA's Pi Gigahertz Sky Survey (PiGSS). We find that the beam's
calculated full width at half maximum (FWHM) values are consistent with the
theoretical values, the values measured by several independent methods, and the
values from the simulation we use to demonstrate the effectiveness of our
method on data from future telescopes such as the expanded ATA and the SKA.
These results are preliminary, and can be expanded upon by fitting more complex
beam shapes. We also investigate, by way of a simulation, the dependence of the
accuracy of the telescope's FWHM on antenna number. We find that the
uncertainty returned by our fitting method is inversely proportional to the
number of antennas in the array.
