The approximative formula for the far-field diffraction of a Gaussian beam through a circular aperture is obtained by using the superposition of Gaussian beams instead of the aperture function, and the explicit expression for calculating the beam divergence is also gained. Using the formula, the influences of the aberrations on the far-field wavefront and the beam's divergence are researched, and the results show that the large aberrations badly affect the far-field wavefront and the divergence. It is suggested that the aberrations and the diffractions should be avoided when designing the transmitter.