Using Fourier optics to study features of combined beams in far field

By using Fourier optics analyzing method, the expression to the far field of combined beams is deduced and the expressions for the coherently combined beams emitted from sources positioned on the circle have been given. For the cases where the sources are uniformly distributed, the dark lines in the far field are studied for beam numbers of 2, 3 and 4, respectively. It is found that when the sources number is 2, there are only dark lines (instead of rings) on the far field pattern and when the sources numbers are 3 and 4, the dark rings are far from being the circles. Since Fourier optics method is easy to implement and can be applied to non-Gaussian beams (such as those from the fiber lasers, semiconductor lasers, etc.), so it possessed unique advantages and is of practical significance