Effect of phase and amplitude fluctuation of single laser element on far field characteristics of coherently combined beam

With Fourier optics, the general expression of far-field intensity of coherently combined beam has been derived, which is affected by single beams phase and amplitude fluctuation due to jitters in the system. The analysis using one-dimensional laser array shows that, the intensity peak becomes sharper and the energy centers in a smaller angle as the number of combined beams increases. The maximum intensity of far field reduces due to the jitters and the background appears, deteriorating the symmetry and quality of far field. Therefore, the stochastic fluctuation of phase should be controlled within 3/8 for single light source of the laser array; the more the beams are combined, the less the influence of the system jitters on far field characteristics is.