从瑞利-索末菲衍射积分公式出发, 推导出径向阵列非傍轴离轴椭圆高斯光束相干合成和非相干合成在自由空间中的解析传输公式, 给出其远场分布和傍轴表示式。研究表明:合成光束的光强分布与f参数、径向阵列半径、光束数、传输距离和合成方式有关;N束光相干合成和非相干合成在远场的光强最大值分别为单光束在远场最大值的N2和N倍。

Starting from the Rayleigh-Sommerfeld diffraction integral, analytical expressions for the free-space propagation of radial array nonparaxial elliptical Gaussian beams in coherent and incoherent combinations are derived, and some special cases including the far-field distributions and paraxial expressions are given. It is shown that the intensity distribution of the resulting beam depends on the f-parameter, radial array radius, beam number, propagation distance and combination scheme. The far-field maximum intensity of the resulting beam with N beamlets in coherent and incoherent combinations is N2- and N-times of that of the single beamlet, respectively.