建立了发射光束通过带有波像差的望远镜系统后的远场光斑分布数学模型,采用数值计算,结合Monte Carlo方法分析了波像差方均根(RMS)值对发射光束远场发散角的影响,据此确定望远镜波像差的容差,以实现特定发射光束的远场发散角。结果表明:对于采用偏轴发射方案的激光通信系统,当望远镜的波像差RMS值优于0.13λ(λ为光束的波长)时,发射光束远场发散角小于10 μrad,当RMS值小于0.2λ时,发射光束远场发散角小于16.2 μrad,且仍有60%的概率小于10 μrad。在实验室中,不同温度下望远镜波像差及其对应的发射光束远场发散角的测试结果很好地验证了以上分析结果。

A mathematical model of the far-field beam distribution is built after the transmitted beam passes through the telescope with wave-front error. The effect of root mean square (RMS) value of wave-front error on the divergence angle of the transmitted beam is analyzed by numerical calculation combined with Monte Carlo method. Based on this, the tolerance of the telescope wave-front error required by the far-field divergence angle of the transmitted beam is determined. The analysis results show that for the laser communication system which the transmitted beam is off-axis on the telescope pupil, the far-field divergence angle is smaller than 10 μrad when the RMS of wave-front error is smaller than 0.13λ(λ is the light wavelength). The far-field divergence angle is smaller than 16.2 μrad when the RMS is smaller than 0.2λ and the probability of the divergence angle smaller than 10 μrad is 60%. The testing results of the wave-front errors of the telescope at different temperatures and the corresponding far-field divergence angles of the transmitted beams are well coincided with the analysis results.