1.Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China 2.School of Remote Sensing & Geomatics Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. U1631240, 11903066)
Received Date:03 February 2021
Accepted Date:14 March 2021
Available Online:07 June 2021
Published Online:05 August 2021
Abstract:Corner cube retroreflector (CCR) as a main optical component of laser ranging retroreflector array plays a key role in satellite laser ranging (SLR) to cooperative targets. To accurately estimate the echo energy of SLR, it is necessary to precompute photons’ distribution in the distance of SLR station by calculating the Far field diffraction pattern (FFDP) of CCR under various conditions. In this paper, the analysis of the effective reflection area and optical reflectivity of CCR for arbitrary incidence angle are carried out, in which a method to calculate the CCR effective reflection area with a wider applicability is used, and the difference between optical reflectivity of metal-coated CCR and uncoated (total internal reflection) CCR is also discussed. On this basis, combined with optical diffraction theory, a simulation program for CCR FFDP calculation is established, thereby producing FFDPs of CCR for a variety of incidence angles under different coating conditions. The results show that the FFDP of metal-coated CCR is almost unrelated to the azimuth angle of incident light or polarization, but is determined only by elevation angle of incident light. The pattern is always like Airy spot or its tensile deformation. Relatively, uncoated CCR’s FFDP has a more complex figure, its reflected energy is divided into several lobes whose size, number and position are all influenced by elevation and azimuth angle of incidence, and also by the polarization. Generally, the incidence direction which has a large total intensity of far optical field is to an extent the same as that of large effective reflection area and optical reflectivity. Furthermore, simulation results with uncoated CCR presents a higher relevance of incidence direction and FFDP.To verify the reliability and correctness of these simulation results, a diffraction optical experimental system at a wavelength of 1550 nm is set up to conduct laboratory confirmation, including laser, camera, beam expander, rotating platform and other essential optics. A silver-coated CCR and an uncoated CCR (both made of fuse silica, each has different dihedral angle offset) are chosen to measure their FFDPs with random polarization directions at several random incidence angles. All the measurement results are in good agreement with the simulations of FFDPs. Keywords:corner cube retro-reflector/ effective reflection area/ far field diffraction pattern/ simulation calculation
特别地, 当切割系数$\eta $为0时为三角形切割角锥, 边界方程数量减少为6个. 利用以上方法, 对于任意切割系数的六边形角锥棱镜(包括三角形角锥), 在任意入射角度可利用统一的算法计算出有效反射面积. 对于圆切割反射器甚至不规则形状的角锥棱镜, 只需通光孔径的边界方程可以得到, 同样可以利用该方法求解不同入射方向的有效反射面积. 如图5所示, 以边长60 mm的熔石英($n$ ≈ 1.44@1550 nm)三角形角锥棱镜为例, 绘制了其不同切割系数下的有效反射面积随入射方位角度和入射角度的分布. 可以看出, 不同形状的角锥棱镜其有效反射面积随激光入射方向的分布有很大不同. 三角形切割角锥棱镜的有效反射面积分布在大入射角时具有类似三角形的分布, 在小入射角时随方位分布均匀, 如图5(a); 圆形切割角锥棱镜的有效反射面积分布是完美的圆对称图样, 如图5(c); 六边形切割角锥棱镜的分布则明显介于三角形和圆形切割角锥之间, 如图5(b). 图 5 不同形状角锥棱镜有效反射面积(mm2)随入射角(θ, 0o?90o)和方位角(φ, 0o?360o)的分布 Figure5. CCR active reflecting area in dependence of incidence and azimuth angle for different cutting mode. Polar axis refers to incident angle (θ, 0o?90o) in degree, the other axis refers to azimuth angle (φ, 0o?360o) in degree, the color bar refers to the active reflecting area in square millimeter