基于Levenberg-Marquardt算法的旋转双棱镜指向偏差修正

Correction of Pointing Deviation of Risley Prisms Based on Levenberg-Marquardt Algorithm

针对旋转双棱镜系统指向误差较大、误差源较多等指向精度较差的问题,提出了一种新的旋转双棱镜指向偏差修正方案。采用非近轴光线追迹方法建立旋转双棱镜指向模型和二维转台指向模型,在全视场区域内均匀选取若干点,比较旋转双棱镜理论出射光束与实际出射光束的偏差,通过Levenberg-Marquardt迭代算法对旋转双棱镜前镜和后镜的转角误差、楔角和折射率进行修正。在整个视场区域内修正后,指向最大偏差由8.37 mrad变为3.75 mrad,平均指向偏差由4.00 mrad变为1.38 mrad,并且当俯仰角较小时,修正效果较好;在俯仰角小于15°的视场区域进行单独修正后,最大指向偏差变为1.51 mrad,平均偏差变为0.84 mrad。所提修正方法提高了旋转双棱镜的指向精度,对旋转双棱镜指向偏差的补偿修正具有一定的参考价值。

Objective A space laser communication terminal generally comprises two basic systems a laser communication system and an optical tracking system.The former is for information transmission between two satellites,and the latter is for pointing,acquisition,and tracking(PAT).The space laser communication system is advancing toward miniaturization and is lightweight.However,traditional optical tracking and sighting systems usually use gimbal turrets and gimbal turning mirrors to attain significant beam angles.Furthermore,such structures are large in size,large in inertia,poor in dynamic performance,slow in response time,and sensitive to vibration,which is not conducive to the installation of the carrier platform and the balance of the carrier posture.Compared with the traditional structure,Risley prisms are small in size,have excellent viewing axis adjustment function,and can realize large-angle deflection of the beam;therefore,the rotating biprism is more suitable for space laser communication.However,since Risley prisms are composed of two coaxial wedge prisms,there is no linear relationship between the outgoing light and the wedge prism s rotation angle,making it challenging to solve the outgoing beam of Risley prisms.Additionally,there are several error sources of Risley prisms,and the pointing is not sufficiently accurate.Therefore,it should be corrected to obtain a more precise pointing,which can be used in space laser communication.Methods A new method of correcting the pointing deviation of Risley prisms is proposed to aim at the problem of poor pointing accuracies,including the significant pointing error of Risley prisms and more error sources.This study uses a non-paraxial ray tracing method to establish a Risley prism pointing model and a two-dimensional turntable pointing model.Many points are uniformly chosen in the entire field of view,and the deviation between the rotating double prism s theoretical and actual output beams is compared.The Levenberg-Marquardt iterative algorithm corrects the rotation angle error,wedge angle,and refractive index of the front and back mirrors of Risley prisms.Higher-precision pointing is achieved by correcting the inaccuracy of the initial incident beam relative to the ideal optical axis and separately correcting the region with a small pitch angle to address the issue of low pointing accuracy in the area with a big pitch angle.Results and Discussions From the simulation findings of the final convergence of the Levenberg-Marquardt algorithm with various initial values,different initial values have little impact on the final optimization results of this experiment(Fig.2).The entire field of view of Risley prisms is pitch angle 0°-29.22°,azimuth angle 0°-360°.After optimizing the whole area of view by the Levenberg-Marquardt algorithm,the maximum pointing deviation is 5.33 mrad and the average pointing deviation is 1.82 mrad(Fig.6).It can be observed that the pointing error of the initial incident beam relative to the ideal optical axis will have a relatively large impact on the pointing accuracy of Risley prisms from the effect of the simulation error on the pointing deviation between the actual outgoing beam and the theoretical outgoing beam(Fig.7).After adding the correction of the error of the initial incident beam relative to the ideal optical axis by the Levenberg-Marquardt algorithm,the maximum pointing deviation is 3.75 mrad and the average pointing deviation is 1.38 mrad(Fig.8).After using the Levenberg-Marquardt algorithm to correct the points with a pitch angle of less than 15°,the maximum pointing deviation is 1.51 mrad and the average deviation is 0.84 mrad(Fig.9).Conclusions In this study,the non-paraxial ray tracing method is used to develop the pointing model of Risley prisms.Numerous points are evenly chosen in the entire area,and a two-dimensional turntable pointing model is shown to accurately measure the actual outgoing beam of the Risley prisms.Comparison is made between the deviation of the theoretical and real output beams of Risley prisms.The rotation angle error,wedge angle,and refractive index of the front and rear mirrors of Risley prisms are corrected via the Levenberg-Marquardt iterative procedure.After correction in the entire field of view,the maximum pointing deviation changes from 8.37 mrad to 3.75 mrad,and the average pointing deviation changes from 4.00 mrad to 1.38 mrad.Moreover,the correction effect is better when the pitch angle is small.For example,after individually correcting the field of view area with the pitch angle less than 15°,the maximum pointing deviation becomes 1.51 mrad and the average deviation becomes 0.84 mrad.This method improves the pointing accuracy of Risley prisms,and it has a particular reference value for correcting the pointing deviation of Risley prisms.