制造约束下自由曲面离轴多反光学系统设计方法

Design Method of Off-Axis Reflective Optical System for Freeform Surfaces under Manufacturing Constraints

在离轴多反光学系统的装调过程中,光学对准工作成本高、操作复杂。光学系统的一体化加工制造方法通过在设计过程中加入制造约束避免了离轴多反系统的反复装调。然而,现有自由曲面离轴多反系统的设计方法很少考虑制造约束,设计的光学系统无法满足一体化加工制造的要求。针对这一问题,提出了一种符合制造约束的离轴多反系统自动生成方法。首先,提出了由共圆程度函数和遮拦评估函数构成的制造约束模块,对初始结构的合理性进行判断;其次,通过对离轴多反系统的光路结构进行光线追迹,构建了光学系统初始结构的综合目标搜索函数;然后,以搜索获取的初始结构参数为输入,结合改进的Wassermann-Wolf(W-W)法,提出了制造约束下自由曲面离轴多反系统的设计方法。实验结果表明,所提方法可以在保证较高成像质量的前提下,快速、准确地设计出符合制造约束的自由曲面离轴多反系统。

Objective Off-axis reflective optical systems for freeform surfaces have the advantages of no chromatic aberration,no central obscuration,and a large field of view in one direction,so they are widely used in many optical observation fields.The optical system design and machining,as well as precise system assembly,are three key core technologies to obtain high quality optical imaging systems.Current design methods for freeform optical systems rely on the experience of optical designers to obtain initial structural parameters before calculating the coordinates of the discrete points on a mirror surface.To solve this problem,it is necessary to design a fast and accurate method for obtaining the initial structural parameters of an off-axis reflective optical system during the design.Furthermore,the optical alignment to assembly the manufactured system is also a high-cost and complex operation.Current integrated processing and manufacturing methods avoid the repeated assembly process of off-axis reflective systems using incorporating manufacturing constraints during the design.However,the manufacturing constraints are not considered by most design methods for freeform off-axis reflective systems,resulting in the designed system being unable to meet the requirements of integrated machining and manufacturing.Therefore,design methods are needed to guide the design of initial structural parameters and freeform offaxis reflective optical system under manufacturing constraints.Methods We propose an automatic generation method to design the starting points for off-axis freeform systems based on manufacturing constraints.First,the unified description of the surface shape and pose of mirrors in a global coordinate system is provided and the method for ray tracing is given.Second,the manufacturing constraint module is designed.When designing the initial structure of the off-axis system based on manufacturing constraints,it is necessary to take into account both the removal of the obstruction and the fit degree of the mirrors to the cylindrical reference surface.Therefore,a manufacturing constraint module composed of a degree of co-circularity function and obstruction evaluation function is proposed to assess the rationality of the initial structure.Then,we conduct a comprehensive objective function for the initial structure of the optical system by tracing the optical path structure of the off-axis reflective system.The most suitable initial structure parameters for the design requirements are achieved by searching the minimum value of the comprehensive objective function.Finally,taking the initial structural parameters as the input,combined with the improved Wassermann-Wolf(W-W)method,we propose a design method for a freeform off-axis reflective system under manufacturing constraints.Results and Discussions Two freeform off-axis three-mirror reflective systems are designed by the proposed method.The field of view of the first system is 4°×4°and the F-number is 3.3.The entrance pupil diameter is 90 mm and the radius of the cylindrical reference surface is 150 mm.The initial structural parameters are searched based on these design requirements,and the starting point of the freeform off-axis three-mirror system is obtained through the combination of the improved W-W method(Fig.5).To further quantify and verify the performance of the designed optical system,we change the tilt angle and mirror spacing of the mirrors.In addition,10 different mirror pose combinations are randomly generated to simulate the possible combinations of mirror positions,which are used by the improved W-W method directly without searching for the initial structural parameters.The imaging quality of these 10 systems has significant uncertainty,and the average manufacturing error value is higher than the design starting point generated by the proposed method.The field of view of the second system is 2°×2°,the F-number is 3.5,and the entrance pupil diameter is 85 mm.In the generated design starting point,the three mirrors are close to the cylindrical reference plane,and the rays of each field of view converge at the image plane.After obtaining 10 random mirror position combinations,the obstruction is manually removed to simulate the possible mirror position combinations used to generate the design starting points directly by the improved W-W method when the initial structural parameters were obtained by manual off-axis.Among the 10 design starting points generated directly by the improved W-W method,the average root mean square(RMS)wavefront error is 0.95λ(λis wavelenth)and the average RMS spot radius is 36.10μm(Fig.10),both are higher than the design starting point generated by the proposed method,and the imaging qualities are unstable.This indicates that even in the absence of obstruction in the initial structure,the RMS wavefront error and RMS spot radius of the system generated directly by the improved W-W method are strongly affected by the changes in the distance between mirrors,and the manufacturing error is still greater than the design starting point generated using the proposed method.Conclusions We propose a design method for off-axis reflective optical systems with freeform surfaces under manufacturing constraints.Under the consideration of manufacturing constraints,the initial structural parameters that meet the design requirements are automatically obtained through simple searching,and then the design starting point of the freeform off-axis reflective system is obtained.The experimental results show that by searching the minimum values of the comprehensive objective function proposed in this study and passing these values into the improved W-W method,the cocircularity characteristics can be significantly improved with no optical path blocking,and the problem of unstable imaging quality is avoided.The proposed method can effectively guide the freeform off-axis reflective systems manufactured by the integrated ultra-precision grating milling technology,and also can be applied to design more general reflective systems.The designers can choose or change the range of application of the subfunctions in the objective function.