Study On The Design Of Freeform Surface Illumination System Based On Mathematical Method

Compared with the traditional illumination optical system,the freeform surface illumination optical system not only has more flexible space layout but has higher design freedom,which can finely control the outgoing light and realize complex irradiation output.This provides a solid foundation to realize healthy lighting,energy-efficient lighting and green lighting.With the development of society and the advancement of technology,freeform surface lighting will have a wider range of applications,and research on its design methods will have greater application value.Based on this,the thesis intends to study the design of freeform surface illumination optical system,and provides a set of reliable optical solutions to make the design simple,efficient and flexible.During the research,three stages were performed.The first stage involves the design of freeform surface illumination optical system based on the first-order differential equations,which is oriented to symmetric radiation output.The second stage extends to realize the design from 2-dimensional(2D)to 3-dimensional(3D),and obtains the freeform optical system with fine control of the outgoing light.During the third stage,two mathematical models of the freeform surface illumination optical system in the form of Monge-Ampère equation are constructed,and better designed effect is obtained.The main contributions and innovations of this thesis are as follows:1)Two mathematical models,explicit and implicit,and for the optical system with symmetric illumination output,are obtained.And the design method,combing the implicit design and B-spline generatrix construction,is confirmed by simulating and analyzing the designed result of the two models,which realizes ideal irradiation output with a few number of sampling points.Then the optical system,obtained by the design method,is experimentally verified,and the output characteristics of the system are studied.By comparing the experimental results with the solar simulator optical system having similar irradiation targets,the characteristics of such systems are obtained.2)The spectral method is adopted to process the Monge-Ampère system equation.For the simple output,such as uniform square irradiation output,the system equation is processed by the Chebyshev spectral method.The designed result is simulated and the result demonstrates that the unevenness of the irradiation output is 4.91%.Since the sampling points of the Chebyshev spectrum method are sparse in the center and dense at edge,the design effect of the center area for high-resolution complex irradiation output is insufficient.For this issue,the Fourier spectral method is adopted to process the system equation,and its boundary sampling nodes are specially processed to eliminate the influence of its internal periodicity on the calculated results.Finally,the solution which fits for the high-resolution complex irradiation output is realized.3)When the system design expands from 2D to 3D,the design efficiency is low because of the complexity of the system equation,and the energy utilization of the light source is always insufficient because it is difficult to deal with the mapping between topological squares and topological circular.For this condition,two simplified system models in the form of Monge-Ampère equations,one based on the mapping of the light source to the target irradiation and the other based on the mapping of the target irradiation to the light source,are constructed according to the essence of the system,which lies in energy handling and redistribution.The design difficulty and efficiency are reduced and improved,and the constraints of the geometric relationship of the freeform illumination optical system are excluded.The system model,based on the mapping from the target to light source,further enhances the design capability.The design method is verified by using two typical expected irradiation outputs,and the obtained systems are evaluated by the combination of simulation and experiment.The final results reveal that the outputs of the two optical systems are consistent with the expected results,the expected complex irradiation output is realized,the mapping between the topology square and topological circular is also realized,and the energy efficiency of light source is improved.In summary,the design method of the freeform surface illumination optical system studied in this thesis can not only deal with the design of high-resolution complex irradiation output optical system,but also realize the mutual mapping of topological circular and topological square between light source and target irradiation,to achieve higher energy utilization of light source.Therefore,it is a universal,simple,efficient,flexible and practical design method for freeform illumination optical system.