| Illumination,as one of the basic mankind’s needs,has been developed greatly in the recent years and more problems need to be solved due to the social changes.In non-imaging optics,a lot of design methods have been proposed to solve illumination problems to meet our bizarre needs.For example,the ODE and PDE methods which take solving the differential equations as the core,the tailoring method which the solution are found step by step through vectors relationship,and SQM with discrete mappings and so on.However,these methods generally only for one or several special circumstances,the scope of application is relatively narrow.The reason,on the one hand,is the different illumination needs,the corresponding optical model is difficult to unify,the design methods used must be different,and even the results obtained by two methods may be very different;On the other hand,man-made mappings are generally relatively simple,it is difficult to be optimal,resulting in a deviation between the obtained surface and the ideal,and even the surface itself may be discontinuous and non-smooth.SQM is a method which is notdependent on the mapping relation directly,but the resulting is composed of quadric surface envelope,and is not smooth.A good result of the surface optimization with solving the elliptical Monge-Ampére equation from an initialized surface generated by the SQM.The solution is complex,so the model is difficult to be built,and it often consumes many hours.There are three aspects of optimization methods are proposed in this thesis: Firstly,a mesh partitioning algorithm based on the topological conservation principle is proposed to improve the mapping.Combined with the gradient,this algorithm aims to divide the target area of arbitrary boundary into all quadrilaterals;Secondly,an iterative algorithm of SQM is improved.The gradient and divergence conversion between the actual flux and the ideal is used to guide the modification of the optical constant,finally reducing the time consumption;Thirdly,on the basis of SQM,orthogonal polynomials are used in surface interpolation on the initial surface in order to obtain a continuous smooth free-form surface that satisfies the mapping.Simulations and experiments show that the proposed optimization algorithm can get good results for the general illumination design and even the image light distribution problems.It’s easier to be understand,solved quickly,and can be applied widely. |
