Optical Freeform Surface Shape Description Method And Ray Tracing Model

With the development of optical system, free-form surface is more and more important in some special optical system. However, some related techniques are limited by the imperfect basic theory of its surface description and ray tracing method, including the designing, manufacturing and measurement.Based on the development of free-form surface description and ray tracing method, the basic theory of free-form surface is studied in this paper. On the one hand, the radical basis functions with Gaussian form is applied to describe free-form surface shape. The number and central distribution of basis functions are determined firstly, and then the coefficients of each basis function are solved by the radical basis fitting. Finally, the shape expression of free-form surface is accumulated with the production of basis function and its coefficient. The simulation result shows that high fitting accuracy is acquired after this method applying to fit sphere, asphere and extended polynomial surface. On the other hand, a novel method based on segmentation and iteration of sub-surface is presented as the description of optical free-form surface, aiming at the complex and relatively smooth character of its figure. Three steps are executed in the whole process of ray tracing of free-form surface. Firstly, free-form surface is divided into some sub-surfaces by discrete points, and then target sub-surface is determined by angle sum of a triangle theorem. Finally, iteration algorithm is utilized on the target sub-surface. The corresponding simulation is done in MATLAB, including even asphere, biconic surface, extended polynomial surface and radial basis function surface. Compared with the tracing result in ZEMAX, the method presented is of high accuracy, good versatility and high speed. The deviation of the intersection between ray and surface is about 10-3nm, and the deviation of the direction cosine of refracted ray is about 10-3"A novel free-form surface design method is presented to eliminate astigmatic in chapter 5. Two basis theory presented above are utilized on the system designed that verify the usefulness of those two theories. The diameter of spot diagram and PV of wavefront of free-form optical system are much less than them of the traditional optical system.