Design Method For Imaging Freeform Lens Based On Distortion Correction

With the demands of lightweight, compactness and novelty of the modern optical system, traditional optical elements like spherical and aspherical surfaces cannot meet the needs any more. Freeform surface has larger degrees of freedom, so it can control the illumination distribution and the outgoing direction of every ray as needed. Using freeform surface in optical system is a big trend in the recent years.In this paper, we started from the novelty and market demand of the non-planar imaging system. We aware that use ordinary imaging lens in non-planar imaging system will cause large distortion. Based on the analysis of the existing distortion correction methods, we propose that there is possibility that we can correct the non-planar imaging distortion using freeform surface.First of all, this paper analyzed the reason of the distortion on non-planar surface. Based on the visual principle of distortion correction, a new relationship between object points and image points is proposed. Employing the Snell’s law on the chief ray of each field of view, freeform design method based on partial differential equation was proposed. Based on the original imaging lens, each chief ray was reflected to their new imaging point, so the visual distortion can be corrected. Using this method, a freeform lens was designed to realize spherical projection. The distortion of the system was low enough to observe, and the image quality was high enough for projection system but not as high as the original one.In partial differential equation method, only the chief ray of each field of view was considered. This may correct the distortion while at the same time influence the image quality. Then this paper proposed another design method, which can design two rotationally symmetric freeform surfaces simultaneously, based on the micro spheres. In this method, we realize three rays (one chief ray and two marginal rays in the tangential plane) of each field of view reflecting to the new image point by using a macro spherical lens. Employing the middle point of each macro sphere, the profiles of the freeform surface can be obtained. For comparability with the partial differential method, a freeform lens with two freeform surfaces was designed for spherical projection using this method. Not only the distortion was corrected well but also the image quality was better than that in the partial differential equation method.With the deep study of the macro sphere method, we found that consider two marginal rays both from the tangential plane will cause a problem, which was the image quality of the sagittal plane was much lower than the image quality of the tangential plane. That is because the rays from the sagittal plane did not focused as well as that in tangential plane. Then we proposed a design method for non-rotationally symmetric surface based on the macro sphere by considering one marginal ray from the tangential plane, one marginal ray from the sagittal plane and also a chief ray. This extends the macro sphere method to3D, and makes it more general. Then using this method, a non-rotationally symmetric freeform lens was design for cylinder projection system. Both the distortion and the image quality of the system have satisfied our need.At last, this paper put a summary and outlook on freeform lens design and the non-planar imaging. The freeform design methods proposed in this paper aimed to distortion correction of the non-planar imaging, but the freeform lens had much wider application. The research of freeform surface will focus on better description method, more precise imaging aberration calculation, higher ray tracing efficiency and optimization efficiency in the near future.