A new approach for tolerance sensitivity reduction in lens optimization by controlling the first order derivatives of real ray height on pupil

During the production of a new designed lens system, overweighted assembling and manufacturing errors can cause the degradation of the performance of the whole system. Therefore, optimizations to improve the assembling and manufacturing tolerances sensitivity are greatly required in lens design industry. Following the principle of Gaussian optics, there are some practical implications of the first order derivatives which are of great significance to analyse the sensitivity of a lens system with its structural parameters changing. It is demonstrated that manufacturing errors, such as tilting, decentering and so on, induce the real rays' height shifting on each surface of an imaging system, which subsequently induces the decline of image quality. Thus, we proposed a scheme to use the first order derivatives of the height of a real ray on the image surface in a lens system versus that on the pupil surface, which indicate the height variations of the real ray on the image surface of the lens system caused by the displacement of its corresponding height on the pupil surface, as a merit function to improve the tolerance sensitivity of the whole system. A test program using the ZPL language in Opticstudio has preliminarily confirmed the effectiveness of our proposed methods. And as it is aimed at controlling the real rays of a lens system to reduce its sensitivity according to assembling and manufacturing errors, our scheme is theoretically able to appropriate to all lens design systems.