Integral Design of Optical Systems with a Free-form Surface based on Theoretical Calculation and Optical Design Software

For recent years, with the development of manufacture, free-form surfaces are widely used in optical systems because of the degrees of freedom and the capacity of correcting optical aberrations. Nowadays, commercial optical design software such as Optics Studio are commonly applied to optimize an optical system from a suitable initial structure to obtain high-quality imaging characteristics. The initial structure optimized by software must include the surface types and its parameters. Notice that the free-form surface type is unknown, let alone the parameters. Therefore, the initial structure of a free-form surface cannot be designed by commercial optical design software directly. The software cannot optimize or analyze the system with free-form surfaces either. This paper proposed an integral design method of optical system with free-form surfaces based on theoretical calculation and optimization of optical design software. Firstly, Fermat's principle, equal optical path length between object and image, is applied to calculate the sampling data points of the free-form surface. Data points are fitted using least-square fitting algorithm to obtain a the surface type and its parameters, which are used as the initial structure. Secondly, a commercial optical design software further optimize the optical system containing the free-form surface. Not only the free-form surface but also other parameters can be optimized by the software. With the powerful functions of image quality and tolerance analysis of the software, we can obtain a high-quality imaging system with free-form surfaces in a short time. This method solves the problem that commercial software cannot design optical systems with free-form surfaces directly. Meanwhile initial structure with free-form surface can be acquired directly by this method. In addition,the powerful functions of the software such as optimization, image quality and tolerance analysis are fully utilized in the process of integral optimization. Since the system will be further optimized by the software, a small amount of sampling data points is enough to calculate the initial structure which speeds up the calculation. A passive ranging and three-dimensional imaging system with chiral phase mask is designed as an example. Different from conventional imaging system, two image points will be obtained by the system when one point is used as the object. Apparently, it is difficult for any commercial optical design software to design. The novel integral method proposed in this paper is applied to this system. Firstly, the system is designed in reverse sequence for the sake of simplification. A doublet with effective focal length 200mm and f-number 8 is used as the initial structure. Two points at (0,0.3,256.1) and (0,-0.3,256.1) are used as the "object" which will image at (0,0,-63.6)as the "image" in the reverse sequence. A free-form surface is added in front of the doublet, thus the whole system turns to a triplet system. 6X12 sampling data points are calculated to fit an XY polynomial surface. Secondly a commercial optical design software further optimizes the optical system with the free-form surface. Finally, we obtain a high-quality imaging system with a free-form surface. The MTF (Modulation Transfer Function) performance of the system is closed to diffraction limit.