Virtual reality head-mounted displays (VR-HMDs) are experiencing increasing demands for improved imaging performance and enhanced user comfort. This has led to the popularity of VR lenses that offer a wide field of view (FOV), large pupil size, and compact form factor. However, achieving these desired properties simultaneously presents significant challenges. Three generations of VR optical solutions have been developed, each with its own limitations. The earlier smooth aspherical VR lenses, while capable of providing a wide FOV, are bulky and fall short in terms of image quality. Fresnel VR lens offers a larger FOV and reduced weight, but it suffers from "ring artifacts" that result in low contrast and poor resolution. A more recent solution, an ultrashort focal polarization catadioptric VR lens, takes advantage of polarized light transmission to fold the optical path three times within a short physical length. This design reduces the thickness of the catadioptric optical module to approximately half that of the Fresnel lens, alleviates focusing challenges, and enables smoother optical surfaces. As a result, ultrashort focal polarization catadioptric VR lenses have become the mainstream optical solution for VR-HMDs, offering significant benefits such as a large FOV, large exit pupil, ultra-thin structure, and high resolution. However, despite their advantages, most of these lenses employ aspherical surfaces, and the theoretical model and design process of the system have not been extensively elaborated upon, nor has the image quality of the system been thoroughly explored. Consequently, there is an urgent need for new optimization design methods to guide the development of ultrashort focal polarization catadioptric VR lenses. These methods will not only contribute to the design process but also facilitate the high-definition, lightweight, and market-oriented evolution of VR-HMDs.

A mathematical model is established to describe the ultrashort focal polarization catadioptric VR lens, demonstrating its structural and imaging advantages compared with traditional straight-through optical schemes (Fig. 1). The selection of polarization elements (Fig. 2) and the conversion of the polarization state of light within the lenses are explained. By constraining the shape of each lens, the birefringence of the plastic lens is minimized, resulting in improved optical efficiency. The optical focal length distribution formula is derived based on the optical path diagram of the three-piece ultrashort focal polarization catadioptric VR lens (Fig. 4), enabling the determination of the initial structure of low birefringence lenses with uniform focal distribution and smooth optical surfaces (Fig. 5). Additionally, the application of annular stitched aspheric surfaces to enhance imaging quality is introduced, along with the mathematical definition of the annular stitched aspheric surface and the constraints necessary for smooth stitching (Fig. 6). Finally, an automatic image quality balance optimization algorithm based on an error function is presented, allowing for the improvement of image quality in each field.

By combining the three optimization strategies of optical focus allocation, stitched aspheric surface, and the weight adjustment method, an ultrashort focal polarization catadioptric VR lens with a field angle of view of 47° and a total length of less than 9.5 mm is designed (Fig. 9), with a maximum distortion of less than 3%. Compared with that of the ordinary aspheric ultrashort focal polarization catadioptric VR lens (Fig. 8), the aberration of the edge FOV is significantly reduced, while the aberration maintains small. Another ultrashort focal polarization catadioptric VR optics with a field angle of view of 96° is designed with the same optimization strategy, and the image quality of the system before and after using the stitched aspheric surface is compared (Fig. 10). The image quality improvement is more obvious in the lens with a FOV of 96° compared with that in the lens with a FOV of 47°. Finally, the development process of a ultrashort focal polarization catadioptric VR lens (Fig. 11) is introduced, and a prototype with a large pupil, large FOV, high resolution, and ultra-thin structure is displayed (Fig. 12). Stray light test is carried out (Fig. 13), verifying the effectiveness of the stray light suppression method described in the previous section.

The structural advantages and polarization principle of the ultrashort focal polarization catadioptric VR lens are analyzed, the factors affecting the optical efficiency of the system are explored, and the focal-distribution strategy and the process of solving the initial structure are introduced. The method to suppress the stray light caused by the birefringence on the component surface is obtained in the optimization stage. The transformation of an ordinary aspheric surface into an annular stitched aspheric surface is proposed for the first time to improve design freedom. The mathematical definition, establishment process, and optimization strategy of ring splicing aspheric surface are studied. Combined with the error function, the automatic image performance balance algorithm of each FOV is discussed. The feasibility of stitched aspheric surfaces is proved via the design results, providing a higher degree of freedom for VR lens optimization. Additionally, the image quality balancing algorithm is verified to realize image quality balance and improvement effect on VR lens of medium and high FOVs. The fabrication process of ultrashort focal polarization catadioptric VR lens is introduced, and the prototype demonstrates good performance and compact sunglass form after comprehensive analysis and experimental test. The proposed design approach is instructive for the development of high-definition and lightweight VR-HMDs.