Objective  Telephoto lens is widely used in astronomy, space optics, aerial reconnaissance, security monitoring and other fields due to its ability to image distant objects. For devices with high requirement of miniaturization and lightweight, such as telephoto lens mounted on mobile phone, the majority solution is to use one or more prisms to fold the optical path to form a periscopic-type lens. Although this approach allows the element to be placed in an ultra-thin mobile terminal, it does not solve the lengthy, voluminous and weighty problem caused by the characteristics of telephoto lens. Instead, multiple prisms are added to the system as reflective elements, making the structure even bulkier. For the purpose of designing a compact and lightweight telephoto lens, this paper explores the solution of compact system design based on the structure of off-axis three-mirror imager. The initial structure is designed by utilizing the optical properties of conical surface to achieve ideal imaging of the on-axis object. Freeform surface is applied to extend field of view (FOV) to complete the design of a compact telephoto optical system.

  Methods  Off-axis three-mirror imager has the advantages of lightness, compactness, non-chromatic, unobstructed aperture, high reflectiveness, and low optical energy loss for all wavelengths after being coated. A compact telephoto lens design method is proposed based on the off-axis three-mirror structure. Firstly, positive-negative-positive (PNP) power distribution was decided for the purpose of compactness. Unobscured PNP reflective imagers with different layouts of elements are listed (Fig.2). Then they are analysed and compared in terms of both compactness and imaging performance. After the structure type has been determined, parameters such as distance and angle can be calculated (Fig.3). Next, the optical properties of conical surfaces whose focal points conjugate between each other are used to calculate surface parameters such as conical coefficients and vertex radius of curvature to construct the initial structure (Fig.4), which can image on-axis object ideally. Taking telephoto lens applied to smartphone as an example, after calculating initial structural parameters with the above design method, the judgment condition that ray is obscured or not is established, and an optimized design strategy is developed to construct freeform surface, extend FOV (Fig.5) and optimize the system (Fig.6). The design of a compact telephoto lens is implemented and the feasibility of the design method is verified.

  Results and Discussions   The result (Fig.7) is a compact telephoto lens with an F-number of 5, equivalent focal length of 196 mm and FOV of ±3.8°, consisting of only three reflective mirror and volume of 26 mm × 24 mm × 10 mm. The design results show that modulation transfer function (MTF) is greater than 0.2 at 114 lp/mm for all FOV (Fig.8), relative distortion is less than 0.5% (Fig.9) and displays good performance of imaging quality (Fig.10), meeting the imaging requirements of mobile phone lens. Our design is comparable to the current market indicators of periscopic-type telephoto lens in terms of design parameters. Although the F-number is slightly larger, effective focal length is longer, and it has obvious advantages in miniaturization and light weight.

  Conclusions  In order to achieve a compact and lightweight telephoto lens design, this paper proposes a design method for a compact telephoto system based on optical characteristics of conical surface, combined with the off-axis three-mirror structure type. With the initial structure of off-axis three-mirror with ideal imaging at on-axis object, freeform surface is used to achieve a compact, lightweight, and high image quality telephoto system based on the unobstructed judgment condition and FOV expansion optimization strategy. The solution contains only three mirrors to fold ray path and compress volume, resulting in a lighter system with fewer lenses and less optical energy loss than a refractive telephoto imager, and an unrestricted wavelength band which means non-chromatic. Additionally, conical surface is used to calculate off-axis initial structure directly without aberrations at on-axis object, and subsequently controlling optimization process in combination with unobstruction judgement, avoiding the problem of aperture obstructed in the reflective telephoto. The result is a compact telephoto lens with an F-number of 5, an equivalent focal length of 196 mm and a field of view of ±3.8°, which meets the imaging requirements and has obvious advantages in terms of miniaturization and lightness compared to periscopic-type telephoto lens, providing a new solution to the design of compact telephoto lenses.