Objective The actual working environment of vehicle-mounted LiDAR is complex, including seasonal long- time limit temperature and rapid changes in indoor and outdoor high and low temperatures. These temperature variations possibly change the internal optics and structure of the lens, which results in image plane drift and reduces imaging quality. For telephoto lenses, the image plane drift can be more obvious with the ambient temperature changes. The current passive athermalization design method has the problems of complex structure and large volume caused by multi-layer lens barrels, or the introduction of diffractive elements and aspheric lenses to increase the production cost, and the narrow temperature range of thermal-free, which is difficult to adapt to the practical applications in the complex environment of vehicle-mounted LiDAR. Therefore, it is necessary to reduce the image plane temperature drift and improve the environmental adaptability of telephoto lenses with an advanced athermal design method. Methods The telephoto lens which can accurately capture distant targets and magnify the details is integrated with a line array detector to improve the resolution. Meanwhile, based on the fact that the total length of the optical system of the telephoto structure is smaller than the focal length, the volume of the telephoto receiving optical system is compressed to a certain extent to realize the requirements of lightweight miniaturization and high resolution of the vehicle- mounted LiDAR. Aiming at the problem that the telephoto lens is susceptible to temperature, we improve the two-group compensation design method of the passive optical and mechanical athermalization to maximally offset the optical focal length change of the optical parts from the thermal difference brought by thermal expansion and contraction of the structural parts, and to reduce the image plane drift, thus realizing the athermalization of the telephoto lens. Finally, the image plane drift of the as-designed lens is less than the depth of focus over a wide temperature variation range from -40 to 100 degrees C. This is conducive to ensuring the imaging quality of the lens, and the designed structure has a simple preparation process and is easy to engineer and produce. Results and Discussions Different combinations of optical materials and optical focal length distributions are determined, structural components of different thermal expansion coefficients (TCEs) are matched, and the thermal difference of the optical system compensates for each other, with the system athermalization design achieved. Without the thermal expansion and contraction of the barrel holder taken into account, the focal shift of the lens with temperature change is always minimized and the image plane drift is 0.075 mm when the temperature increases to 100 degrees C (Fig. 7). The thermal expansion and contraction of the barrel holder is considered as a material to compensate for thermal aberration to make the sensor detecting surface always in the image plane. In the wide temperature range from - 40 to 100 degrees C, with the temperature change, the receiving optical system obtained from the selected optics and structural component materials has almost no significant focal shift, even when the temperature is as high as 100 degrees C, and meanwhile the amount of focal shift is only 0.021 mm, smaller than its depth of focus at room temperature (0.074 mm), and the field curvature and distortion of this optical system have small changes ( Fig. 8). The MTF at 30 lp/mm is all larger than 0.5 for each field of view (FOV), and the focal plane shifts are all small, which indicates that the designed lenses can maintain sound image quality over a wide range of temperatures from - 40 to 100 degrees C (Figs. 9 and 10). The diffuse spot radius in the full FOV is smaller than 7 mu m, which reveals that the focal shift of the lens is little affected by temperature ( Fig. 11). The results of photographing vehicles traveling on the road show clear imaging of the vehicles and obvious feature areas such as the outer contours of the vehicles ( Fig. 14). The above results prove that the imaging quality and temperature adaptability of the lens can be guaranteed by the above athermalization design to compensate the system thermal difference. Conclusions We employ the telephoto lens with a long focal length and small FOV to subdivide the scanning area and integrate a line array detector to achieve an image-level imaging effect. Based on the characteristic that the total length of the optical system of telephoto structure is smaller than the focal length, a receiving optical system with a telephoto ratio of 0.38 is designed, which has a smaller lens length and lower cost and meets the requirements of vehicle-mounted LiDAR in terms of high resolution, light weight, and small size. Given the large temperature difference in the working environment of vehicle- mounted LiDAR and the image plane drift of the telephoto lens, a passive optical and mechanical athermalization is implemented to confirm the reasonable combination of multi-plane spherical glass lens and structural components. Finally, a four- piece telephoto lens optical system with a simple structure and a focal shift of 0.021 mm less than the depth of focus of 0.074 mm over a wide temperature range from - 40 to 100 degrees C is designed. The MTF of each FOV at 30 lp/ mm is larger than 0.5 and the diffuse spot radius in the full FOV is smaller than 7 mu m. The vehicle imaging is clear, and the outer contour of the vehicle and other characteristics of the area are obvious, which achieves athermalization and shows favorable environmental adaptability.
