在单视点结构约束条件下推导了给定红外探测器参数(像元规模和像元中心距)和俯仰角范围时, 二次曲面反射镜面型(离心率)、反射镜厚度、反射镜与折射镜头之间的安装距离、折射镜头焦距等参数的数学公式, 为建立单视点双曲面折反射红外全景成像系统提供了几何约束关系。与此同时, 针对双曲面反射镜的特点, 推导了其用于单视点折反射红外全景成像系统时空间分辨力(垂直方向瞬时视场和水平方向瞬时视场)的数学公式, 并在理想大气、假设目标对比度足够高、探测方程相关参数最简化的条件下将其与现有的NVThermIP模型结合获得系统作用距离的公式。采用不同像元规模和灵敏度(噪声等效温差)进行了仿真, 发现: (1) 系统空间分辨力随像元规模的增大而增大; (2) 系统作用距离随像元规模和灵敏度的增大而提高, 但灵敏度的增大对作用距离的改善不明显。

Under the constrains of single-viewpoint and the requirements of the specific detector and vertical field of view, the equations of eccentricity, thickness of the hyperbolic mirror, install distance and the geometric constraints of single viewpoint hyperbolic catadioptric infrared panoramic imaging system which utilizes the quadratic surface of reflective mirror were derived. At the same time, as for the hyperbolic mirror, the equation of the resolution which include instantaneous field of view in the vertical direction and instantaneous field of view in the horizontal direction of the single viewpoint hyperbolic catadioptric infrared panoramic imaging system were deduced. Under the situation of ideal atmosphere, high target contrast, the simplest range equation which combined with the NVThermIP model was established. The simulation was under the conditions of different size and sensitivity of the detector. The simulation results show that: the spatial resolution of the system increases with the increase of the size of the detector; the range performance of the system increases with the increase of the size and sensitivity of the detector. However the increase of sensitivity is not obvious to the improvement of the range performance.