Objective Compared with visible light systems, cooled infrared imaging optical systems have better application effects in terrible climatic conditions. Compared with uncooled infrared imaging optical systems, they have higher detection sensitivity, longer viewing distances, and more excellent image quality. Therefore, the cooled infrared imaging optical systems are widely used in many fields, such as aerospace and military applications. Cooled infrared imaging optical systems with long focal lengths and large apertures have the problems of long barrel lengths, large volume, and high cost.To solve these problems and achieve a cold shield efficiency of 100%, the design of the catadioptric optical system is generally adopted, such as the Cassegrainbased catadioptric optical system. As sufficient theoretical guidance for determining the initial structure of such systems is lacking, we propose a method for optimal values of key parameters. We design a catadioptric cooled midwave infrared imaging optical system based on Cassegrain, which provides important theoretical guidance for the determination of the initial structure of this kind of system .Methods We derive the calculation formulas which are expressed by three key parameters: the shading coefficient α, magnification of the second mirror of Cassegrain β sec , and the vertical magnification of relay mirror β relay , including the initial structure parameters of the optical system, the T value of system length, the primary aberration, and the primary coma aberration of the Cassegrain system. The variation of the difficulty in correcting aberration and compactness of the system with α, β sec , and β relay are analyzed through derived calculation formulas. Based on the contradictory relationship
