Abstract: In passive space exploration, the target signals are typically extremely weak and the detection system needs to achieve high sensitivity and low noise requirements. To satisfy these demands, cold optics has become indispensable. This method integrates optical components (such as lenses and mirrors) into cryogenic environments and combining them with cryogenic detectors to achieve the detection needs. However, conventional optical design faces constraints due to the limited cooling capacity of spaceborne instruments. The research presents a cold optical model based on multi-reflection and optimizes the window size design according to this model. A design for a 10 THz focal-plane array imaging system, employing pulse-tube coupled with J-T refrigeration for space application was proposed. The thermal leakage of the system is evaluated analytically, and a cold optical experiment validates the theoretical model, demonstrating strong agreement between the predicted result and the experimental result.