Abstract
A simplified mathematical model was proposed to describe the relationship between image quality and temperature gradient. It can be used to determine the maximal allowable temperature gradient in which optical system was applicable, as well as the applicability of optical system in given temperature gradient condition. Firstly, under some assumption conditions, the thermal deformation of optical surface and refractive index distribution caused by temperature gradient distribution were analyzed, and a simplified mathematical model was built to describe the impact of radial temperature gradient on optical parameters. Secondly, the model was validated by using finite element analysis software analyze an infrared lens. Finally, an application example was given. The image quality of a refractive infrared optical system in thermal environment with radial temperature gradient was analyzed by using the mathematical model proposed above and optical design software.
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