Calculating model for equivalent thermal defocus amount in infrared imaging system

• Analyze the equivalent effect of temperature variation and room-temperature defocus.
• A parameter called equivalent thermal defocus amount (ETDA) is defined.
• Room-temperature defocus has the same imaging effect as temperature changes by ETDA.
• Experiments on focal shift, aberration with temperature and ETDA prove our model.

The main effect of temperature change on infrared imaging system is the focus shift of infrared lenses. This paper analyzes the equivalent influence on imaging between the temperature change and the defocus at room temperature. In order to quantify the equivalence, we define an equivalent thermal defocus amount (ETDA). The ETDA describes the distance of the photosensitive surface shifting at room temperature, which has the same effect on imaging as the temperature changes. To model the ETDA, the expression of the focal shift as a function of temperature is obtained by solving partial differential equations for the thermal effect on light path firstly with some approximations. Then point spread functions of the thermal effect and defocus at room temperature are modeled based on wave aberration. The calculating model of ETDA is finally established by making their PSFs equal under the condition that the cutoff frequency of infrared imaging systems is much smaller than that of infrared lens. The experimental results indicate that defocus of ETDA at room temperature has the same influence on imaging as the thermal effect. Prospectively, experiments at high/low temperature can be replaced by experiments at room temperature with ETDA.