Thermography equation for Non-Perpendicular infrared Measurements: Derivation, Analysis, and experimental Validation

Abstract

The thermography equation quantitatively describes the relationship between the infrared radiation emitted from a measured surface and its temperature. A thermal camera captures this radiation and calculates the surface temperature based on this equation. In practice, a conceptually derived thermography equation is often used, which does not clearly describe the dependence of the total radiant flux on the scanned area, especially during oblique measurements. In such cases, it is assumed that the emission intensity decreases with the cosine of the angle of deviation from the normal. To clarify this dependence, the brand new thermography equation from fundamental physical principles was derived. It was found that the total radiant flux incident on the thermal camera's sensor from the surface area corresponding to a single pixel does not depend on the physical size of that area, but only on two parameters: the instantaneous Field of View and the size of the entrance pupil of the lens. The relationship also indicates that the measurement angle does not affect the value of the total radiant flux, which contradicts the common intuitive assumption based on Lambert's law. The validity of the newly derived equation was tested experimentally within a defined range of conditions. The results of experiment showed that in the case of oblique scanning (this applies to both large and small scanning angles), the emissivity (and therefore the temperature) of the analyzed surface with a homogeneous temperature remains the same, regardless of the scanning angle. The experimental results were consistent with the theoretical predictions and did not falsify the assumptions of the model.