Developing a new mathematical model and evaluation of the effect of parabolic mirror edge rounding on the collimated field quality of an infrared collimator used in single-channel aerial vehicle testing equipment

Abstract

Parabolic-mirror infrared (IR) collimators are widely used in single-channel flight vehicle testing to generate quasi-plane-wave radiation fields. However, edge diffraction degrades field uniformity and limits measurement accuracy. This paper presents a mathematical model of an IR collimator with rounded mirror edges to evaluate their influence on the radiation field. The model is formulated using the two-dimensional Helmholtz equation and solved by the boundary integral equation method to determine the induced surface current and the resulting radiation field. Numerical results demonstrate that rounded edges effectively suppress diffraction-induced amplitude ripples and improve field uniformity compared with conventional sharp-edge mirrors. The proposed model provides a theoretical basis for optimizing parabolic IR collimators for high-accuracy flight vehicle testing.