Optimising Blackbody Cavity Shape for Spatially Uniform Integrated Emissivity

The emissivity of a blackbody cavity, as seen by a radiation thermometer viewing the cavity, depends on both the field of view of the thermometer and the distribution of local effective emissivity values within the field of view. For cylindro-conical cavities, the local effective emissivity generally attains a maximum value at the apex of the cone and drops along the conical section. Thus, radiation thermometers with different fields of view see different blackbody emissivity values. This impacts, particularly, on the calibration of wide-angle low-temperature radiation thermometers and thermal imaging systems where each pixel responds to a different radiance. The spatial uniformity of the effective emissivity profile depends principally on the cone angle, with a weaker dependence on the length-to-diameter ratio of the cavity, the intrinsic emissivity of the cavity surfaces, and the temperature gradient along the cavity. In this paper, a nonlinear least-squares method is used to determine the optimal cone angle as a function of the cavity parameters. It is concluded that full cone angles close to 160∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${^{\circ }}$$\end{document} provide the flattest effective emissivity profile across the conical section of the cavity for typical cavity parameters. A method is also described for calculating the value of integrated emissivity, which includes the umbral and penumbral regions seen by an imaging radiation thermometer.