TG35 Emissivity of Blackbody Cavities

Blackbodies are commonly used as a transfer medium in the calibration of radiation thermometers. The ideal blackbody is perfectly isothermal and has an emissivity of precisely 1 at all wavelengths. However, no real material has an emissivity as high as 1, so practical blackbodies are created by forming a cavity, made to be as isothermal as possible, inside a material with a relatively high intrinsic emissivity (~0.9). These cavities take advantage of multiple internal reflections to provide an effective emissivity very close to 1 (~0.995 or higher). A radiation thermometer can then view the approximately-blackbody radiation emerging through an aperture at the front of the cavity. In general, the local effective emissivity of a blackbody cavity varies at each point along the inside of the cavity walls, and depends largely on the intrinsic emissivity of the cavity material and the geometry of the cavity. When a radiation thermometer views the inside of a blackbody cavity, the effective emissivity that it sees is a weighted average of the local effective emissivities of the cavity walls within the thermometer’s field of view. This integrated emissivity will vary from thermometer to thermometer, and will vary for a single thermometer if its focal point is changed – for example, by moving the thermometer so that it is focused either on the cavity aperture or on the cavity base. The local effective emissivity of the cavity walls is also affected by any temperature non-uniformities along the length of the cavity. Often, the front of the cavity is cooler than the base due to heat loss through the aperture. This effect causes the local effective emissivity to become dependent on wavelength, and thus the integrated emissivity for a given radiation thermometer will depend on its operating wavelength and bandwidth. In order to properly calibrate a radiation thermometer, it is essential that the integrated emissivity of the cavity is known for the device under calibration (DUC). When a radiation thermometer is also used as the reference device (REF), it is also essential that the integrated emissivity is known for the REF, as the integrated emissivities for the two devices will differ if the DUC and REF have different fields of view or operate at different wavelengths. The purpose of this technical guide is to provide advice on how to calculate the integrated emissivity for any cavity/thermometer combination. If high accuracy is not required, and if the cavity is approximately isothermal, then a simple formula can be used to determine the integrated emissivity. However, for high accuracy, methods for calculating the integrated emissivity are highly mathematical and require iterative algorithms to achieve a solution. Hence, this technical guide is accompanied by a software application that implements algorithms to calculate both the local effective emissivity at all points on the inside of a cavity and the integrated emissivity for a radiation thermometer viewing the cavity. Instructions for using the software are included in this technical guide, and for those readers interested, the mathematical details are given in the appendices.