Correcting Radiation Thermometry Measurements for the Size-of-Source Effect

The size-of-source effect (SSE) is a major contributor to error and uncertainty in both the calibration and use of a radiation thermometer, and correcting for the SSE is necessary to achieve high accuracy. There are several recognized methods for measuring the SSE; each measures a slightly different quantity and may depend on one of various parameters, such as the diameter of the black spot or the maximum aperture diameter. When applying corrections, it is necessary, in principle, to recognize which SSE quantity has been measured and under which conditions, as the correction formulae for each quantity differ and may also be functions of the measurement parameters. In this article, the formulae for each quantity are derived, and it is shown that the differences are only second order, so that for sufficiently small SSE, a single simple approximation can be made, independent of whether the SSE values are close to 1, as in the direct method, or close to 0, as in the indirect method. It is also shown that when measuring the radiance distribution surrounding the target in order to apply SSE corrections for the target, these surrounding measurements, which are also subject to the SSE, do not themselves require corrections, even for the highest level of target temperature accuracy.