An Attempt to Simplify the Determination or the Size-of-Source Effect in Radiation Thermometers

Abstract

The knowledge of \(\sigma _{d}\), the parameter that measures the size-of-source effect of a radiation thermometer, as a function of the diameter d of a radiation source is mandatory to estimate the appropriate corrections to temperature values measured when aiming to radiation sources of different sizes. To obtain \(\sigma _{d}\) as a function of d is a complicated task because there is no universally recognized mathematical function that relates them. The direct method to evaluate \(\sigma _{d}\) usually requires a radiation source of appropriate size and a set of many diaphragms with increasing diameter. How good is the approximation to \(\sigma _{d}\) estimated in this way depends on the number of diaphragms used. To reduce the time and cost to evaluate \(\sigma _{d}\), it is desirable to have methods that provide good approximations with a reduced number of diaphragms. In this paper, we present a method to obtain an approximation to \(\sigma _{d}\) as a function of d with a limited number of diaphragms. When using this method, deviations of less than \(1\;{^{\circ }}\hbox {C}\) are obtained when measuring radiance temperatures of \(500\;{^{\circ }}\hbox {C}\), between the measured temperatures and those calculated from values of \(\sigma _{d}\). We also propose a simple equation to interpolate approximated values of \(\sigma _{d}\) for those diameters between those used in its evaluation, but a limitation is that \(\sigma _{d}\) must be bigger than 0.98.