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

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## 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.

## Keywords

Radiation thermometer Size-of-source effect calculation Size-of-source effect function## Nomenclature

*Q*Quotient between of the diaphragm’s diameters used to quantify the size-of-source effect and the exponential function of parameter \(\sigma _{d}\).

*d*Diameter of each diaphragm’s aperture.

- \(\sigma _{d}\)
A parameter that denotes the size-of-source effect for a given diaphragm’s diameter

*d*, equal to 1 when the thermometer is irradiated from a hemispherical source that produces a maximum signal in its detector or a fraction of 1 when the diaphragm’s diameter is not big enough to produce such a signal.*S*(*T*)Calculated values of detector’s signal of a radiation thermometer, as function of measured temperatures, in arbitrary units.

*T*Measured or calculated temperatures, in K.

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