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

• H. Rodríguez-Arteaga
• D. Cárdenas-García
TEMPMEKO 2016
Part of the following topical collections:
1. TEMPMEKO 2016: Selected Papers of the 13th International Symposium on Temperature, Humidity, Moisture and Thermal Measurements in Industry and Science

## 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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