The thermographic camera measures the intensity of the infrared radiance that the surface of the part emits according to its temperature. The relationship between the temperature
T of an ideal black body and its spectral radiance
\(L_{\lambda \textrm{Bb}}\) is described by Planck’s law as
$$\begin{aligned} L_{\lambda \textrm{Bb}}(\lambda , T) = \frac{2\cdot h\cdot c^2}{\lambda ^5} \frac{1}{e^{\left( \frac{h\cdot c}{\lambda \cdot k_\textrm{B}\cdot T}\right) }-1} . \end{aligned}$$
(1)
Here,
h is the Planck constant,
c is the speed of light,
\(\lambda \) is the wavelength, and
\(k\mathrm {_B}\) is the Boltzmann constant. Real bodies emit less radiation than a black body at the same temperature. The ratio between the two radiations is described by the emissivity
\(\varepsilon \), which depends on the material, the surface conditions, and the temperature of the target object [
15]. The emissivity is also dependent on the wavelength and is affected by the viewing angle [
16]. The signal level is further reduced by losses due to the optical elements in the measurement path. The transmissivity of the optical path can be expressed as
\(\tau _\textrm{optics}\) where
\(\tau _\textrm{optics}<\) 1. The apparent emissivity takes these losses into account by
\(\varepsilon _\textrm{app}=\varepsilon _\textrm{surface}\cdot \tau _\textrm{optics}\). It is therefore lower than the actual emissivity of the material. The apparent emissivity needs to be determined for the specific measuring task to enable conclusions to be made about the absolute temperature. The focus of this work is on the cooling rates starting at the solidification temperature. An absolute temperature calibration of the entire temperature range was beyond the scope of the study. The thermographic data were corrected using the single-point correction method. Here, the apparent emissivity is determined for a single temperature value and assumed to be constant over the measured temperature range. Deviations from this assumption could influence the progress of the measured cooling curve. This error was considered to be small since the cooling rate was determined at the detected solidification temperature
\(T_\textrm{s}\). Single-point correction requires a pair of correlating temperatures. Here, these are the solidification temperature (
\(T_\textrm{s,true}\) of 316L) of 1663.15 K and the apparent temperature corresponding to the solidification signal
\(T_\textrm{s,app}\) obtained in the previous step. The solidification signal was converted into an apparent temperature using the black body calibration curve of the camera. Using this temperature couple, the apparent emissivity at the solidification temperature
\(\varepsilon _\textrm{app}(T_\textrm{s})\) was calculated by
$$\begin{aligned} \varepsilon _\textrm{app}(T_\textrm{s}) = \frac{\int _{\lambda _1}^{\lambda _2} L_{\lambda \textrm{TC}}(\lambda , T_\textrm{s,app})d\lambda }{\int _{\lambda _1}^{\lambda _2} L_{\lambda \textrm{Bb}}(\lambda , T_\textrm{s,true})d\lambda } . \end{aligned}$$
(2)
In Eq. (
2),
\(\lambda _1\) and
\(\lambda _2\) are the limits of the spectral range of the camera, and
\(L_{\lambda \textrm{TC}}\) and
\(L_{\lambda \textrm{Bb}}\) are the spectral radiance values for
\(T_\textrm{s,app}\) and
\(T_\textrm{s,true}\) calculated by Eq. (
1).
The apparent emissivity calculated by Eq. (
2) neglects the spectral responsivity of the thermographic camera sensor
\(r(\lambda )\). If
\(r(\lambda )\) shows a high dependency on the wavelength,
\(r(\lambda )\) must be included in Eq. (
2). The thermographic camera sensor used in this study had a
\(r(\lambda )~>\) 80 % within its spectral range. Thus,
\(r(\lambda )\) was neglected. The apparent temperature values obtained from the thermographic camera were corrected using
\(\varepsilon _\textrm{app}\) and a numerical solution of the integrals in Eq. (
2).