Contents I. Introduction
For the temperature determination of electrode surfaces, different optical methods can be applied, each having its benefits but also drawbacks. Thus, it is advisable to combine them in an experiment to improve the reliability of data. The temperature measurements of a surface by means of optical methods is based on the thermal radiation. Several factors have to be considered:
The spectral radiance of a black-body radiator at a certain temperature according to Planck's law \begin{equation*} B_{\lambda}(\lambda, T)=\varepsilon(\lambda, T)\frac{2hc^{2}}{\lambda^{5}}\frac{1}{\exp\left(\frac{hc}{\lambda k_{B}T}\right)-1} \tag{1} \end{equation*} in the applied wavelength range with the Boltzmann constant , the Planck constant , and the speed of light . It can either be determined by means of optical emission spectroscopy within a certain wavelength rage or at one or two predefined wavelengths or small wavelength bands.
The emissivity of the surface usually is below that of a black body . For polished or liquid metals, it can be considerably lower due to their high reflectivity. For Cu surfaces the emissivity is often below whereas it is higher for Cr [1]. In case of Cu-Cr alloys the value is typically , depending on wavelength, temperature, amount of copper, and the surface structure. Molten surfaces have much lower emissivity. Furthermore, the emissivity depends on the angle of observation with a considerable increase for small angles, i.e. in glazing incident to the surface.
The transmission of the windows of the discharge chamber is an often-neglected parameter. It is in the range of about 10% for rather clean windows. However, especially for cases of high current densities with increased electrode erosion, the windows become covered by deposited vapor, nanoparticles, and droplets. Here, it has to be considered that the deposition is often not fixed but changes from shot to shot. In a first approach, a temporarily constant deposition and exponential decrease of transmission with the number of shots can be assumed. If different currents and conditioning of the electrodes are taken into consideration the determination before and after an experiment might be not enough. In such cases, measurement between the shots would be necessary.
The influence of the plasma radiation in the gap between the electrodes is another factor that has to be considered in the active phase. In a previous work [2] it was shown that during the high-current phase the plasma radiation can dominate the emission not only in the visible but also in the near infrared (NIR) wavelength range. Even beside the known line emission, a considerable continuum radiation of the plasma can be very strong. It can be caused by recombination radiation that might be applied for the determination of electron densities [3]. The intensity of plasma radiation in the wavelength range applied for temperature determination can be roughly estimated by measurements in parallel to the electrode surface, i.e. with the line of sight through the plasma in close distance to the electrode. Principally that component could be subtracted from the measured signal. Nevertheless, this demands several sophisticated assumptions concerning temporal, lateral, and spectral distribution of the plasma emission.
