Introduction

Some methods of spectroscopic plasma monitoring and control are based on a passive optical emission spectroscopy. They are pretty simple, but the interpretation of these data in terms of plasma physical parameters is very non-straightforward. So, the conventional passive optical emission spectroscopy is suitable only for more qualitative interpretations than quantitative.

On the other hand, the power of an optical spectroscopy is much more and enables a much deeper non-invasive process analytics, especially when we talk about physical process parameters, such as plasma composition (chemical species density), particle density and energy, plasma density and electron temperature. The practical example of such a tool is the optical interferometer. Due to its superior spectral resolution it enables the measurements of a plasma species temperature and group velocity.

The Fabry-Perot Interferometer is the high-resolution spectroscopic tool enabling a superior spectral resolution $\delta \nu$ (typically $0.02~pm$), which is not accessible by conventional grating spectrometers. The technical aspects of the Fabry-Perot Interferometer have been described earlier.

Application schema

A Fabry-Perot Interferometer due to its superior spectral resolution can be utilized for the measurement of a temperature and group velocity of particles (atoms, molecules, ions, radicals). Due to its superior spectral resolution, a Fabry-Perot Interferometer is an excellent tool to measure the Doppler broadening of any spectral lines or spectral line shifts (which enables temperature and velocity measurements). It allows to study the fine structure of spectral lines and, for example, Zeeman and Stark splitting.

The feature of the Fabry-Perot interferometer is that its instrumental function consists of numerous thin transmission peaks (bandwidth of each $\delta \nu$), equidistantly separated by a frequency $\Delta \nu$, as shown in the picture below. Therefore, the straightforward utilization of the Fabry-Perot Interferometer to characterize broadband plasma emission is impractical.

In this case, the FPI should be used in combination with another low resolution spectrometer/monochromator or optical filter. Such a scheme is shown here

The bandwidth of the interferometer is typically much less than the spectral line width $\Delta \nu_{line}$ or the bandwidth of a monochromator $\Delta \nu_{monochromator}$, as shown below.

\begin{equation} \label{comparison} \delta \nu \ll \Delta \nu_{line} , \Delta \nu_{monochromator} \end{equation}

The emission light from the plasma source is filtered out by the FPI and then second time filtered by the monochromator or spectrometer. The monochromator cuts out all spectral lines except for those of our interest. The fine structure of the preselected spectral lines can then be resolved by the interferometer.

Tuning

Most of the commercially available interferometers are tunable, i.e. the position of the transmission peaks can be precisely tuned. This is achieved, for instance, by varying the distance between two interferometer mirrors, thus varying the resonance condition. Tuning the transmission peak position one can scan through the emission line profile, resolving its width or shift.

The high resolution of the interferometer enables it to resolve the spectral line width and line displacement due to species group velocity. If the line width is caused by the Doppler broadening or thermal motion, then the linewidth can be always converted into the species temperature: \begin{equation} \label{Doppler} \Delta \lambda_{thermal} = 2\sqrt{2~ln 2} \lambda_0 \sqrt{\frac{kT}{Mc^2}}, \end{equation} where $\lambda_0$ is the central wavelength of the measured line, $M$ is the mass of the gas atom, $c$ is the speed of light, $k$ is the Boltzmann constant.

In the same way, the displacement of the spectral line relative to its undisturbed position can be always converted into the collective group velocity in the observation direction.

Examples

There are numerous examples on the spectroscopic measurements of the atomic or ion temperature using the Fabry-Perot interferometer. An example on the measurements of the temperature of Argon and Titan atoms in the magnetron discharge plasma is shown below. The first picture shows the neutral Ar temperature in the discharge as a function of the Ar pressure. The second picture shows similar results for sputtered Ti atom temperature.