**Significance Statement**

High-speed measurement of the gas temperature in microscopic dimensions has long been a challenging task for experimentalists, in particular for sharp temperature peaks under non-stationary conditions. Now, a device and method called Laser Schlieren Deflectometry (LSD) is introduced that overcomes limitations of other methods regarding temporal and spatial resolution. Laser Schlieren Deflectometry was invented by J. Schäfer in Leibniz Institute for Plasma Science and Technology in 2011. Interestingly, the idea of Laser Schlieren Deflectometry represents a direct mathematical and physical analogy to the famous scattering experiment of Ernest Rutherford from 1911. However, instead of alpha particles scattered by gold atoms, here an optical ray is deflected by hot spots with unknown temperature. The deflection of the ray by a cylindrically symmetric temperature profile is evaluated. A fundamental relation has been derived describing the dependence of the maximum deflection of the ray on the local maximum of the neutral gas temperature. Applying Laser Schlieren Deflectometry to a non-thermal atmospheric pressure plasma jet as a prime example for a steep gas temperature gradient allows unmatched spatio-temporally high-resolved analysis of energy balance, heat transfer processes and temperature in the small gas volume of atmospheric plasmas. Thus, the method makes a strong impact on the characterization of plasma sources which have drawn increasing attention in the last years and which represent a new approach for a large variety of technological applications such as surface treatment, coatings, nanomaterial and nanostructure fabrication, and plasma medicine.

**Journal Reference **

Eur. Phys. J. Appl. Phys. (2015) 71: 20804.

Jan Schäfer^{1}, Zdeněk Bonaventura^{2} , Rüdiger Foest^{1}** **

- Leibniz Institute for Plasma Science and Technology, Felix-Hausdorff-Str. 2, 17489, Greifswald, Germany
- Department of Physical Electronics, Faculty of Science, Masaryk University, Kotláĭská 2, 61137, Brno, Czech Republic

**Abstract**

Recently, laser schlieren deflectometry (LSD) had been successfully employed as a temperature measurement method to reveal the heat convection generated by micro filaments of a self-organized non-thermal atmospheric plasma jet. Based on the theory of the temperature measurements using Laser Schlieren Deflectometry, in this work, three approaches for an application of the method are introduced: (i) a hyperbolic-like model of refractive index is applied which allows an analytical theory for the evaluation of the deflection angle to be developed, (ii) a Gaussian shape model for the filament temperature is implemented which is analyzed numerically and (iii) an experimental calibration of the laser deflection with a gas mixture of helium and argon is performed. Thus, these approaches demonstrate that a universal relation between the relative maximum temperature of the filament core (*T*_{1}/*T*_{0}) and a the maximum deflection angle *δ*_{1} of the laser beam can be written as *T*_{1}/*T*_{0}=(1 − *δ*_{1}/*δ*_{0})^{−1}, where *δ*_{0} is a parameter that is defined by the configuration of the experiment and by the assumed model for the shape of the temperature profile.

**Figure Legend**

Scheme of Laser Schlieren Deflectometry (LSD) and a representative result of the method obtained for a self-organized non-thermal atmospheric pressure plasma jet (ntAPPJ). The 2D graph shows a cross-section of three hot filaments in perpendicular direction to the gas flow. The model used for the reconstructions of the temperature field considers the Fourier low of heat transfer and rotation of plasma patterns at 30 Hz obtained also by LSD. In the fundamental relation of LSD: T_{0} – laboratory temperature, T_{1} – maximum temperature in the center of the filament, d_{0} – calibration constant (depends on used model and configuration of experiment), d_{1} – maximum deflection of the optical ray.