## 3 Thermoelastic Topography of GESA Coating: Experimental Setup
Figure 4: Schematics of a wavenumber excitation setup using a diffraction phase mask to split a pump laser beam into a set of excitation beams, phase shifted with a Phase Retarder (PR). Here, only the first diffraction orders are shown. Using an imaging lens system with magnification factor \(M=f_{2}/f_{1}\) the two waves are mixed under an angle \(\theta_{0}\) on the surface resulting in a periodic interference pattern. Figure 3: Schematics of the GILD setup. In this setup, grating excitation, explained in Figure 4 and laser beam deflection (Figure 5) are combined to excite and detect narrow band SAWs. A first polarizing beam splitter (PBS) guides the pump beam in the path of the probe beam. A QWP in front of the sample alters the polarization of the probe beam to guide the reflected probe beam towards the photodetectors by a second PBS. The phase mask and sample were mounted on stepping motors to allow for the experimental extraction of thermal dispersion curves, and for topographical mapping. Roughly speaking, the spatial resolution of the method is determined by the size of the grating patterns. In the implemented setup the excitation region had a length of about 2 mm (along the grating axis) and a width of about 2 mm (perpendicular to the grating axis). The probe beam spot diameter was about 5 microns. Two distinct GILBD scanning approaches were taken: (i) \"local detailed grating spectroscopy\" for a set of 10 grating spacings varying between 7 and 200 \(\upmu\)m (range in which the signal quality was ok for the used laser spot sizes) and (ii) \"topographic mapping\" of a sample surface area (2 mm \(\times\) 2 mm), by performing an XY scan for a set of four different grating spacings (15, 25, 45 and 200 \(\upmu\)m with a scanning step of 50 \(\upmu\)m (and 1 \(\upmu\)m for signal optimization) in the \(x\)-direction and 100 \(\upmu\)m in the \(y\)-direction. To limit the total measurement time to a reasonable amount, the combined experiment, i.e., scanning the grating mask for a set of gratings while the surface area is scanned was not implemented. The first experimental approach aimed at the extraction of a detailed acoustic and thermal dispersion curves on one representative location on the sample surface. Analysis of photoacoustic and photothermal components of the GILBD signals for 10 grating spacings yielded the SAW phase velocity and effective thermal diffusivity corresponding to respective penetration depths of the acoustic and thermal fields. Scanning the position of the diffraction grating with respect to the probe beam and taking a spatial Fourier transform of the signal allowed the accurate determination of the absolute excited fringe distance, of which the value was needed for calculating the Rayleigh velocity and thermal diffusivity. In the second experimental approach, the SAW phase velocities were measured along the surface of the sample by scanning the probe and pump beams. Four grating spacings were used: SAWs generated at grating spacings (15, 25 \(\upmu\)m) mainly allowed sampling of the coating, a grating spacing of 45 \(\upmu\)m yielded points on the SAW dispersion curve in the transition region from the coating to the substrate regime, and a SAW wavelength of 200 \(\upmu\)m was employed to probe deep into the substrate. For each of the four wavelengths, the GILBD signal was acquired by scanning the probe beam along a linear array of points within the targeted surface area, over multiple maxima and minima of the excitation laser grating, and the magnitude of the signal grating \(S(x,t)\) (\(V_{pp}\)) was determined by a spatiotemporal Fourier transform of the signal. As the laser beam deflection detection setup is quite sensitive to scattering caused by the roughness of the sample surface, an iterative position optimization  
Figure 5: Schematics of the LBD detection setup. A surface deformation, resulting from laser excitation of thermoelastic phenomena, deflects an incident probe beam. The deflection is monitored by a differential photodetector using knife-edging mirrors.