## 3 Application to Experimental Data
### Individual Measurements and Processing  
For crack detection, three different inspection techniques were used that are well-suited for the automated nondestructive evaluation of cracks in ferromagnetic metals. The first method is called _eddy current testing_ (ET). An excitation coil is run over the specimen surface. Using this coil, an alternating current induces circular eddy currents in the specimen's near-surface region. These currents are blocked by the presence of defects, thus affecting the impedance of the probe coil, which is the measured signal. The second method employed here is the laser-induced _active thermography testing_ (TT). A high-power laser is run across the specimen to locally heat up the surface. In defect-free regions, the heat flow is able to dissipate, whereas defects cause localized heat accumulation. An infrared camera monitors the heat flow decay and generates a digital image sequence for processing. The third method is _magnetic flux leakage testing_ (MFL). The specimen is exposed locally to a static magnetic field, which spreads inside the ferromagnetic material. At near-surface defects, the field is forced to \"leak\" out of the specimen into the air, although air has lower magnetic permeability than the specimen. This leakage can be detected by magnetic field sensors, such as _giant magneto resistance_ (GMR) sensors. The following three inspections were performed sequentially during the course of about one year. ET was carried out at an excitation frequency of 500 kHz, which is well-suited to inspect surface defects due to the skin effect [17]. An automated scanning device rotates the specimen under the fixed probe. Signal processing is based only on the imaginary part of the measured impedance. The obtained one-dimensional signals are preprocessed by high-pass filtering for trend correction, and by low-pass filtering to improve SNR. An image is formed by stacking the line scans in axial direction of the ring. The MFL data were collected using the same scanner as for ET, and a GMR sensor array developed at BAM [18]. Using these gradiometers, the normal component of the magnetic stray field was measured while the specimen was locally magnetized. Preprocessing comprised trend correction by high-pass filtering per line scan, and an adaptive 2D wiener filter (We used MATLAB's function _wiener_2. See [19]) for noise suppression. The image was then Sobel-filtered to highlight the steep flanks that are generated by the gradiometers over the grooves. Thermography testing was performed by rotating the specimen under a 40 W powered laser while recording with an infrared camera. The movie frames were then composed to form an image of \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**Groove** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** \\ \hline Depth/\(\upmu\)m & 354 & 224 & 170 & 105 & 82 & 61 & 57 & 53 & 43 & 40 & 39 & 27 & 29 & 20 & 11 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Groove depths. Labels correspond to those shown in Figure 4.  
Figure 4: Schematic view of the ring specimen, not to scale. (**Top**) outer proportions of the ring; (**Bottom**) unrolled outer surface. Short vertical lines indicate the positions of the 15 grooves. the specimen surface. This image is processed by 2D background subtraction using median filtering, and noise was suppressed by an adaptive 2D wiener filter. We note that the presented signal acquisition is tailored to the known groove orientation. In a realistic setting, a second scan should be performed for ET and MFL testing to detect any circumferentially oriented defects as well. We further emphasize that for our specific ring specimen, the GMR sensors yield far superior results compared to ET and TT, and would suffice by themselves for surface crack detection. Specifically, the MFL data facilitate zero false alarm rate even for the second shallowest of only 20 \(\upmu\)m depth.