## 6 Opportunities for Out-of-Sight Damage Detection  
In Sections 4.1 and 5, it was observed that higher harmonic frequency components are generated at the location of a defect, especially when the defect is locally resonating. These higher harmonic components can radiate away from the defect into the damage-free material. This is clearly visible in the amplitude map of the second harmonic component shown in Figure 7e,f. The intensity of the harmonic component decreases with the distance to the side-delamination because of geometrical wave spreading (-distance) and wave attenuation (which is relatively high in this frequency range). The nonlinear radiation of defects is further exploited in order to detect out-of-sight defects. Such defects are typically encountered if certain parts of the component are hidden and cannot be reached by the laser beams, or simply if one wants to reduce the measurement time. As an example, the inspection area of the CFRP plate with side-delaminations is reduced to two small square areas of around \(40\times 40\) mm\({}^{2}\) (indicated _Area 1_ and _Area 2_ in Figure 8a). The measurement results at these small areas are used to not only detect [32], but also to localize the out-of-sight side-delaminations. To start, the second harmonic component is extracted using time-frequency filtering (see Section 3.1). The subsequent processing steps are applied individually at each scan area. First, the extracted second  
Figure 8: Detection of out-of-sight side-damage by using the second harmonic component measured at two small areas: (**a**) second harmonic amplitude map at 76 kHz with indication of the measurement areas, (**b**,**c**) wavenumber maps corresponding to the second harmonic component at 76 kHz with indication of the direction of the incoming wavefield. harmonic component is transformed from the time domain to the wavenumber-frequency domain using three-dimensional FFT:  
\[ \begin{array}{l}V_{z}^{HH2}\Big{(}k_{x}(r),k_{y}(s),f(k)\Big{)}\\ =\frac{1}{N.P.Q}\sum\limits_{p=1}^{P}\left[\sum\limits_{q=1}^{Q}\left(\sum \limits_{u=1}^{N}\sum\limits_{z}^{WH2}(x(p),y(q),t(n))e^{-2\pi i\frac{k_{x}}{N} }\right)e^{-2\pi i\frac{z}{Q}t}\right]\!\!-\!2n!\frac{r!}{P}\end{array}  \tag{7}\]  
where the number of scan points in horizontal and vertical directions are denoted as \(P\) and \(Q\), respectively. In order to 'increase' the resolution in wavenumber domain, the \(V_{Z}^{HH2}\) signal is zero-padded in \(x\) and \(y\) direction. The resulting signal \(V_{z}^{HH2}\Big{(}k_{x}(r),k_{y}(s),f(k)\Big{)}\) is now represented in the wavenumber-frequency domain where \(k_{x}\) and \(k_{y}\) are the wavenumbers in horizontal and vertical direction, respectively. The wavenumber maps corresponding to the nonlinear \(HH2\) response at \(f\) = 76 kHz, \(V_{z}^{HH2}\Big{(}k_{x},k_{y},76 kHz\Big{)}\) are shown in Figure 8b,c. Distinctive spots of high intensity are found in both wavenumber maps. These spots correspond to the second harmonic radiation induced by a nonlinear source (defect). The direction of the source can be found as: \(\theta=\arctan\Big{(}\frac{k_{y}}{k_{x}}\Big{)}\) if \(k_{x}\)\(<\) 0 or \(\theta=\arctan\Big{(}\frac{k_{y}}{k_{x}}\Big{)}+\pi\) if \(k_{x}\)\(>\)0. In Figure 8, arrows are drawn in these directions. The arrows correctly point towards the source of the higher harmonic components, namely the side-delaminations at the top side of the component. Note that for one of the observed directions in Figure 8b, the wavefield originates at the side-delamination but is reflected at the bottom edge. The edge is perceived as a virtual nonlinear source, and as such can be employed to further improve the localization of the actual defect. Hence, the out-of-sight damage can be detected and even localized without the need for a baseline measurement. One important requirement for out-of-sight defect detection is that the defect must behave as a source of nonlinear components. At 76 kHz, this was the case for the delamination at the center and the delamination at the right side of the top edge.