# Induction of Highly Dynamic Shock Waves in
## 2 Materials and Methods  
### Measuring Principle and Measuring Setup of Speckle Photography  
When a rough surface is illuminated with coherent laser light, bright and dark areas appear in the image plane of the camera, caused by constructive and destructive interference. According to surface statistics, these form a dot or so-called subjective speckle pattern. In a typical imaging system, many scattering waves with very different phases participate in the scattering process. This usually results in a very fine pattern with speckle diameters smaller than the pixel size of the camera chip. If the light path is restricted by inserting an aperture, the size of the speckle can be adjusted as desired (see Figure 2).  
An outstanding characteristic of subjective speckles is that they are assigned to specific surface points according to the imaging system. To calculate surface displacements, a small evaluation window scans across the non-deformed (time t\({}_{n}\)) and the deformed speckle image (time t\({}_{n+1}\)) and calculates the cross correlation between the states at both time points at each evaluation position. The size of the evaluation window can be calculated automatically and should contain at least three speckles on the diagonal. According to [PERSON] and [PERSON], a speckle diameter of 3-5 pixels should be used for the optimum size of the speckle to be set [12]. Deformation fields for surface deformations in the object plane (in-plane) with a measurement uncertainty of less than 22 nm can be determined from the displacement of the correlation maxima [8]. After the calculation of the deformation fields, the corresponding strain fields can be quantified via gradient formation according to [PERSON] [13].  
Figure 2: Image of the printed logo of the Transregional Collaborative Research Center and the behavior of the subjective speckle pattern when decreasing the aperture (increasing the f-number).  
In practical terms, the measuring system is integrated into the production machine (Precitech Freeform 3000, Precitech, Inc., Keene, USA) in such a way that measurements can be taken on the front face of the workpiece (42 CrMo4) (see Figure 3a).  
Since the spindle of the tool is located above the workpiece, it occupies the possible mounting space for the camera so that the required field of view cannot be observed directly. Therefore, a special periscope lens had to be developed for the camera (Figure 3b). In order to ensure a constant position of the workpiece during image acquisition, trigger marks are attached to both the tool holder and the counterweight. Triggered images can thus be taken when the tool is engaged and when it is replaced by the counterweight (Figure 3c). Compared to the conventional turning process [14], the cutting conditions were set slightly higher with a cutting speed of \(\mathrm{v_{c}}=7.7\ \frac{m}{s}\), a cutting depth of \(\mathrm{a_{p}}=0.5\ \mathrm{mm}\), and a feed speed of \(\mathrm{v_{f}}=0.75\ \frac{mm}{s}\) in order to test the resolution limits with respect to the measuring speed of the measuring system. The corresponding cutting geometry is illustrated in Figure 4.  
To enable in-process measurements with displacement resolutions in the small two-digit nanometer range at the high cutting speeds, it is necessary that the object to be measured moves by a maximum of ten nanometers during camera exposure. This is achieved by using a short-pulse laser with a pulse length of less than one nanosecond. Both on the forming chip and on the rotating tool a non-smeared speckle pattern suitable for evaluation can be observed (see Figure 3c) even in dynamic production processes with tool speeds of up to \(\mathrm{v_{c}}=7.7\ \frac{m}{s}\).