## 5 Conclusions and Outlook  
Laboratory investigations in the context of the analysis of the functional relationship between the decorrelation of measured speckle patterns or the broadening of the correlation function \(\Delta\sigma\) and the out-of-plane deformation \(\Delta\zeta\) confirm a linear behavior. Moreover, the additional computational effort for the determination of \(\Delta\sigma\) in the sub-pixel evaluation is negligible, which means that the parallelizability of the algorithms remains given and three-dimensional in-process deformation measurements during the rolling process become possible. The measurements during deep rolling show the dynamic deformations below the tool. From these deformations, the strain and thus the load during the die engagement can be calculated directly via the formation of the gradients. In particular, the 'bow wave' of out-of-plane deformation moving ahead of the tool shows that the local mechanical material loads can be much more pronounced than the workpiece modifications remaining in the material. In order to better understand manufacturing processes, 3D speckle photography can thus make an important contribution in the context of the sought-after process signatures.  
While the calibration of the \(\zeta\)- and \(\psi\)-displacement can be performed via the imaging scale of the camera system, this is only possible for the \(\zeta\)-axis via a subsequent reference measurement with a stylus instrument. The ambiguity with regard to the direction of the displacement can also be eliminated by the additional information from the reference measurement. In order to ensure in-process capability in various manufacturing processes, the realization of a self-calibration of the measuring system is planned for the future. For this purpose, a three-axis piezo stack is to be used, via which the system can be calibrated before each individual measurement by means of defined, homogeneous  
Figure 8: 3D deformation measurement in the deep rolling process. (**a**) Tactilely measured burr; (**b**) width of the correlation function as a function of the out-of-plane displacement of the burr; (**c**) speckle-photographically measured deformation field in the \(\zeta\)-direction after calibration.  
displacements. In addition to the calibration, it is thus simultaneously possible to eliminate optical distortions--for example due to misalignments of the measuring system--already during the measurement and to carry out quantitative 3D deformation measurements in running manufacturing processes.  
Conceptualization, A.T.; investigation, A.T.; methodology, D.S. and A.F.; supervision, A.F.; writing--original draft, A.T.; writing--review and editing, D.S. and A.F. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the German Research Foundation (DFG) for subproject C06 'Surface optical measurement of mechanical working material loads' within the Transregional Cooperative Research Center SFB/TRR136.  
Not applicable.  
The data presented in this study are not available.  
The authors thank [PERSON] (SFB/TRR136, subproject C01) and their colleagues from the Leibniz Institute for Materials Engineering IWT for the friendly support during the conduction of the in-process measurements.  
The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.