_Applied_  
_sciences_  
_In-Process Measurement of Three-Dimensional Deformations_  
**Based on Speckle Photography**  
**[PERSON] 1,*, [PERSON] 1,2 and [PERSON] 1,2**  
1 Bremen Institute for Metrology, Automation and Quality Science, University of Bremen, Linzer Str. 13, 28359 Bremen, Germany; [EMAIL_ADDRESS] (D.S. ); [EMAIL_ADDRESS] (A.F)  
2 MAPEX Center for Materials and Processes, University of Bremen, P.O. Box 330440, 28334 Bremen, Germany  
* [2 pt] Correspondence: [EMAIL_ADDRESS] or [EMAIL_ADDRESS]  
**Abstract** In the concept of the process signature, the relationship between a material load and the modification remaining in the workpiece is used to better understand and optimize manufacturing processes. The basic prerequisite for this is to be able to measure the loads occurring during the machining process in the form of mechanical deformations. Speckle photography is suitable for this in-process measurement task and is already used in a variety of ways for in-plane deformation measurements. The shortcoming of this fast and robust measurement technique based on image correlation techniques is that out-of-plane deformations in the direction of the measurement system cannot be detected and increases the measurement error of in-plane deformations. In this paper, we investigate a method that infers local out-of-plane motions of the workpiece surface from the decorrelation of speckle patterns and is thus able to reconstruct three-dimensional deformation fields. The implementation of the evaluation method enables a fast reconstruction of 3D deformation fields, so that the in-process capability remains given. First measurements in a deep rolling process show that dynamic deformations underneath the die can be captured and demonstrate the suitability of the speckle method for manufacturing process analysis. speckle photography; in-process measurement; deep rolling process  
**1. Introduction**  
The functionality of technical surfaces is significantly influenced by the manufacturing process [1; 2; 3]. This applies in particular to processes which aim to change the surface layer properties of the workpiece in a suitable manner. However, the targeted generation of, e.g., depth hardness gradients is challenging--even under laboratory conditions [2]. The reasons are that material loads occurring during the machining process in the form of displacements and strains, which are responsible for the material modifications, cannot be measured and that a lack of process knowledge exists. Therefore, the targeted material modifications are only adjusted via the machining parameters or process variables of the machine tools in an iterative way [4; 5; 6]. A remedy can be provided by the introduced concept of process signatures [7], which focuses on the internal mechanisms and the influencing quantities [8], leading to a material change to describing the workpiece modification. To gain a deeper understanding of the manufacturing process, the study of process signatures, which correlate the material changes occurring with the acting internal mechanical material loads, is ongoing. The use of process signatures not only enables a better understanding of the process, but also allows a comparison of seemingly different manufacturing processes. As a result, processes and process chains can be optimized to improve functional properties and reduce manufacturing costs [7]. Although a variety of characterization methods for the resulting material modifications exists, the metrological recording of the material loads in the ongoing production process remains a needed prerequisite. Mechanical workpiece loads can be calculated by comparing or correlating images taken before and during the occurrence of the deformation. In contrast to Digital Image Correlation (DIC), the method of Digital Speckle Photography (DSP) [9] is much more precise, especially on low-contrast surfaces. In terms of its maximum achievable resolution, the method is limited only by [PERSON]'s uncertainty principle [10].