## 3 Basic Principles of 3 MA
### Set-up Optimization and Calibration  
The 3 MA software offers the possibility of running sweeps of several set-up parameters (e.g., H\({}_{\rm t}\), f\({}_{\rm LF}\), and f\({}_{\rm HF}\)) in order to select their values, which are optimized according to the inspection situation. In general, the optimum set-up parameters should provide the clearest signal differences between the grades of the interesting target quantity, e.g., hardness, residual stress, or case depth. For example, for case hardening depth (CHD), it is beneficial if the interaction depth of the used electromagnetic  
Figure 3: Measurements on a steel sample before (I) and after (II) plastic deformation: (**a**) hysteresis measurements and (**b**) IP measurements. field is in the range of the highest value of CHD. The set-up frequencies (f\({}_{\text{LF}}\), f\({}_{\text{HF}}\)) and magnetization amplitude (H\({}_{\text{t}}\)) can adjust this interaction depth. If the interaction depth is much higher than the maximum CHD, then the 3 MA measurement explores a large amount of unhardened bulk material, which impairs the sensitivity to CHD variations. A preceding calibration is mandatory for using 3 MA to non-destructively determine the quantitative values of a target quantity. Here, calibration means the determination of a mathematical model--the so-called calibration function, which describes the functional relationship between the target quantity and the 3 MA measuring parameters. At the early stages of micromagnetic characterization, several scientists tried to develop physical models that describe the functional dependency between micromagnetic parameters and microstructure features or material properties. [PERSON] and [PERSON] both described a linear dependency between the coercive field and Bloch wall diameter. They observed that the coercive field is the field that is necessary to obtain an irreversible displacement of the Bloch walls [27; 28]. Later, [PERSON] extended this work by considering the demagnetizing field in the calculation of total energy. He noticed that the volume and size of inclusions affects the coercive field [29]. Other scientists have developed mathematical functions describing the coercive field, while taking into account the shape and size of particles [30], the grain size [31], and anisotropy effects [32; 33]. [PERSON] investigated the influence of alloying elements, like Al, Ni, and Co, as well as measuring and calculating the coercive field for Alcomax(r) isotropic steel [34]. Such theoretical calculations of microstructure-property relations have been shown to be reliable for simple materials and processes. However, most of the ferromagnetic materials that were used in industry, e.g., steels and cast iron, show complex microstructures and behavior. In order to theoretically develop a model describing the interrelation between targets and measuring parameters, the inverse problem has to be solved, i.e., the microstructure characteristics as a function of the micro-magnetic measuring parameters must be theoretically described. This is not usually possible. Moreover, in the case of industrial 3 MA application, calibration functions have to be determined in a fast uncomplicated manner. However, the development of simulation models for calibration is time consuming and expensive. Therefore, the application of physical models based on theoretical considerations for 3 MA calibration remains limited so far. Currently, 3 MA is usually calibrated based on empirical data. In order to determine a calibration function, the values of the target quantity, as well as the values of the 3 MA measuring parameters, must be measured on a set of parts with graded values of the target quantity. To measure these target values (mostly destructive), the reference methods have to be applied, like hardness indenter tests, tensile tests, or x-ray diffraction for residual stress. The measuring values of both, 3 MA parameters and target quantity are stored in a common database, and then the correlations between both are analyzed.