## 3 Materials and Methods  
### Dough Volume Monitoring  
To create a topology of the inside of the fermentation chamber, we developed a three-dimensional measuring system consisting of a linear motor (Figure 3: Linear motor), a holder with adjustable angle around the x-axis (Figure 3: Holder), a two-dimensional light detection and ranging (LIDAR) scanner (RPLidar A1M8) (Figure 3: LIDAR), and a time of flight distance sensor (Adafruit VL53L0X) (Figure 3: Time of flight distance sensor) to extend the LIDAR data to the third dimension. The system needed to be as rigid as possible to obtain highly accurate measurements. We integrated the measurement system to the back of the chamber interior. Figure 3 illustrates the system schematically on the left and shows the real module on the right side.  
The two sensor outputs were fused by means of an Arduino microcontroller to create a single data stream containing the X, Y, and Z-coordinate of a measurement point. Therefore, the polar coordinates that are generated by the LIDAR and represented by the particular angle \(\theta\) and the corresponding distance r are transformed into Cartesian coordinates by means of the transformation:  
\[x=r*cos(\theta) \tag{1}\]  
\[y=r*sin(\theta) \tag{2}\]  
The distance sensor directing vertically to the bottom of the fermentation chamber returns measurements of the current height of the measurement sensor system. By moving the system along the Z-axis, a complete topology of one row of the observed situation is captured and serves as the basis for further image processing that detects and investigates the volume of each dough piece. The tilting of the LIDAR scanner by the angle \(\alpha\) enables the possibility of monitoring multiple rows of dough pieces laying behind each other. In Figure 4, the general setup of the measurement system is illustrated. This represents the real setup of bread dough pieces within a typical fermentation setup on the left and the schematic overview of the measurement process on the right side.  
Figure 4: Test setup (**left**) and schematic (**right**).  
Figure 3: Schematical illustration of the measurement system (**left**) and real measurement module (**right**).  
In the example of one object (Figure 4 right), the measurement can be described as follows. Due to the known height of the sensor system z and the tilt angle \(\alpha\), the height of an object \(z_{dough}\) at a certain position can be calculated as equation 3 by using simple trigonometric relationships:  
\[z_{dough}=z-r\times\cos(90^{\circ}-\alpha) \tag{3}\]  
The motion of the linear motor in the Z-direction is performed automatically by means of a continuous loop moving between the maximal top and bottom positions with a step speed of \(2\frac{mm}{s}\) to generate a sufficiently dense point cloud. In order to analyze the gradient of the volume development of the dough pieces, the topology of the fermentation chamber is measured continuously in five-minute steps. The underlying setup of the measurements in this paper generates point cloud files of approximately 6500 three-dimensional coordinate points in that way with an accuracy of 0.5-1% of the range, respectively 0.5 mm when measuring within 1.5 m, which is mostly the case in our setup. In comparison to the use of a camera, we are able to obtain depth information of the whole fermentation chamber interior, which allowed us to perform three-dimensional object recognition directly.