# A New Sensor System for Accurate 3D Surface Measurements and Modeling of Underwater Objects
## 3 Experiments and Results  
### Evaluation Measurements with Static Sensor  
The quality of calibration determines the magnitude of systematic measurement error. The systematic error is analyzed in all regions in the measurement volume by means of given specimens with a known geometry. For evaluation, we used length measurements of a calibrated ball bar with a spherical diameter of 100 mm, a center-point distance of 500 mm, and flatness measurements of a plane normal with a surface of 800 mm \(\times\) 100 mm. The ball bar and plane normal were placed in different regions of the measurement volume at distances of 1.5 m to 2.4 m from the sensor in 100 mm steps. Figure 3 shows the specimen and the sensor device in a basin during evaluation measurement of the specimen. Characteristic quantities we used for quality evaluation are length measurement error, \(l_{e}\); flatness error, \(f_{e}\) (see [34; 51]); and their variation over the measurement volume, as well as the noise of the 3D measurement data. Noise was determined as standard deviation of the 3D point distances of a fitted plane (for the plane normal) or fitted sphere surface (for the ball bar). Measurements were realized as follows. The specimens were placed on the floor of the basin. The sensor was carried by a triaxial gantry system and placed at different heights (distances) over the measurement objects. At least ten consecutive 3D measurements of the complete scene were performed for each height. Every 3D scan provided 3D measurement data on the sphere surfaces, the sphere distance, and the plane-normal surface. Figure 3: Specim ball bars, plane-normal, and cylinder during evaluation measurements. This procedure was repeated by a lateral shift of the UWS with respect to the scene to realize a modified location of the specimen in the vision field. The first results of the length measurement of the ball-bar showed a significant correlation between measurement distance and length measurement error, namely a proportional dependence. Hence, an appropriate error compensation function in the 3D object space was generated by:  
\[ \begin{array}{l}x^{\prime}=x+k(x-x_{0})(z-z_{0})\\ y^{\prime}=y+k(y-y_{0})(z-z_{0})\\ z^{\prime}=z\end{array}  \tag{3}\]  
according to a virtually defined sensor axis (\(x_{0},y_{0},z\)). The parameters were found heuristically by analysis of first measurement data and were set to \(x_{0}\) = 490 mm, \(y_{0}\) = \(-\)100 mm, \(z_{0}\) = 1950 mm, and \(k\) = \(-\)1.5 \(\times\) 10\({}^{-6}\). Refined evaluation data were obtained by additional independent measurements. A more detailed description concerning determination of a 3D compensation function is given by [PERSON] et al. [52]. Table 1 documents the results of the static measurements of the ball bar during underwater measurements (spherical diameters and distance between sphere center points). Refinement includes a 3D correction function according to Equation (3) applied to the whole set of 3D measurement points. Figure 4 shows the results of the ball-bar length measurement depending on measurement distance. A drift of the length values is clearly visible, whereas refinement reduces this effect drastically. Figure 5 shows three examples (1.7 m, 2.0 m, and 2.4 m) of the plane-normal measurements. Here, flatness deviation is quite low until 2 m measurement distance and then rises slowly. Refinement did not cause an improvement because of the omission of Z-coordinate correction by the error compensation function. Here, too few data were available to achieve a meaningful estimation of the systematic error function. Table 2 shows the determined noise of the 3D measurement points on the surfaces of sphere1 and sphere2, and the surface of the plane normal depending on object distance. As expected, noise increases with longer measurement distance.