# Deepwater 3D Measurements with a Novel Sensor System
## 2 Materials and Methods
### Data Recording
#### 2.2.2 Geometric Modeling, Calibration, and 3D Data Calculation  
In addition to the recording conditions underwater (water turbidity) and the technical properties of the recording components (cameras and lenses), camera modeling and calibration, as well as the algorithms for 3D calculation, are primarily responsible for the quality of 3D data. Since the beam path underwater differs from the straight beam path in the air due to refraction at the boundaries of different media (air to glass and glass to water), the usual use of the pinhole camera model for camera modeling must be supplemented by appropriate extensions. Through the intensive analysis of the beam paths in the cameras of the specific sensor system, optimized modeling was achieved using an extended pinhole camera model [32]. The 3D calculation was carried out through the usual method of triangulation [24] of corresponding point pairs of the stereo camera pair. The consideration of special conditions when recording images using cameras underwater, especially refraction at the media transitions between air and glass and glass and water when modeling the visual rays in the camera model, is described in detail in [32]. In brief, the approximate orthogonal alignment of the optical axes of the camera systems to planar viewing windows is assumed. The beam paths are then modeled as radially symmetrical with changing values for the camera constants (principal distances). Based on this modeling, the 3D points are calculated using beam cutting between corresponding image points of the stereo camera pair. Furthermore, the special method for the 3D point calculation takes into account the fact that the typical distortion effects of the lenses and the effects of ray refraction at the media transitions have opposite effects and, ideally, can even cancel each other out. This depends on other boundary conditions, such as the refractive index of the viewing glass, its thickness, and the distance between the camera and the viewing glass (see [32]). A special procedure was developed and tested for optimized calibration and underwater use, which achieves a good compromise between time expenditure, manageability, and measurement accuracy. Glass plates containing so-called ArUco markers were produced (see Figure 4) and used for calibration. Alternative calibration strategies are described by [PERSON] [33]. The calibration is carried out according to a defined scheme. The ArUco marker plates are fixed in a suitable manner (e.g., using a crane jib or laying them out on the seabed). The sensor system is slowly moved underwater (<0.1 m/s) past the marker plates at a defined distance. Images are continuously captured and saved by all the cameras. In a pre-processing step, optimal calibration points were automatically extracted from the image data using our own software. This image data serves as an input for the commercial BINGO calibration software [34], which calculates a calibration parameter set for the two monochrome measurement cameras using the classic pinhole camera model. In accordance with the statements in [35], the calibration data set is adjusted if necessary. To evaluate the calibration data set, measurements of defined reference bodies (ball-bars, plane standards, cylindrical bodies) are carried out at different distances within the specified measurement volume immediately after the calibration is carried out. If necessary, correction functions are calculated and become part of the calibration parameters (see [35]). Three-dimensional data are calculated according to the well-known triangulation principle [24]. Up to 50 volumes of 3D data are generated per second. The individual 3D data sets are merged into an overall 3D model in two separate ways. On the one hand, a rough, data-reduced 3D model is calculated, which can be displayed immediately and is used to visually assess the quality of the measurement carried out. This visualization occurs with a short latency of less than 0.2 s using the developed user interface (see Section 2.2).