# Technological Development and Application of Photo and Video Theodolites
## 3 Measurement and Processing Approaches
### IATS System and Camera Calibration  
The use of an appropriately calibrated camera is of crucial importance for displacement monitoring. It allows a two-dimensional image coordinate to be presented in angular units, i.e., field angle in the object space, which can then be expressed in linear units. All intrinsic and extrinsic parameters must be known for each captured image, which means that the images are directly georeferenced. They can be used for displacement monitoring with no need for object control points or further photogrammetric orientation processes. Photogrammetric image measurement methods, in order to detect signalized and unsignalized targets, can be combined with functions of the TS to generate precise angle and distance measurements [8]. In this section, we explain the camera calibration placed in the IATS telescope, i.e., in the optical path of the telescope. We focus on this camera and not the overview camera, because it is better to use the telescope camera for the purpose of displacement monitoring since we need highly accurate data for the determination of dynamic displacements with high speed and small amplitudes. Highly accurate data can be obtained using a telescope camera, because it uses telescope optics and magnification; however, we must also perform camera calibration, which involves the determination of intrinsic camera parameters. The intersection of the optical axis with the image sensor plane, i.e., principal point image coordinates, the focal length in the horizontal and vertical directions, and an arbitrary number of coefficients to compensate for radial and tangential lens distortions are intrinsic parameters which must be determined during camera calibration [59]. The distance between the camera center and the principal point is the focal length of pinhole cameras integrated in today's IATS. Two focal lengths (horizontal and vertical) must be determined because the pixels on the image sensor are non-square for some cameras [60]. Imperfect manufacturing of the lens and defects in the assembling of the camera result in radial and tangential lens distortions of the linear model for projecting points in the real world to the image plane [60]. Since monitoring assumes measurements between two or more different series or epochs of point measurements, the constant image coordinates of the principal point are void and, for this reason, they do not need to be known in advance. The distortion effects exhibit a spatial regularity, such that neighboring pixels are affected similarly. Thus, distortion effects are reduced to an insignificant extent when computing differences between objects located in similar regions on the image sensor. The frequencies included in a time series, which can be computed via Fourier analysis, are independent of the physical unit of the time series. This is due to the linear property of the Fourier transform (Equation (1)), where a constant factor \(c\) may be applied before or after the transformation [59]. \[F\{cf\left(t\right)\}=cF\{f\left(t\right)\}. \tag{1}\]  
The frequencies of structure vibrations can be computed from the raw image coordinates, i.e., from the image coordinates of measured points. Thus, no camera calibration is needed for this purpose. To present the displacements obtained from two epochs of measurement in linear units (e.g., m, dm, cm, or mm), the camera's angular resolution must be known. The displacements on the image are determined in pixels and can be computed as angular quantities, which can then be presented as linear units when the measured distance from the instrument to the monitored object is known. The angular resolution expresses the size of one pixel of the image sensor as an angular unit. It presents the angle between two objects that are presented on two neighboring pixels. For a pinhole camera model, the angular resolution \(\alpha\) is related to the focal length\(f\) by Equation (2).