Determination of the coordinates of a circle using distributed fibreoptic length changes

Distributed fiber optic sensors (DFOS) are used to determine the deformation of engineering structures (objects). This measurement method analyzes changes in the backscatter signal along a fiber in order to determine changes in length and/or temperature. Various analytical and setup procedures make it possible to separate thermal and mechanical influences affecting the fiber. The geometric object changes can be directly derived as strain. The information of strain is not sufficient for a number of object state descriptions, so that further variables, such as inclinations, curvatures and coordinates, must be derived. In order to determine these variables, several fibers are often installed in a suitable geometric arrangement along the deformation directions. For example, a curvature can be determined from two fibers running parallel at a known distance. Deriving coordinates from curvatures or other intermediate values is much more complex and uncertain. This work focuses on the derivation of coordinates and coordinate changes for circular or elliptical objects (e.g. boreholes, tunnels or shafts) by means of length change measurements. Two approaches are evaluated in which some of the geometric constraints can be controlled. On the one hand, a popular approach using an adjustment of local circles is evaluated. On the other hand, an approach based on divided lines and a line network adjustment is developed. A highly precise test data set is created for the development and evaluation of the methods. The test dataset consists of DFOS, laser tracker and photogrammetric measurements of a test object in different deformation states.