Background: The mechanical properties of small minimally invasive instruments are limited and thus must be treated as flexible instruments. Proper functional behavior of these instruments can be significantly enhanced when the instrument is equipped with a shape sensor to track the path of the flexible instrument. MRI compatible instruments, and thus the corresponding paths, are long in particular. Therefore, the accuracy of the tip position is stringent. Approach: We have developed and realized a thin Fiber Bragg Grating (FBG) based fiber optical shape sensor. The main advantages of this fiber optical sensor are its minimum dimensions, the intrinsic MRI compatibility, and the ability of sensing deformation with submicro-strain accuracy. The shape sensor consists of three fibers, each equipped with multiple FBG's, which are integrated physically by gluing and can be positioned inside an flexible instrument. In this study a critical component analysis and numerical error analysis were performed. To improve performance, a calibration procedure was developed for the shape sensor. Results and Conclusion: With current state of the art interrogators it is possible to measure a local deformation with a triplet of FBG sensor very accurately. At high radii of curvature, the accuracy is dominated by the interrogator, whereas at low radii of curvature, the position of the fibers is leading. The results show that position error of a single segment of the shape sensor (outer diameter of 220 μm, a segment length of 23.5 mm and a minimum bending radius of 30 mm) could be measured with accuracies (3σ) of 100 μm for low radius of curvature upto 8 μm for high radii of curvature.