One- and two-dimensional single-mode differential fiber-optic displacement sensor for submillimeter measurements

Using the overlap integral method and the Gaussian approximation for the single-mode fiber-optic field, the working principle of one- and two-dimensional differential fiber-optic displacement sensors for submillimeter measurements is demonstrated. The sensors consist of one emitting fiber and two or three receiving fibers, respectively, for the one- and two-dimensional sensors. Sensor responses are intrinsically linear over a wide range of travels. Moreover, for the two-dimensional sensor, each axis of displacement can be measured independently. Sensor responses are simulated experimentally using a highly precise robot. Linearity, travel, and sensitivity are characterized for the different gap distance between the emitting and receiving fibers. A design chart that includes nonlinearity error, travel, sensitivity, and gap is finally proposed.