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In this research we introduce the application of an optical fiber Fabry-Pérot interferometer in smart manufacturing. We used an optical fiber Fabry-Pérot interferometer to measure the distance between a moving target and a fixed optical fiber. When the target moves, the distance between the fiber and the target can be precisely determined. First, we monitored the distance between a fixed fiber and the surface of a rotating tool. By measuring the distance, we reconstructed the three-dimensional (3D) profile of the tool. We also introduce the method to calculate the runout and tool wear. To further improve the speed of this method, we developed machine learning models to find out the distance from the spectrum of the interferometer since the spectrum analyzing method is relatively slow. It was found that the Deep Neural Network model predicts the distance between the fiber and the target surface with a sufficient precision (< 4 μm) when measuring the straightness error of a computer numerical control (CNC) machine tool. The proposed method provides possibilities for noncontact precise monitoring especially in a limited space.