Nano-Displacements Tests for a Motorized Linear Translation Stage With a Fabry-Perot Interferometer

A novel method based on the Fourier transform (FT) and the Vernier effect (VE) is proposed for testing the minimum step motion (resolution) of a motorized linear translation stage (MLTS) using a single extrinsic fiber-optic Fabry-Perot interferometer (FFPI). The reference (FFPI_R) and sensing (FFPI_S) interference patterns obtained with the FFPI are connected virtually in parallel with a phase shift of 180° (−FSR_R ≈ FSR_S). The Vernier effect generated is analyzed through a theoretical envelope function (F_E), a tuning angle is added in order to match it to the envelope of the experimental spectrum. The F_E allows to determine the current length of the sensing cavity. By tracking the displacements of the first/second (λ_A/λ_B) intersection of the envelopes towards larger/shorter wavelengths it was possible to measure the displacements of the MLTS in real-time with a sensibility of 133 nm/μm and an estimated resolution of 8 pm. This displacement resolution can be achieved regardless of the Fabry-Perot cavity length (FPCL) up to a maximum cavity length of 10 mm. The interrogation method proposed here improves the displacement performance of the FFPI in terms of simplicity, dynamic range, sensitivity, and resolution.