Optical Cantilever for High-Resolution Displacement Measurement Using Diffraction Grating and Sampling Moiré Method

Cantilever-type sensors play a critical role in precision measurement across various fields. Among the available detection principles, the optical lever method detects minute cantilever displacements via the reflection angle of a laser, achieving high-resolution displacement and force detection. Generally, a bi-cell or quadrant photodiode (PD) is used, and the reflected light must be initially positioned at the center. Additionally, if the reflected light moves beyond the dividing line of the PD, measurement becomes impossible. Conversely, the sampling moiré (SM) method has attracted attention for similar optical displacement measurement methods. The SM method enables high-resolution displacement measurement of the captured periodic pattern. The periodic pattern is captured in camera images, eliminating the need to adjust the light centered on PDs, and the detectable range of displacement in the sensing mechanism is not limited. This study proposes a measurement method that integrates the optical lever and the SM methods using a glass cantilever with a diffraction grating. When the cantilever is irradiated with laser light, the grating diffracts the reflected light at the cantilever surface, forming a diffraction pattern. As the cantilever is deformed, the diffraction pattern shift is captured by a camera and analyzed using the SM method, yielding the displacement value. In the experiment, the diffraction pattern spanning over approximately $200~\mu $ m was captured by a lens-less camera. With a cantilever displacement of $4~\mu $ m, the diffraction pattern captured by the camera shifted by $80~\mu $ m, corresponding to a 20-fold amplification of the cantilever displacement. The resolution of cantilever displacement, determined through an analysis of pattern shifts, was calculated to be under 3.5 nm. The proposed method offers a robust and adjustment-free technique for cantilever-type sensor measurements.