Axial and lateral displacement measurements of a microsphere based on the critical-angle method

A method has been developed for optically measuring nanometer-scale displacements of transparent and metal-coated microspheres in both the axial (vertical) and lateral (horizontal) directions. This method works by detecting changes in the internal reflection of a laser beam reflected from the microsphere after it passes through critical-angle prisms. For weakly reflective 10-μm-diameter polystyrene microspheres in water (relative refractive index n = 1.2), the detection resolutions as estimated from the full-width at half maximum (FWHM) noise level in the frequency region above 500 Hz in the axial and lateral directions were experimentally found to be as good as 1.7 and 1.1 nm, respectively. Furthermore, the lateral displacement resolution (0.2 nm) of a 10-μm-diameter metal-coated microsphere was better than the axial displacement resolution (0.9 nm) of a conventional flat mirror by more than a factor of four.