FM and double modulation interferometry with sub-nanometer resolution using the iLens technique

We report a modulation technique applicable to optical two-beam interferometers with unequal arm lengths that allows for highly precise, low-noise displacement measurements below the nanometer regime with a compact optical layout. The technique is inspired by frequency modulation spectroscopy and employs an external electro-optic modulator with sinusoidally phase-modulated laser light in the radio frequency (RF) regime (megahertz frequencies). By combining the RF modulation with a secondary mechanical modulation at a lower frequency to a super-heterodyne scheme we achieve continuous sign-resolved tracking of the arm length difference over many wavelengths, and low-frequency laser noise is effectively suppressed. Our setup is based on the compact interference lens technique and can measure displacements of samples with a wide variety of surface qualities. We examined the system performance using two samples, a mirror surface, and a commercial aneroid capsule without specular reflectivity. Stable multi-fringe operation with sub-nanometer resolution is demonstrated; the noise floor reaches 10 pm/Hz at frequencies above 10 Hz in a regular laboratory environment. This work demonstrates a versatile, simple setup capable of sign-resolved, sub-nanometer displacement sensing suitable even for non-ideal surface conditions.