Picometer-scale optical vortex interferometer using azimuthal complex spectrum analysis

An interferogram demodulation method based on azimuthal complex spectrum analysis is proposed for achieving picometer-scale accuracy with an optical vortex interferometer (OVI). The OVI uses conjugated p-radial-order Laguerre-Gaussian beams to produce a high-order petal-like interferogram. A camera with a multi-ring pattern written on its sensor is used to convert the interferogram into multiple azimuthal intensity profiles. A phase shift subjected to either uniform surface displacement or axisymmetric non-uniform surface deformation can be retrieved from the complex spectra of the azimuthal intensity profiles at the main frequency components. The experiment verified that the measurement error is 84 pm for a displacement of 10 nm and 0.359 nm for a deformation magnitude of 100 nm. The effect of surface misalignment on the measurement result is also discussed. The proposed method provides an effective and highly accurate method of interferogram demodulation for the OVI and extends the applicability of OVI from uniform surface displacement measurement to axisymmetric non-uniform surface deformation measurement.