Picometer-scale OAM interferometry using an adaptive polar transform algorithm

A phase demodulation algorithm based on an adaptive polar transform is proposed that can achieve picometer-scale measurements in orbital angular momentum (OAM) interferometry. The proposed algorithm converts the rotational movement in a petal-shaped interference pattern into translational movement of the grayscale projection curves, so that can be easily measured using correlation operations to determine the pixel displacement in determining the rotation angle. Displacements ranging from -120 nm to 120 nm have been measured for various topological charges, with a minimum average deviation of 0.07 nm. Furthermore, we have studied the effects of piezoelectric transducer alignment, various binary threshold values, fringe occlusion, and charge-coupled device (CCD) camera resolutions on displacement measurement. Comparative experiments indicate that the proposed algorithm can effectively manage the local measurement challenges in traditional OAM interferometers, demonstrating better measurement accuracy and robustness than several existing phase demodulation algorithms.