Terahertz microscopy using laser feedback interferometry based on a generalised phase-stepping algorithm

In this paper we report an improved method of coherent sensing through the use of a generalized phase-stepping algorithm to extract magnitude and phase information from interferometric fringes acquired by laser feedback interferometry (LFI). Our approach allows for significantly reduced optical sampling and acquisition times whilst also avoiding the need for fitting to complex models of lasers under optical feedback in post-processing. We investigate theoretically the applicability of this method under different levels of optical feedback, different laser parameters, and for different sampling conditions. We furthermore validate its use experimentally for LFI-based sensing using a terahertz (THz)-frequency laser in both far-field and near-field sensing configurations. Finally we demonstrate our approach for two-dimensional nanoscale imaging of the out-of-plane field supported by individual micro-resonators at THz frequencies. Our results show that fully coherent sensing can be achieved reliably with as little as 4 sampling points per imaging pixel, opening up opportunities for fast coherent sensing not only at THz frequencies but across the visible and infra-red spectrum.