Fourier Analysis of Interference Scanning Optical Probe Microscopy

As opposed to popular far-field and near-field optical microscopy techniques, Interference Scanning Optical probe Microscopy (ISOM) operates in the intermediate-field region, where the probing distance is typically of the order of the wavelength of incident light. Specifically, ISOM enables the imaging of nanostructures through numerical inverse scattering of standing waves generated by the interference between the incident (or reflected) and scattered waves. In this work, we shed new light on this microscopy modality through an in-depth Fourier analysis. Our analysis reveals insights on the required acquisition sampling step as well as on the resolution limit of the system. Moreover, we propose two novel methods to address the associated inverse scattering problem, leveraging the intrinsic structure of the image formation model to reduce computational complexity and sensitivity to errors in model parameters. Finally, we illustrate our theoretical findings with numerical experiments.