Shearing interferometry via geometric phase

We propose an approach based on geometric phase for per- forming several types of shearing interferometry through a robust, compact, common-path setup. The key elements are two identical parallel plates with spatially varying birefringence distributions, which perform the shearing by writing opposite geometric phases on the two circular polarization components of the linearly polarized incident wavefront. This setup allows the independent control of the shearing magnitude and relative phase of the two wavefront replicas. The approach is first illustrated for the simplest case of lateral shearing, and then extended to other geometries where the magnitude and direction of the shear vary smoothly over the wavefront

Birefringent Fourier filtering for single molecule Coordinate and Height super-resolution Imaging with Dithering and Orientation

Super-resolution imaging based on single molecule localization allows accessing nanometric-scale information in biological samples with high precision. However, complete measurements including molecule orientation are still challenging. Orientation is intrinsically coupled to position in microscopy imaging, and molecular wobbling during the image integration time can bias orientation measurements. Providing 3D molecular orientation and orientational fluctuations can offer new ways to assess the degree of alignment of protein structures, which cannot be monitored by pure localization. Here we demonstrate that by adding polarization control to phase control in the Fourier plane of the imaging path, all parameters can be determined unambiguously from single molecules: 3D spatial position, 3D orientation and wobbling or dithering angle. The method, applied to fluorescent labels attached to single actin filaments, provides precisions within tens of nanometers in position and few degrees in direction