Optical phase mining by adjustable spatial differentiator

Phase is a fundamental resource for optical imaging but cannot be directly observed with intensity measurements. The existing methods to quantify a phase distribution rely on complex devices and structures and lead to difficulties of optical alignment and adjustment. We experimentally demonstrate a phase mining method based on the so-called adjustable spatial differentiation, by analyzing the polarization of light reflection from a single planar dielectric interface. Introducing an adjustable bias, we create a virtual light source to render the measured images with a shadow-cast effect. From the virtual shadowed images, we can further recover the phase distribution of a transparent object with the accuracy of 0.05λ RMS. Without any dependence on wavelength or material dispersion, this method directly stems from the intrinsic properties of light and can be generally extended to a broad frequency range.