Capturing appearance often requires dense sampling in light-view space, which is often achieved in specialized, expensive hardware setups. With the aim of realizing a compact acquisition setup without multiple angu- lar samples of light and view, we sought to leverage an alternative optical property of light, polarization. To this end, we capture a set of polarimetric images with linear polarizers in front of a single projector and camera to obtain the appearance and normals of real-world objects. We encountered two technical challenges: First, no complete polarimetric BRDF model is available for modeling mixed polarization of both specular and diffuse reflec- tion. Second, existing polarization-based inverse rendering methods are not applicable to a single local illumination setup since they are formulated with the assumption of spherical illumination. To this end, we first present a com- plete polarimetric BRDF (pBRDF) model that can define mixed polarization of both specular and diffuse reflection. Second, by leveraging our pBRDF model, we propose a novel inverse-rendering method with joint optimization of pBRDF and normals to capture spatially-varying material appearance: per-material specular properties (including the refractive index, specular roughness and specular coefficient), per-pixel diffuse albedo and normals. Our method can solve the severely ill-posed inverse-rendering problem by carefully accounting for the physical relationship between polarimetric appearance and geometric properties. We demonstrate how our method overcomes limited sampling in light-view space for inverse rendering by means of polarization.