  We propose a stereographical-visualization scheme for a polarization state by
two-dimensional imaging of a weak value with a single setup. The key idea is to
employ Laguerre-Gaussian modes or an optical vortex beam for a probe state in
weak measurement. Our scheme has the advantage that we can extract information
on the polarization state from the single image in which the zero-intensity
point of the optical vortex beam corresponds to a stereographic projection
point of the Poincare sphere. We experimentally perform single-setup weak
measurement to validate the stereographical relationship between the
polarization state on the Poincare sphere and the location of the
zero-intensity point.
