  Contextuality is a foundational phenomenon underlying key differences between
quantum theory and classical realistic descriptions of the world. Here we
propose an experimental test which is capable of revealing contextuality in all
qutrit systems, except the completely mixed state, provided we choose the
measurement basis appropriately. The 3-level system is furnished by the
polarization and spatial degrees of freedom of a single photon, which encompass
three orthogonal modes. Projective measurements along rays in the 3-dimensional
Hilbert space are made by linear optical elements and detectors which are
sensitive to a single mode. We also discuss the impact of detector inefficiency
and losses and review the theoretical foundations of this test.
