Electromagnetism is described in terms of two scalar gauge-invariant variables. The role of gauge freedom in the quantization process when Aμ(x) is written in momentum space appears as the indetermination of a two-dimensional space-like plane orthogonal to the (null) momentum kμ plus a c-number arbitrary function. Duality rotations can naturally be described as the freedom to choose two orthonormal vectors in the two-dimensional space-like plane. The action written in terms of the two dynamical degrees of freedom is explicitly invariant under finite duality rotations and the associated Noether current is gauge invariant. Finally, we establish the equivalence for the Poisson bracket relations (PBR's) (based on equal time and equal null-time PBR for the two degrees of freedom) between Aμ(x) and Aν(x′) for any gauge.