  We set forth a method to analyze the orbital angular momentum of a light
field. Instead of using the canonical formalism for the conjugate pair
angle-angular momentum, we model this latter variable by the superposition of
two independent harmonic oscillators along two orthogonal axes. By describing
each oscillator by a standard Wigner function, we derive, via a consistent
change of variables, a comprehensive picture of the orbital angular momentum.
We compare with previous approaches and show how this method works in some
relevant examples.
