Holographic information in the Wigner function

The Wigner function of a Schrodinger-cat state f0+f1 is the Wigner function of f0 plus that of f1, plus a strongly oscillating cross-term, called the smile function of the cat state. We show that the marginal projection of the smile yields the transmissivity of the physical hologram of the object beam f1 with the reference beam f0. We review properties of linear covariance for possible applications in computer hologram interpretation or design.