Existing experimental results show that thinner Zn films (dN < 3 μm) yield larger values of ReZN(E)/ZN(0) than those obtained with thicker films (dN ≥ 3μn), whereas both produce the same ImZN(E). As ZN(E) is analytic, ReZN(E) and ImZN(E) are Hilbert transforms of one another. We compute the transforms of ReZN(E) and ImZN(E), which we compare with their experimental counterparts. Thicker Zn films yield better internal agreement and bulk results.