where it is assumed that both the incident electric field and incident magnetic field have been decomposed into two parallel and perpendicular polarizations and Γ<sub>||</sub> and Γ<sub>⊥</sub> denote the reflection coefficients at the interface between air and the impedance surface for the cases of parallel and perpendicular polarizations, respectively. These reflection coefficients are given by:
:<math> R_{\|} = \frac{Z_0\eta_0\cos\theta - Z_s} {Z_0\eta_0\cos\theta + Z_s} </math>
:<math> R_{\perp} = \frac{Z_s\cos\theta - Z_0\eta_0} {Z_s\cos\theta + Z_0\eta_0} </math>
where <math>\eta_0 = 120\pi \; \Omega</math> is the intrinsic impedance of the free space.
:<math> \mathbf{J(r)} = (1+\alpha) \mathbf{\hat{n} \times H(r)} </math> :<math> \mathbf{M(r)} = -(1-\alpha) \mathbf{\hat{n} \times E(r)} </math><!--[[File:PO1(1).png]]--> where '''E(r)''' and '''H(r)''' are the incident electric and magnetic fields on the object and '''n''' is the local outward normal unit vector as shown in the figure below. a is a parameter related to the impedance Z of the surface (expressed in Ohms), which is defined in the following way: :<math> \alpha = \frac{1-Z/\eta_0}{1+Z/\eta_0} </math><!--[[File:PO2.png]]--> where <math>\eta_0 = 120\pi \; \Omega</math> is the intrinsic impedance of the free space. Then, the electric and magnetic currents reduce to:
:<math> \mathbf{J(r)} = \frac{2\eta_0}{\eta_0 + Z} \mathbf{\hat{n} \times H(r)} </math>