where θ is the incident angle between the propagation vector of the incident field and the normal to the surface and <math>\eta_0 = 120\pi \; \Omega</math> is the intrinsic impedance of the free space.
In the case of an impedance-matched surface(Z<sub>s</sub> = η<sub>0</sub>), one can write:
:<math> R_{\|} = -R_{\perp} = \frac{1-\cos\theta} {1+\cos\theta} </math>
</table>
Two special limiting cases of an impedance surface are perfect electric conductor (PEC) and perfect magnetic conductor (PMC) surface. For a PEC surface, Z <sub>s</sub> = 0, α = 1, and one can write:
:<math> \mathbf{J(r)} = 2 \mathbf{\hat{n} \times H(r)} </math>
:<math> \mathbf{M(r)} = 0 </math>
<!--[[File:PO4.png]]-->
while for a PMC surface, Z <sub>s</sub> = ∞, α = -1, and one can write:
:<math> \mathbf{J(r)} = 0 </math>
:<math> \mathbf{M(r)} = -2 \mathbf{\hat{n} \times E(r)} </math>
<!--[[File:PO5.png]]-->
Another special case is a Huygens surface with equivalent electric and magnetic surface currents. In that case, Z = η<sub>0</sub>, α = 0, and one can write:
:<math> \mathbf{J(r) = \hat{n} \times H(r)} </math>
:<math> \mathbf{M(r) = -\hat{n} \times E(r)} </math>
<!--[[File:PO10.png]]-->
A major difficulty encountered in determining the PO currents of the scatterer is identification of lit and shadowed facets. Determination of lit and shadowed regions for simple, stand-alone, convex objects is rather simple. Denoting the incidence direction from a source to a point on the scatterer by the unit vector '''k''', the point is considered lit if '''n.k'''< 0, and shadowed if '''n.k'''> 0. These conditions, however, are only valid if there is a direct line of sight (LOS) between the source and the centroid of the cell under consideration. They cannot predict if there are any obstructing objects in the path of the incident beam or ray. For simple convex objects, a Geometrical Optics (GO) approach can be used to finds the optical LOS lines and determine the lit and shadowed areas on the object. The conventional PO can then be used to find the electric and magnetic surface currents.