:<math> \mathbf{\hat{n} \times E(r)} = Z_s \mathbf{\hat{n} \times \hat{n} \times H(r)} </math>
where '''E(r)''' and '''H(r)''' are the electric and magnetic fields on the surface and , '''n''' is the local outward normal unit vector as shown in the figure below. , and Z<sub>s</sub> is the surface impedance having units of Ohms. To treat an object with an arbitrary geometry using PO, the object is first decomposed into many small elementary patches or cells, which have a simple geometry such as a rectangle or triangle. Then, using the tangent plane approximation, the equivalent electric and magnetic surface currents, '''J(r)''' and '''M(r)''', on the lit region of the scatterer are approximated by: :<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>
To treat an object with an arbitrary geometry using PO, the object is first decomposed into many small elementary patches or cells, which have a simple geometry such as a rectangle or triangle. Then, using the tangent plane approximation, the electric and magnetic surface currents, '''J(r)''' and '''M(r)''', on the lit region of the scatterer are approximated by:
:<math> \mathbf{J(r)} = (1+\alpha) \mathbf{\hat{n} \times H(r)} </math>