The induced electric and magnetic surface currents on each point of the scatterer object can be calculated from the Magnetic and Electric Field Integral Equations (MFIE & EFIE):
:<math>\mathbf{J(r)} = (1+\alpha)\mathbf{\hat{n}} \times\left\lbrace \begin{align}& \mathbf{ H^{inc}(r) } - jk_0 \iint_{S_J} \left( 1 - \frac{j}{k_0 R} \right) (\mathbf{ \hat{R} \times J(r') }) \frac{e^{-jk_0 R}}{4\pi R} \,ds' \\& -j k_0 Y_0 \iint_{S_M} \left[ \left( 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right) \mathbf{M(r')} - \left( 1-\frac{3j}{k_0 R}-\frac{3}{(k_0 R)^2} \right) \mathbf{ (\hat{R} \cdot M(r')) \hat{R} } \right] \frac{e^{-jk_0 R}}{4\pi R} \,ds' \end{align} \right\rbrace </math>
& -j k_0 Y_0 \iint_{S_M} \left[ \left( 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right) \mathbf{M(r')} -
\left( 1-\frac{3j}{k_0 R}-\frac{3}{(k_0 R)^2} \right) \mathbf{ (\hat{R} \cdot M(r')) \hat{R} } \right]
\frac{e^{-jk_0 R}}{4\pi R} \,ds'
\end{align}
\right\rbrace
</math>
:<math>\mathbf{M(r)} = -(1-\alpha)\mathbf{\hat{n}} \times\left\lbrace \begin{align}& \mathbf{ E^{inc}(r) } + jk_0 \iint_{S_M} \left( 1 - \frac{j}{k_0 R} \right) (\mathbf{ \hat{R} \times M(r') }) \frac{e^{-jk_0 R}}{4\pi R} \,ds' \\ & -j k_0 Z_0 \iint_{S_J} \left[ \left( 1 - \frac{j}{k_0 R} - \frac{1}{(k_0 R)^2} \right) \mathbf{J(r')} -\left( 1-\frac{3j}{k_0 R}-\frac{3}{(k_0 R)^2} \right) \mathbf{ (\hat{R} \cdot J(r')) \hat{R} } \right]\frac{e^{-jk_0 R}}{4\pi R} \,ds'\end{align}\right\rbrace</math>
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The starting point for the iterative PO solution is the above MFIE and EFIE integral equations. To the first (zero-order) approximation, we can write
:<math>\begin{align}& \mathbf{J^{(0)}(r)} = (1+\alpha) \mathbf{ \hat{n} \times H^{inc}(r) } \\& \mathbf{M^{(0)}(r)} = -(1-\alpha) \mathbf{ \hat{n} \times E^{inc}(r) }\end{align}</math>
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