Given a 2-dimensional plane where A is known, the solution to the Helmholtz equation is given by: A ( x , y , z ) = − − 1 2 π π ∬ ∬ − − ∞ ∞ + ∞ ∞ A ′ ( x ′ , y ′ ) e i k r r z r ( i k − − 1 r ) d x ′ d y ′ ,