Letting k x = k sin ⁡ ⁡ θ θ cos ⁡ ⁡ ϕ ϕ and k y = k sin ⁡ ⁡ θ θ sin ⁡ ⁡ ϕ ϕ , the Fraunhofer region field of the planar aperture assumes the form of a Fourier transform Ψ Ψ ( r ) ∝ ∝ e i k r 4 π π r ∬ ∬ a p e r t u r e E i n c ( x ′ , y ′ ) e − − i ( k x x ′ + k y y ′ ) d x ′ d y ′ ,