Angular spectrum ($A(k_x,k_y;z_0)=\int u(x,y,z_0)e^{-i(k_{x}x+k_{y}y)}dxdy$)

The angular spectrum is the transverse Fourier transform of a monochromatic field on a reference plane. In a uniform medium, each transverse wavevector component propagates with a longitudinal wavenumber satisfying the Helmholtz equation. Components beyond the propagating wavenumber range are evanescent waves. The outgoing angular spectrum chooses the longitudinal branch that propagates or decays away from the plane.