We present a different approach of dealing with integral equations developed to tackle diffraction of scalar harmonic waves by a hole in a perfectly reflecting screen with a thickness assumed to be negligibly small. This approach uses a cartesian representation of the Green's functions which satisfy on the screen the same Dirichlet or Neumann boundary conditions as the total field incident, reflected and diffracted while the continuity of the total field is imposed through the aperture. The solution of the corresponding integral equations is given harmonic plane waves with an application to the diffraction at slits and rectangular apertures.