Abstract: Diffraction is a fundamental phenomenon in optics. Deriving an analytical solution for the diffraction of complex apertures is generally challenging. To obtain the Fraunhofer diffraction patterns of complex apertures, the ear-clipping method is employed to approximate the aperture by dividing it into multiple triangles. Consequently, the total diffraction field of the aperture can be expressed as a superposition of the diffraction fields of these triangles. The Fourier transform of each arbitrary triangle is computed by converting it, through coordinate transformation, into the Fourier transform of a basic right triangle. Subsequently, an experimental setup for Fraunhofer diffraction is constructed to measure the diffraction field distribution for different apertures. The angular distribution uncertainty is calculated to analyze the diffraction field of regular polygonal apertures, verifying the feasibility and accuracy of the proposed analytical algorithm. Finally, the diffraction field of complex fractal apertures is computed and the algorithm's effectiveness in calculating diffraction fields of complex apertures is demonstrated

Key words: triangulation, Ear-Clipping method, complex aperture, Fraunhofer diffraction