Diffraction and the Propagation of Light

Geometric optics is considered and the eikonal equation is introduced. Krirchoff’s diffraction theory is presented with his integral theorem. Rayleigh–Sommerfeld diffraction is discussed and Fresnel’s approximation for the Kirchoff integrals and Babinet’s principle are given. Fraunhoffer diffraction is considered in detail, specifically diffraction by a rectangular and circular aperture. Special emphasis is given to the angular spectrum representation and its applications, including Gaussian beams, Fourier optics, and tight focusing of fields. Finally, the fields and modes of a tightly focused Gaussian beam are considered and the diffraction limits on microscopy are given.