Fourier Optics Basics

This chapter looks into the mathematical theories used to describe the linear superposition approach to optical propagations following Lohmann and others, hopefully providing some insights how they are used in optical systems characterization. The areas covered in the chapter are often referred to as Fourier Optics. The chapter begins with the four major theoretical views of this approach: Rayleigh‐Sommerfeld‐ Debye theory of diffraction, Huygens‐ Fresnel‐ Kirchhoff theory of diffraction, Fresnel diffraction, and Fraunhofer diffraction. Far‐field, or Fraunhofer, diffraction has been the workhorse of all electromagnetic field propagation, for example, optical signal processing, holography, and propagation in a turbulence atmosphere. The chapter establishes that a finite aperture lens is incapable of creating a perfect focus even under the best circumstances. This affects image resolution, which affects our ability to see details in said image. The most widely accepted image quality criterion is called the Rayleigh Criterion for resolution.