Paraxial Optics

Paraxial optics is sometimes known as the Gaussian optics. It is the simplest framework where optical systems are described. A great variety of textbooks in optics include specific chapters to the paraxial approximation of the geometrical optics. Other textbooks focused in geometrical optics propose that the paraxial treatment should be included as part of the first approach to the subject. The paraxial approximation explains how light propagates along an optical system when rays are close to the optical axis. Roughly speaking, paraxial optics applies when the transversal size is small compared with the longitudinal size of the objects, images, and constructive parameters of the optical systems. For an imageforming system, it corresponds with the ideal status where the system can be considered as perfect. Geometrical optics uses the advantages of the paraxial approach to provide a first-order description of the behavior of an optical system. Because of the intensive use of the paraxial approach in geometrical optics, we are sometimes tempted to identify both concepts. However, geometrical optics goes beyond the paraxial approach, and the paraxial approach applies also to physical optics. In this contribution, we will try first to determine what the paraxial approach means, and what the paraxial optics should be dealing with. The influence of the paraxial approach in geometrical optics is analyzed. It produces the paraxial geometrical relations that describe the object– image correspondence. The paraxial approach also allows introducing the cardinal points of an optical system: focal points, principal points and planes, and nodal points. The combination of optical systems is described also inside the paraxial approach. Prisms are presented and the paraxial approach is evaluated properly. Matrix optics is a formalization of the linearization of the Snell law that accompanies the paraxial optics. The definition of the F# is presented in terms of the focal distance and the transversal dimension of the optical system. Finally, the chromatic aberrations are labeled as the paraxial aberrations. Some implications of the paraxial approach in the framework of the physical optics are analyzed in the ‘‘Paraxial Regime.’’ We begin with the application of the paraxial approach to the reflectance and the transmittance. The equations describing the propagation of an electromagnetic wave are expanded and analyzed until the paraxial approach to introduce the paraxial wave equation and to demonstrate that Fraunhofer diffraction lies within the paraxial regime. The link between paraxial geometrical optics and paraxial wave optics is shown with the introduction of the ABCD matrix into the kernel of the Huygens–Fresnel integral. The calculation of the effect of a lens as a phase screen is related with the paraxial equation describing the focal length of a thin lens. Finally, some comments about the extension beyond the paraxial approach are necessary to enhance the fact that geometrical optics is not only the paraxial optics, and the paraxial optics is not only applicable into the geometrical optics. The main conclusions of this contribution are summarized in the ‘‘Conclusion.’’