Can the Applied Optics Employ Modern Approaches Developed in Seismic Prospecting? A Review

Abstract

The concept of infinitesimal elastic deformation and the theory of elastic seismic waves was formed in the first part of the 19th century and was based mainly on the Fermat, Huygens and Snell developments in the theory of optics. At the same time, seismic wave propagation (utilized in geophysical prospecting) and optic wave propagation through defined media are based on the same physical-mathematical principles, making it possible to transfer nonconventional procedures developed in the first domain to the second one and back. In this investigation, we propose transferring advanced methodologies established in seismic prospecting to practical optics. We selected two advanced approaches with the following aims: (a) homeomorphic imaging; (b) novel description of boundary conditions. The first approach is established with the utilization of the revealed local theoretical relationship between the geometrical features of two fundamental beams and the geometrical properties of hidden geological targets of the media under study. The employed geometrical characteristics of the fundamental beams are spreading functions and curvatures of the singular wavefronts. The second approach is based on a novel description of the boundary conditions. It enables the determination of a faultless seismic (optical) system with the preassigned focusing and imaging assets when any aberrations are absent. An optimal optical system is usually determined as some arrangement agreeing to some perfect system with acceptable correctness. Employment of the developed procedures in the optical design will permit the application of a description of the optical surface using: (1) parametric functions, (2) differential equations, and (3) mixed (parametric-differential). On this basis, optical systems with a minimal number of optical features with complicated shapes can be promptly computed. Another important application field of the suggested methods is the design of optical systems with diffractive elements.