From seismic inversion to applied optics: A novel approach to design of complex systems

Propagation of seismic waves studied in geophysical prospecting and optic wave propagation through defined media is based on the same physical-mathematical principles. It makes it possible to transfer modern procedures developed in the first field to the second one and back. This paper suggests transferring novel procedures developed in seismic prospecting to applied optics. We selected two progressive approaches for such conversion: (1) Homeomorphic Imaging and (2) Novel description of boundary conditions. The first approach is based on the employment of revealed local theoretical relationships between the geometrical characteristics of two fundamental beams and the geometrical properties of the studied media's geological layers (bodies). Geometrical characteristics of the fundamental beams are spreading functions and curvatures of the special wavefronts. The second approach – a new description of boundary conditions- permits the determination of a perfect seismic (optical) system with the necessary focusing and imaging properties, free from any aberrations. An optimal optical system is determined as an arrangement corresponding to some perfect system with admissible accuracy. Application of the developed procedures in the optical design will permit the application of a description of an optical surface using: (a) Parametric functions, (b) Differential equations, and (c) Mixed (parametric-differential). On this basis, the optical systems consisting of a minimal number of optical elements with complicated shapes might be promptly computed. Another important application field of the suggested methods is the design of optical systems with diffractive elements.