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FROM SEISMIC INVERSION TO APPLIED OPTICS : A NOVEL APPROACH TO DESIGN OF COMPLEX SYSTEMS

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