The eikonal approximation revisited

Summary Certain problems in optical scattering are best understood when the more complicated exact scattering theory is replaced by an approximation. The Fraunhofer approximation is a well-known example. In the past ten years a considerable amount of work has been done in various disciplines towards assessing the usefulness of a new approximation referred to in the literature either as the eikonal approximation or as the high-energy approximation. The purpose of this paper is to provide a much needed review of this work and in addition to examine the historical evolution of this approximation which essentially started in optics when Bruns introduced the term eikonal in 1895. Part of this work was done when SKS was at Saha Institute of Nuclear Physics, Calcutta, and at Institute of Wetland Management and Ecological Design, Calcutta, India.