Three-dimensional beam forming and Ewald's surfaces

Three-dimensional beam forming is an important task for various applications, e.g., optical scanners and imaging systems. However, optical beams satisfy the wave equation when propagating in free-space, meaning that not any prescribed 3-D distribution is a physical light beam. This paper proposes an iterative algorithm for synthesizing 3-D optical beams that satisfy the wave equation. The algorithm is based on a close inspection at the Fourier transform of optical beams, which involves Ewald's surfaces. It utilizes the error-reduction algorithm that exploits the degrees of freedom existing in the optical system. (C) 2003 Elsevier B.V. All rights reserved.