This book will address the advances, applications, research results, and emerging areas of optics, photonics, computational approaches, nano-photonics, bio-photonics, with applications in information systems. The objectives are to bring together novel approaches, analysis, models, and technologies that enhance sensing, measurement, processing, interpretation, and visualization of information. The book will concentrate on new approaches to information systems, including integration of computational algorithms, bio-inspired models, photonics technologies, information security, bio-photonics, and nano-photonics. Applications include bio-photonics, digitally enhanced sensing and imaging systems, multi-dimensional optical imaging and image processing, bio-inspired imaging, 3D visualization, 3D displays, imaging on nano-scale, quantum optics, super resolution imaging, photonics for biological applications, microscopy, information optics, and holographic information systems.

Beam shaping is used to transform a given intensity distribution into a different, desired intensity distribution. Applications of one-dimensional (rotationally symmetric) beam shaping [1–6] are typically in the area of high power laser operations, where the Gaussian laser beam shape leads to an inefficient usage of the available laser power due to loss at the focusing lens. Unlike one-dimensional beam-shaping, which leads to a simple differential equation which can be integrated in a straightforward manner, the two-dimensional beam shaping problem leads to a nonlinear Monge–Ampere type equation [7–9], for which numerical solutions [10–15] are difficult to obtain. We will first generalize the equations for optical beam shaping with two surfaces, derive the nonlinear Monge–Ampere type differential equation, and present the shifted-base-function (SBF) approach [16] to model the surfaces and to solve this equation.