Development of Numerical Methods for Applications of Coherent Radiation in Studies of the Internal Structure of Objects (Part II)

We consider single-beam 3D imaging, i.e., an approach to reconstructing the complex dielectric constant ε(x, y, z) of a sample in question by processing data read from a detector during successive illumination of a stationary object with different Gaussian beams along the same direction (angle). The propagation of Gaussian beams through an object is described using the parabolic wave equation. The equation for single-beam volume imaging is derived, which relates the data obtained on the detector with the values of the dielectric constants ε(x, y, z). As an example of solving this equation using optimization methods, a simplified case of purely real dielectric constant ε(x, z) in two-dimensional space is considered.