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тАв the interpolation of the pixels array of the basis DOE uses the pixels array of an additional DOE

тАв the iterative calculation of the DOE is capable of forming Gauss-Hermite, Gauss-Laguerre and Bessel light modes

тАв the iterative-analytical calculation of a multifocus DOE for focusing into a set of linesтАФthe calculation employs a nonlinear transform of the phase function of a DOE focusing into a line and is computed via the ray-tracing approach

тАв the solution to the problem of the initial approximation for iterative algorithmsтАФthe initial guess is chosen on the basis of the ray-tracing solution.

All the methods discussed in the book have been verified through the numerical simulation. The fast Fourier transform algorithm gives a computational basis for all the methods considered.

Some of the algorithms have been studied comparatively in terms of their suitability for solving the same problem. For a number of the iterative algorithms, a rigorous proof to their convergence is given.

Note that all the methods presented are aimed at calculating highly effective DOEs forming desired images with a 60тАУ100% energy efficiency.

The introduction gives a brief explanation of major concepts that are employed and detailed in the subsequent chapters. Chapter 1 deals with parametric iterative methods used for designing kinoforms and capable of yielding, via the successive approximation, a Fresnel or a Fourier approximation of nonlinear integral equations of optics. It is shown how to vary the rate of convergence of the iterative procedure by fitting the value of the regularization parameter. Chapter 2 is devoted to the adaptation of iterative algorithms for designing DOEs that have the radially symmetric transmission function, using a Hankel transform instead of a two-dimensional (2D) Fourier transform. Chapter 3 discusses the peculiarities of iterative algorithms in computing DOEs forming reference wavefronts. It is demonstrated that the wavefronts can be formed using amplitude masks. Chapter 4 presents iterative techniques for calculating DOEs forming Gaussian and Bessel modes. Light modes can propagate either all in one direction, thus forming a light beam with the required mode composition, or each in its own direction. Chapter 5 deals with techniques for iteratively calculating multiorder phase diffraction gratings with multilevel and binary phase. Chapter 6 presents analytic-iterative methods for calculating multifocus DOEs for focusing into a set of lines. The methods utilize the nonlinear transformation of the phase function of a basis DOE focusing into a line. Chapter 7 covers the problem of choosing the initial guess for iterative methods for designing DOEs and includes numerical results of a comparison between different methods in solving some special tasks: focusing into a transverse segment and axial segment, into a square, and into a ring. Appendices F and G treat