| We consider the design of diffractive optical elements (DOE) using two alternative methods one iterative and one, non-iterative. While the iterative methods based on alternating constraints between the source and field plane are well-established and popular tools for DOE design, the literature lacks the works that view these iterative methods within a strict mathematical framework that considers convergence. In this dissertation we examine a well-known iterative method, Vector-Space Projection (VSP), as a DOE design tool. We use VSP to design diffractive optical elements for practical applications and while doing this examine the problems associated with convergence of the projection method in different design situations in a vector-space setting. Several examples are furnished which enables us to observe the convergence behavior of the method in different settings. The number and the topologies of the constraint sets involved in the design determine both the type i.e., serial or parallel, and the convergence properties of the VSP method. We also use VSP to design DOEs for certain types of primary aberration compensation. Two single aberration cases, namely spherical aberration and curvature of field, are considered. Although the results are of preliminary nature, they showed that VSP could be a promising method for this application area too.; In the rest of the dissertation, we consider one of the non-iterative DOE design methods, Pseudo Random Encoding (PRE). Using different optimization techniques, namely Monte-Carlo simulation, genetic algorithm, and gradient method, we work on improving this non-iterative method's performance for a specific application, i.e., spot array generation, by optimization of the diffraction efficiency. Genetic algorithm gives the best results, however, other optimization methods also improve the performance significantly compared to the case without optimization.; Finally, we compare the iterative and non-iterative methods we considered in different aspects. In conclusion, while PRE is a promising design method for the cases which require real-time computations and dynamic programming of SLMs (Spatial Light Modulators), VSP is definitely the design method to use for the applications where the DOE transmittance can be computed off-line. |
