Investigations Of Design Methods Of Diffractive Optical Elements To Implement Optical Superresolution

Resolution is the most important performance parameter of an imaging system and in an ideal imaging system it is determined by the diffraction limit. With the techniques and elements of diffractive optics, it is now feasible to break the diffraction limit and achieve optical superresolution. This thesis is concerned with the methods of designing diffractive superresolution elements (DSE). The aim of design is to reduce the size G of the main lobe, to increase the central intensity (or Strehl ratio S), and to suppress the intensity M of the highest side lobe, so that globally optimized performance of superresolution can be obtained. The methods presented have both theoretical significance and practical utility. Based on linear programming, calculus of variation, and theory of generalized matrix eigenvalue problem, the novel methods developed in the thesis can be used to design DSE with transverse, axial or three-dimensional superresolution. The results achieved are globally optimal, which is not guaranteed by the previous methods. Moreover, it is theoretically proven that a DSE with globally optimal performance of superresolution is a phase-only element with a phase shift of 0 or π. An iterative discretization method is also proposed to efficiently improve the computational precision of the locations where a phase break of πradians occurs. The global optimization methods make it possible to present systematically the fundamental limits of optical superresolution, which provide important bases for the design and the performance evaluation of DSE. The following exact bounds are determined: For the transverse superresolution in conventional imaging mode, (1) the exact lower bound of G for a given lower bound on S and a given upper bound on M, (2) the exact lower bound of G for a given upper bound on M, (3) the exact upper bound of S for given upper bounds on both G and M, (4) the exact lower bound of M for a given lower bound on S and a given upper bound on G, and (5) the exact upper bound of S for a given G, when the intensity distribution at the exit pupil can be modulated by introducing a beam shaping system; for the transverse superresolution in confocal imaging mode, the exact upper bound of S for a given G; for the axial superresolution in conventional or confocal imaging mode, the exact upper bound of S for a given main lobe size along the optical axis. In addition, through the generalization of the global optimization design methods, the exact upper bound of bifocal Strehl ratio of a bifocal imaging system is obtained for a fixed bifocal intensity ratio. A diffraction model for the DSE in an imaging system with high numerical aperture is established on the basis of geometrical optics and Rayleigh-Sommerfeld scalar diffraction theory. This model can be conveniently used for designing a DSE, which is difficult for the existing models. The whole process of design, fabrication and experimental measurement of several kinds of DSE is completed. The experimental results are consistent well with the theoretical predictions, so the global optimization design methods are validated.