Design of three-dimensional superresolution filters and limits of axial optical superresolution

Multiring pure-phase binary optical elements to extend depth of focus

Multiring pure-phase binary optical elements (BOEs) are widely used to extend the depth of focus (DOF) in many optical applications. Although researchers have designed various BOEs to extend the DOF, few theories and experiments have been reported to validate the performances of different N-ring pure-phase BOEs to realize the DOF as long as possible. In this paper, aberration theory is used to obtain the simple and straightforward initial phase, and a novel modified Gerchberg-Saxton algorithm is presented for generating N-ring 0-π-phase BOEs to optimally extend the DOF. Theoretical, numerical, and experimental results demonstrate that the DOF can be extended with increased N in the same NA.

Modified Shack-Hartmann wavefront sensor using an array of superresolution pupil filters

A conventional Shack-Hartmann wavefront sensor works with an array of lenslets which produces an array of focal spots in the back focal plane of the lenses. The displacements of the focal spots from a reference position give a measure of the mean local wavefront slopes. To determine the positions of the focal spots, centroiding algorithms have to be used. In this work, the use of superresolution pupil filters to reduce the size of the focal spots is analyzed, as well as its effect on the variance of the centroid estimate, seeking for an enhancing of the sensor accuracy.

Hybrid refractive-diffractive-gradient-index superresolving focusing device

The focusing properties and resolving power of a device consisting of a tapered gradient-index (GRIN) lens with spherical input and output faces are investigated through the use of the ABCD formalism to achieve minimization of the Airy radius for the device. Diffractive elements, such as zone plates, can, with an appropriate choice of their parameters, increase the resolution of an imaging system compared with a conventional lens. We demonstrate that by combining both elements a hybrid refractive-diffractive-GRIN device can be designed that exhibits improved superresolution characteristics.

Particle-swarm optimization of axially superresolving binary-phase diffractive optical elements

A particle-swarm optimization (PSO) algorithm was developed for designing binary-phase-only diffractive optical elements (DOEs) that superresolve the axially focused point-spread function. The method is based on vector diffraction theory to ensure solutions are valid under high-NA conditions. A DOE is identified that superresolves the focal spot by 34% and maintains the sidelobes below 50% of the peak intensity. The algorithm was used to obtain the Pareto front of the fitness-value space, which describes the achievable superresolution versus an allowed upper bound in sidelobe intensity. The results suggest that the algorithm yields solutions that are global in terms of the co-optimized fitness values G and M.

Axial field shaping under high-numerical-aperture focusing

Kant reported [J. Mod. Optics 47, 905 (2000)] a formulation for solving the inverse problem of vector diffraction, which accurately models high-NA focusing. Here, Kant's formulation is adapted to the method of generalized projections to obtain an algorithm for designing diffractive optical elements (DOEs) that reshape the axial point-spread function (PSF). The algorithm is applied to design a binary phase-only DOE that superresolves the axial PSF with controlled increase in axial sidelobes. An 11-zone DOE is identified that axially narrows the PSF central lobe by 29% while maintaining the sidelobe intensity at or below 52% of the peak intensity. This DOE could improve the resolution achievable in several applications without significantly complicating the optical system.

Three-dimensional superresolution by three-zone complex pupil filters

Complex pupil filters are introduced to improve the three-dimensional resolving power of an optical imaging system. Through the design of the essential parameters of such filters, the transmittance and radius of the first zone, three-dimensional superresolution is realized. The Strehl ratio and the transverse and axial gains of such filters are analyzed in detail. A series of simulation examples of such filters are also presented that prove that three-dimensional superresolution can be realized. The advantage of such filters is that it is easy to realize three-dimensional superresolution, and the disadvantage is that the sidelobes of the axial intensity distribution are too high. But this can be overcome by the application of a confocal system.