Design of a 2 diopter holographic progressive lens.

In this contribution, we investigate the use of holographic optical elements (HOEs) as progressive addition lenses (PALs). We design HOEs with high diffraction efficiency (DE) using the Fourier Modal Method (FMM) and optimize an optical system comprising two of these HOEs to fulfill the optical function of a 2 diopter (dpt) PAL. The resulting design is a holographic PAL (hPAL) exhibiting high DE and limited angular color error (CE) with a distribution of spherical power and astigmatism equivalent to its refractive counterpart. To our knowledge, our contribution is the first complete design of an hPAL. While our HOE design method is shown for PALs here, it has the potential to improve other applications of HOEs as well.

Vectorial beam shaping.

An algorithm is reported for the design of a phase-only diffractive optical element (DOE) that reshapes a beam focused using a high numerical aperture (NA) lens. The vector diffraction integrals are used to relate the field distributions in the DOE plane and focal plane. The integrals are evaluated using the chirp-z transform and computed iteratively within the Method of Generalized Projections (MGP) to identify a solution that simultaneously satisfies the beam shaping and DOE constraints. The algorithm is applied to design a DOE that transforms a circularly apodized flat-top beam of wavelength lambda to a square irradiance pattern when focused using a 1.4-NA objective. A DOE profile is identified that generates a 50 lambda x 50 lambda square irradiance pattern having 7% uniformity error and 74.5% diffraction efficiency (fraction of focused power). The diffraction efficiency and uniformity decrease as the size of the focused profile is reduced toward the diffraction limited spot size. These observations can be understood as a manifestation of the uncertainty principle.

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.