Smooth multifocal wavefronts with a prescribed mean curvature for visual optics applications

Extended-depth-of-focus wavefront design from pseudo-umbilical space curves

Designing extended-depth-of-focus wavefronts is required in multiple optical applications. Caustic location and structure analysis offer a powerful tool for designing such wavefronts. An intrinsic limitation of designing extended-depth-of-focus wavefronts is that any smooth surface, with a non-constant mean curvature, unavoidably introduces a separation between caustic sheets, which is proportional to the ratio of change of the mean curvature along a curve embedded in the wavefront. We present a method to obtain extended-depth-of-focus wavefronts where the mean curvature variation ratio is reduced thanks to using a long circle-involute space curve effectively filling the wavefront surface. Additionally, we present a variant of the method in which the wavefront is modified within a small tubular neighborhood of the circle involute in order to partially meet the umbilical condition along that tubular region. Finally, we provide some numerical results showing the potential of our method in an application example.

Robust numerical solution to the Levi-Civita wavefront coupling problem via level set computation of the point characteristic function

The Levi-Civita wavefront coupling problem consists of, given two prescribed wavefronts, obtaining a refractive or reflective surface coupling them. We propose a robust numerical method to solve Levi-Civita's problem, whose rationale is to consider that Levi-Civita's solutions are level surfaces of the point characteristic function established between points of incoming and outgoing wavefronts. The method obtains both surface data points and their normals, enabling a more robust surface reconstruction. We carry out a detailed error analysis of our method by means of comparing the surface data estimation with nominal surfaces obtained in reference tests offering analytical solutions to Levi-Civita's problem. The method offers, in computer simulations, highly accurate results with moderate computational cost.

Multifocal wavefronts with prescribed caustics in axially symmetric optical systems

Multifocal and/or extended depth-of-focus designs are widely used in many optical applications. In most of them, the optical configuration has axial symmetry. A usual design strategy consists of exploring the optimal wavefronts that emerging out of the optical system would provide the desired multifocal properties. Those properties are closely related to light concentration on caustic surfaces. We present a systematic analysis of how to obtain those multifocal wavefronts given some prescriptions on the locations of caustics. In particular, we derive several multifocal wavefronts under archetypical prescriptions in the sagittal caustic alone, or combined with the tangential one at certain points, with some emphasis on visual optics applications.

Trade-Off Asymmetric Profile for Extended-Depth-of-Focus Ocular Lens

We explore the possibility of extending the depth of focus of an imaging lens with an asymmetric quartic phase-mask, while keeping the aberration within a relatively low level. This can be intended, for instance, for ophthalmic applications, where no further digital processing can take place, relying instead on the patient’s neural adaptation to their own aberrations. We propose a computational optimization method to derive the design-strength factor of the asymmetric profile. The numerical and experimental results are shown. The optical experiment was conducted by means of a modulo-2π phase-only spatial light modulator. The proposed combination of the asymmetric mask and the lens can be implemented in a single refractive element. An exemplary case of an extended-depth-of focus intraocular lens based on the proposed element is described and demonstrated with a numerical experiment.