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

Abstract

Multifocal lenses comprising progressive power surfaces are commonly used in contact and intraocular lens designs. Given a visual performance metric, a wavefront engineering approach to design such lenses is based on searching for the optimal wavefront at the exit pupil of the eye. Multifocal wavefronts distribute the energy along the different foci thanks to having a varying mean curvature. Therefore, a fundamental step in the wavefront engineering approach is to generate the wavefront from a prescribed mean curvature function. Conventionally, such a thing is done by superimposing spherical wavefront patches and maybe adding a certain component of spherical aberration to each spherical patch in order to increase the depth-of-field associated with each focus. However, such a procedure does not lead to smooth wavefront solutions and also restricts the type of available multifocal wavefronts. We derive a new, to the best of our knowledge, mathematical method to uniquely construct multifocal wavefronts from mean curvature functions (depending on radial and angular coordinates) under certain numerically justified approximations and restrictions. Additionally, our procedure leads to a particular family of wavefronts (line-umbilical multifocal wavefronts) described by 2 conditions: (1) to be smooth multiplicative separable functions in the radial and angular coordinates; (2) to be umbilical along a specific segment connecting the circle center with its edge. We provide several examples of multifocal wavefronts belonging to this family, including a smooth variant of the so-called light sword element.

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

“…is not only a fundamental issue in geometrical optics but also a practical problem in optical design; for instance, in multifocal designs for visual optics applications [15] or in deformable mirror designs for adaptive optics [14]. We have presented a new robust numerical method to solve the Levi-Civita problem.…”

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

“…In doing so, what is ensured is that equal areas of the wavefront are focused on approximately equal-length segments of the optical axis. The example case used in this paper [8] is applicable in visual optics problems, where it has been shown the benefits of including curvature variation not only along the radial coordinate but also along the angular one [1,[27][28][29]. We assumed an eye output wavefront, with a pupil size of 𝜉 = 3 mm providing 60 D for far vision and 63 D for near vision.…”

“…Multifocal and/or extended-depth-of-focus optical beams are ubiquitous in a wide range of optical engineering applications; to name just a few: ophthalmic corrections for presbyopia [1], microscopy [2], or laser micromachining [3]. Although relatively novel, the analysis or prescription of the caustic structure of such optical beams offers an appealing way of designing them [4][5][6][7][8].…”

Visual Function of a Non-diffractive Extended-depth-of-focus Intraocular Lens According to Epiretinal Membrane Stage

“…The optical design of smooth curves within a restricted area rather than concentric steps throughout the optic area causes less discomfort but provides low additional visual power [18]. Accordingly, EDoF IOL might not enhance intermediate and near vision at an advanced ERM stage, limiting the effects of premium IOL.…”