Calculation of zonal power and astigmatism of a freeform gradient index lens with freeform surfaces.

Freeform gradient index (F-GRIN) lenses have been recently shown to enable compact optical design. However, aberration theory is only fully developed for rotationally symmetric distributions with a well-defined optical axis. The F-GRIN has no well-defined optical axis, and rays are continuously perturbed along their trajectory. Optical performance can be understood without abstracting optical function to numerical evaluation. The present work derives freeform power and astigmatism along an axis through a zone of an F-GRIN lens with freeform surfaces. Zonal power and astigmatism can be assessed without tracing any rays, capturing mixed contributions of the F-GRIN and freeform surface. Theory is compared with a commercial design software numerical raytrace evaluation. The comparison shows that the raytrace-free (RTF) calculation represents all raytrace contributions within a margin of error. In one example, it is demonstrated that linear terms of index and surface alone in an F-GRIN corrector can correct the astigmatism of a tilted spherical mirror. Accounting for the induced effects of the spherical mirror, RTF calculation provides the amount of astigmatism correction of the optimized F-GRIN corrector.

Replacing optical surfaces with gradient index functions which preserve ray trajectory.

Laws of reflection and refraction between homogeneous media and gradient index (GRIN) ray behavior are both derived from Fermat's principle. Design methods for GRIN can be difficult to analytically develop. This Letter proposes a foundation for complete replacement of refracting and total internally reflecting optical interfaces in existing designs with GRIN distribution. The proposed method can aid in incorporating GRIN into existing optical designs. Refraction in GRIN is specified to match the ray striking and leaving the optical interface in both position and angle. This result is shown for a collection of similar GRIN functions. One GRIN function is analyzed over a full space of attainable ray bend angles. A local arbitrarily oriented planar interface is replaced with GRIN distribution, and ray behavior is maintained.

Freeform gradient index generalized Coddington's equations.

Coddington's equations and their generalized forms are useful for lens design and analysis of optical performance. Generalized Coddington's equations (GCE) exist in literature for analysis of decentered systems and freeform surfaces, but not for gradient index (GRIN) lenses. In this work, GCE are presented for the analysis of freeform GRIN lenses with freeform surfaces. Examples are shown where the presented theory converges on Coddington's equations and known paraxial GRIN behavior. The method also correctly shows known afocal behavior proximate to azimuthally directed rays in a cylindrical GRIN. The latter case is one of analytically validated local freeform behavior.

Freeform gradient index progressive addition lens raytrace performance evaluation.

Raytrace evaluation capable of evaluating progressive addition lens (PAL) designs with freeform surface and gradient index (GRIN) contributions is presented. The method is validated on an analytically generated PAL start design and on optimized surface designs. Surface raytrace evaluations are compared with the surface-geometric evaluation commonly presented for freeform surface PAL designs. The evaluation is also tested on analytically generated freeform GRIN PAL designs with spherical and plano surfaces. The raytrace method agrees with the analytic performance and surface-geometric performance near the center of the lens and deviates at the edge of the lens, due to ray obliquity with the surfaces and aggregate contributions of surfaces and/or GRIN. These deviations are expected, as the raytrace model accounts for more physical contributions to optical performance, including pupil diameter and eye position. This raytrace method enables the evaluation of lens performance contributions other than from polished surfaces on homogeneous materials, enabling further exploration of GRIN in PAL designs.

Polychromatic annular folded lenses using freeform gradient-index optics.

The annular folded lens (AFL) is a design form offering large aperture, high-resolution imaging in a very axially compact package. The folded optic can be made monolithic for easier fabrication and alignment, yet the introduction of refractive surfaces with a dispersive optical material gives way to chromatic aberrations. AFL designs using homogeneous media are generally limited to the monochromatic regime, with polychromatic performance greatly reduced. By introducing freeform gradient-index (F-GRIN) media, monolithic AFL designs can achieve higher monochromatic performance as well as provide color correction for diffraction-limited polychromatic imaging. Monochromatic and polychromatic design methodologies are surveyed where the F-GRIN is constrained to remain feasible for fabrication.

Freeform gradient-index media: a new frontier in freeform optics.

Freeform optics enable irregular system geometries and high optical performance by leveraging rotational variance. To this point, for both imaging and illumination, freeform optics has largely been synonymous with freeform surfaces. Here a new frontier in freeform optics is surveyed in the form of freeform gradient-index (F-GRIN) media. F-GRIN leverages arbitrary three-dimensional refractive index distributions to impart unique optical influence. When transversely variant, F-GRIN behaves similarly to freeform surfaces. By introducing a longitudinal refractive index variation as well, F-GRIN optical behavior deviates from that of freeform surfaces due to the effect of volume propagation. F-GRIN is a useful design tool that offers vast degrees of freedom and serves as an important complement to freeform surfaces in the design of advanced optical systems for both imaging and illumination.

Brain-computer interface-based assessment of color vision.

Objective.Present methods for assessing color vision require the person's active participation. Here we describe a brain-computer interface-based method for assessing color vision that does not require the person's participation.Approach.This method uses steady-state visual evoked potentials to identify metamers-two light sources that have different spectral distributions but appear to the person to be the same color.Main results.We demonstrate that: minimization of the visual evoked potential elicited by two flickering light sources identifies the metamer; this approach can distinguish people with color-vision deficits from those with normal color vision; and this metamer-identification process can be automated.Significance.This new method has numerous potential clinical, scientific, and industrial applications.