Holographic pancake optics for thin and lightweight optical see-through augmented reality.

Holographic pancake optics have been designed and fabricated in eyewear display optics literature dating back to 1985, however, a see-through pancake optic solution has not been demonstrated to date. The key contribution here is the first full-color volume holographic pancake optic in an optical see-through configuration for applications in mobile augmented reality. Specifically, the full-color volume holographic pancake is combined with a flat lightguide in order to achieve the optical see-through property. The fabricated hardware optics has a measured field of view of 29 degrees (horizontal) by 12 degrees (vertical) and a measured large eyebox that allows a ±10 mm horizontal motion and ∼±3 mm vertical motion for a 4 mm diameter pupil. The measured modulation transfer function (average orientation) is 10% contrast at 10 lp/deg. Three holograms were characterized with respect to their diffraction efficiency, angular bandwidth, focal length, haze, and thickness parameters. The phase function in the reflection mode hologram implements a spherical mirror that has a relatively simple recording geometry.

Varifocal augmented reality adopting electrically tunable uniaxial plane-parallel plates.

Vergence-accommodation conflict (VAC) is a major challenge in optical-see through augmented reality (AR) system. To resolve this conflict, many approaches are proposed, for instance, by means of adjustment of the projected virtual image to coincide with the surroundings, called image registration, which is more often referred to as varifocal function. In this paper, a varifocal AR system is demonstrated by adopting electrically tunable liquid crystal (LC) plane-parallel plates to solve VAC problem. The LC plates provide electrically tunable optical paths when the directors of LC molecules are re-orientated with applied voltages, which leads to a corresponding change of light speed for an extraordinary wave. To provide a sufficient tunable optical path, three pieces of multiple-layered LC structures are used with the total thickness of the active LC layers (∼510 µm). In experiments, the projected virtual image can be adjusted from 1.4 m to 2.1 m away from the AR system, while the thickness of LC plane-parallel plates are only less than 3 mm without any mechanical moving part. When light propagates in the uniaxial LC layers, the wave vector and the Poynting vector are different. The longitudinal displacement of the image plane is determined by Poynting vectors rather than wave vectors. As a result, the analysis of the AR system should be based on Poynting vectors during geometrical optical analysis. Surprisingly, the tunable range of the longitudinal displacement of Poynting vectors is 2-fold larger than the tunable range of the wave vectors. Moreover, the virtual image shifts in opposite directions with respect to the Poynting vectors and wave vectors. The proposed AR system is not only simple but also thin, and it exhibits a large clear aperture. The investigation here paves the way to a simple solution of the VAC problem for augmented reality systems.

Polarization aberrations of electrically tunable liquid crystal mirrors.

Curved mirrors are able to fold optical paths and play important roles in compact optical systems in general. In this paper, we investigate the polarization aberrations of electrically tunable liquid crystal (LC) mirrors with two kinds of configurations (flat and curved ones). The LC mirrors exhibit spatially-continuous tunable wavefronts. The detailed wavefronts of two LC mirrors are related to angles of incidence, polarization of light, and the alignment direction of LC molecules. The key contribution of this paper is the development and characterization of a tunable liquid crystal mirror. The tunability of polarization aberration of LC mirrors should be able to provide extra parameters for optical engineers to design versatile optical systems.

Phase modulators with tunability in wavefronts and optical axes originating from anisotropic molecular tilts under symmetric electric field II: experiments.

We demonstrate, for the first time, an electrically-tunable and physically-planar freeform optical element made up of nematic liquid crystals (LCs). Continued on numerical study in previous paper (Part I), experimental results here show that it is possible to break the rotational symmetry of the wavefront through the use of uneven tilt angles of the LC molecules even though the electric potential is rotationally symmetric. Our optical element offers the ability to electrically tune the direction of the optical axis, the wavefront deviation, as well as the Zernike polynomials for general descriptions of wavefronts. Corresponding Zernike coefficients of a Zernike polynomial that are related to defocus and spherical aberration, which can be adjusted individually or together. The minimum wavefront deviation is >λ/6. The Zernike coefficients related to coma aberration or the tilt of the optical axis are also electrically tunable. By incorporating our LC phase modulator with tunability of freeform wavefronts into a simple reflective optical system, we demonstrate convincing image performance for off-axis image aberration correction. This approach will inspire further development and design of LC optical elements for applications, such as hyperspectral imagers in aerospace optics, augmented reality, virtual reality, quantum information systems, innovative miniaturized reflective telescopic systems for astrophysics, planetary science, and earth science.

A perceptual eyebox for near-eye displays.

In near-eye display systems that support three-dimensional (3D) augmented and virtual reality, a central factor in determining the user experience is the size of the eyebox. The eyebox refers to a volume where the eye receives an acceptable view of the image with respect to a set of criteria and thresholds. The size and location of this volume are primarily driven by optical architecture choices in which designers trade-off a number of constraints, such as field of view, image quality, and product design. It is thus important to clearly quantify how design decisions affect the properties of the eyebox. Recent work has started evaluating the eyebox in 3D based purely on optical criteria. However, such analyses do not incorporate perceptual criteria that determine visual quality, which are particularly important for binocular 3D systems. To address this limitation, we introduce the framework of a perceptual eyebox. The perceptual eyebox is the volume where the eye(s) must be located for the user to experience a visual percept falling within a perceptually-defined criterion. We combine optical and perceptual data to characterize an example perceptual eyebox for display visibility in augmented reality. The key contributions in this paper include: comparing the perceptual eyebox for monocular and binocular display designs, modeling the effects of user eye separation, and examining the effects of eye rotation on the eyebox volume.

Computational optical distortion correction using a radial basis function-based mapping method.

A distortion mapping and computational image unwarping method based on a network interpolation that uses radial basis functions is presented. The method is applied to correct distortion in an off-axis head-worn display (HWD) presenting up to 23% highly asymmetric distortion over a 27°x21° field of view. A 10(-5) mm absolute error of the mapping function over the field of view was achieved. The unwarping efficacy was assessed using the image-rendering feature of optical design software. Correlation coefficients between unwarped images seen through the HWD and the original images, as well as edge superimposition results, are presented. In an experiment, images are prewarped using radial basis functions for a recently built, off-axis HWD with a 20° diagonal field of view in a 4:3 ratio. Real-time video is generated by a custom application with 2 ms added latency and is demonstrated.

Optimal local shape description for rotationally non-symmetric optical surface design and analysis.

A local optical surface representation as a sum of basis functions is proposed and implemented. Specifically, we investigate the use of linear combination of Gaussians. The proposed approach is a local descriptor of shape and we show how such surfaces are optimized to represent rotationally non-symmetric surfaces as well as rotationally symmetric surfaces. As an optical design example, a single surface off-axis mirror with multiple fields is optimized, analyzed, and compared to existing shape descriptors. For the specific case of the single surface off-axis magnifier with a 3 mm pupil, >15 mm eye relief, 24 degree diagonal full field of view, we found the linear combination of Gaussians surface to yield an 18.5% gain in the average MTF across 17 field points compared to a Zernike polynomial up to and including 10th order. The sum of local basis representation is not limited to circular apertures.

Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry.

It has been found that the field dependence of the aberrations of misaligned optical systems made of otherwise rotationally symmetric optical surfaces are often multinodal, including low-order astigmatism and distortion and higher-order coma, astigmatism, oblique spherical, elliptical coma (trifoil), and distortion. The exact location of the nodes in the image is a weighted sum of individual surface contributions. The location of the center of rotational symmetry for the field dependence for all aberrations contributed by a particular rotationally symmetric surface is along the line that connects the center of curvature of the surface with the center of the pupil. Previously, a paraxial ray-trace method was developed to locate the aberration field center for a series of rotationally symmetric surfaces with small tilt and decenter perturbations. The method is based on rotating the coordinate system into the local coordinate system of the surface and then advancing using the conventional paraxial ray-trace equations. This method, developed by Buchroeder [Ph.D. dissertation (University of Arizona, 1976)], heavily constrains how tilts and decenters were implemented in the optical system model, which prevented integration of these equations into an optical design environment. In this paper, a method for locating the aberration field centers using real-ray-trace data that is entirely model independent and, significantly, that is not restricted to small tilts and decenters, is presented. With this new insight, it is now possible to extend any optical design and analysis environment to include multinodal aberration analysis.

Application of radial basis functions to shape description in a dual-element off-axis magnifier.

We previously demonstrated that radial basis functions may be preferred as a descriptor of free-form shape for a single mirror magnifier when compared to other conventional descriptions such as polynomials [Opt. Express 16, 1583 (2008)]. A key contribution is the application of radial basis functions to describe and optimize the shape of a free-form mirror in a dual-element magnifier with the specific goal of optimizing the pupil size given a 20 degrees field of view. We demonstrate a 12 mm exit pupil, 20 degrees diagonal full field of view, 15.5 mm eye clearance, 1.5 arc min resolution catadioptric dual-element magnifier design operating across the photopic visual regime. A second contribution is the explanation of why it is possible to approximate any optical mirror shape using radial basis functions.

Design and fabrication of a dual-element off-axis near-eye optical magnifier.

The key contribution is the design, analysis, and fabrication of a dual-element off-axis magnifier to improve the state of the art in catadioptric magnifiers. The catadioptric magnifier is composed of a free-form mirror and a lens with a diffractive optical element. A monocular magnifier was prototyped, to our knowledge for the first time, with the specifications of an 8 mm exit pupil, 20 degrees diagonal full field of view, 15 mm eye clearance, 1.5 arcmin resolution, and operating in the photopic visual regime.

Comparative analysis of doublets versus single-layer diffractive optical elements in eyepiece or magnifier design.

We quantify the impact of eye clearance requirement on the performance of eyepieces utilizing doublets versus diffractive optical elements on aspheric substrates. In this study, the doublets were designed to be cemented on-axis elements. Specifically, four different values of eye clearance were implemented: 17, 20, 23, and 26 mm. For each value, axial and lateral color, spherical aberration, coma, astigmatism, field curvature, and distortion were compared. Each system under comparison was optimized for the same focal length, a 9 mm exit pupil, photopic wavelengths (513-608 nm), and a 40 degrees full field of view. We demonstrate that the single-layer diffractive optical element supports an eye clearance value of approximately 80% of the effective focal length, while the doublet drops below desired specifications at approximately 65% of the effective focal length.