Meshfree Approximation Methods For Free-form Optical Surfaces With Applications To Head-worn Displays

Compact and lightweight optical designs achieving acceptable image quality, field of view, eye clearance, eyebox size, operating across the visible spectrum, are the key to the success of next generation head-worn displays. The first part of this thesis reports on the design, fabrication, and analysis of off-axis magnifier designs. The first design is catadioptric and consists of two elements. The lens utilizes a diffractive optical element and the mirror has a free-form surface described with an x-y polynomial. A comparison of color correction between doublets and single layer diffractive optical elements in an eyepiece as a function of eye clearance is provided to justify the use of a diffractive optical element. The dual-element design has an 8 mm diameter eyebox, 15 mm eye clearance, 20 degree diagonal full field, and is designed to operate across the visible spectrum between 450-650 nm. 20% MTF at the Nyquist frequency with less than 3% distortion has been achieved in the dual-element head-worn display. An ideal solution for a head-worn display would be a single free-form surface mirror design. A single surface mirror does not have dispersion; therefore, color correction is not required. A single surface mirror can be made see-through by machining the appropriate surface shape on the opposite side to form a zero power shell. The second design consists of a single off-axis free-form mirror described with an x-y polynomial, which achieves a 3 mm diameter exit pupil, 15 mm eye relief, and a 24 degree diagonal full field of view. The second design achieves 10% MTF at the Nyquist frequency set by the pixel spacing of the VGA microdisplay with less than 3% distortion. Both designs have been fabricated using diamond turning techniques. Finally, this thesis addresses the question of what is the optimal surface shape for a single mirror constrained in an off-axis magnifier configuration with multiple fields? Typical optical surfaces implemented in raytrace codes today are functions mapping two dimensional vectors to real numbers. The majority of optical designs to-date have relied on conic sections and polynomials as the functions of choice. The choice of conic sections is justified since conic sections are stigmatic surfaces under certain imaging geometries. The choice of polynomials from the point of view of surface description can be challenged. A polynomial surface description may link a designer s understanding of the wavefront aberrations and the surface description. The limitations of using multivariate polynomials are described by a theorem due to Mairhuber and Curtis from approximation theory. This thesis proposes and applies radial basis functions to represent free-form optical surfaces as an alternative to multivariate polynomials. We compare the polynomial descriptions to radial basis functions using the MTF criteria. The benefits of using radial basis functions for surface description are summarized in the context of specific head-worn displays. The benefits include, for example, the performance increase measured by the MTF, or the ability to increase the field of view or pupil size. Even though Zernike polynomials are a complete and orthogonal set of basis over the unit circle and they can be orthogonalized for rectangular or hexagonal pupils using Gram-Schmidt, taking practical considerations into account, such as optimization time and the maximum number of variables available in current raytrace codes, for the specific case of the single off-axis magnifier with a 3 mm pupil, 15 mm eye relief, 24 degree diagonal full field of view, we found the Gaussian radial basis functions to yield a 20% gain in the average MTF at 17 field points compared to a Zernike (using 66 terms) and an x-y polynomial up to and including 10th order. The linear combination of radial basis function representation is not limited to circular apertures. Visualization tools such as field map plots provided by nodal aberration theory have been applied during the analysis of the off-axis systems discussed in this thesis. Full-field displays are used to establish node locations within the field of view for the dual-element head-worn display. The judicious separation of the nodes along the x-direction in the field of view results in well-behaved MTF plots. This is in contrast to an expectation of achieving better performance through restoring symmetry via collapsing the nodes to yield field-quadratic astigmatism

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, \u3e 15mm 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

Imaging System for Eyeglass-Based Display Devices

Disclosed are imaging systems and eyeglass-based display devices. In one embodiment, an imaging system includes an image source and a partial mirror that defines a non-rotationally symmetric surface, wherein the partial mirror reflects images generated by the image source to an eye of an observer

Interaction Methods for Smart Glasses : A Survey

Since the launch of Google Glass in 2014, smart glasses have mainly been designed to support micro-interactions. The ultimate goal for them to become an augmented reality interface has not yet been attained due to an encumbrance of controls. Augmented reality involves superimposing interactive computer graphics images onto physical objects in the real world. This survey reviews current research issues in the area of human-computer interaction for smart glasses. The survey first studies the smart glasses available in the market and afterwards investigates the interaction methods proposed in the wide body of literature. The interaction methods can be classified into hand-held, touch, and touchless input. This paper mainly focuses on the touch and touchless input. Touch input can be further divided into on-device and on-body, while touchless input can be classified into hands-free and freehand. Next, we summarize the existing research efforts and trends, in which touch and touchless input are evaluated by a total of eight interaction goals. Finally, we discuss several key design challenges and the possibility of multi-modal input for smart glasses.Peer reviewe

Recent Advances in Cockpit Aids for Military Operations

The object of this paper is to review same rccent developmentsin cockpit displays and to suggest thc way irhead in arcas of newtcchnology. There is steady progress in most types of display technology butperhaps the most interesting topic is that of flat panels wheri new display media are promised to compete with the CRT. Thc paper alsocovers aspects of Head Up, Head Down and tlelmet Mounted Displays

Double surface imaging designs with unconstrained object to image mapping under rotational symmetry

In this work, we present a novel imaging design formed by two optical surfaces with rotational symmetry. In these designs, both object and image shapes are given but mapping from object to image is obtained through the design process. In the examples considered, the image from a planar object surface is virtual and located at infinity and is seen from a known pupil, which can emulate a human eye. The differential equation method is used to provide single optical surface imaging designs by considering the local properties of the imaging surface and the wavefronts. In the first introductory part, both the rotational symmetrical and the freeform single surface imaging designs are presented using the differential equation method. In these designs, not only the mapping is obtained in the design process, but also the shape of the object is found. In the second part, the method is extended to two surface designs with rotational symmetry and the astigmatism of the image has been studied. By adding one more optical surface to the system, the shape of the rotational symmetrical object can be designed while controlling the tangential rays and sagittal rays simultaneously. As a result, designs without astigmatism (at the small pupil limit) on a planar object surface have been obtained. © (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only

Head Mounted Display with a Roof Mirror Array Fold

The present invention includes a head mounted display (HMD) worn by a user. The HMD includes a display projecting an image through an optical lens. The HMD also includes a one-dimensional retro reflective array receiving the image through the optical lens at a first angle with respect to the display and deflecting the image at a second angle different than the first angle with respect to the display. The one-dimensional retro reflective array reflects the image in order to project the image onto an eye of the user