Wearality Sky Field of View

Transcription

1 Wearality Sky Field of View Wearality Technical Staff Introduction The Panorama Lens in Wearality Sky represents five years of research optimizing wide field of view (FOV) optics for head-mounted displays (HMDs) in visual simulation and training. This patented and patent pending approach uses a coordinated pair of spherical-section Fresnel lenses to wrap input images around each eye, creating an immersive, wide field of view output image with broad focus, low chromatic aberration, and high brightness. Its telecentric arrangement allows use of prescription eyewear and supports personal variation in interpupillary distance (IPD) without adjustment. The vision dome created by the Panorama Lens requires careful attention in measurement. Output field of view (light from the near lens that defines the eye s field of view) must not be confused with the input extent, which is the greatest physical area that can be seen through the lens system from the eyepoint. The input extent defines the useful display screen size rather than the angular field of view over which that screen is seen by the human eye. The 60mm lens in Wearality Sky outputs 130 horizontally for each eye using one half of a shared display, making it well-suited for mobile phone applications. The ultimate single-eye output FOV would be the full of the human visual system with an input extent closely matching a small display device screen. The larger 90mm Wearality Panorama Lens outputs this uniquely wide 180 field using a tangential display device at each lens. Marginal input rays at the bottom of Figures 1a and 1b show how the Panorama Lens closely approaches this ideal. This report details the output field of view of the Panorama Lens used in Wearality Sky by illustrating the physical geometry, reviewing key equations, systematically deriving view angles, and considering variations. The values presented here are consistent with optical bench analysis of production units. Panorama Lens Geometry The design eyepoint of the Panorama Lens system in Wearality Sky is 18mm from the center of the near lens. The outer 3mm, inner 2.8mm, upper 2.9mm and, lower 3.2mm are unused due to lens frame shadowing, with the remaining 55.6mm 50.1mm area forming the output image viewing geometry as shown in Figure 1. 1

2 2 (a) Horizontal (b) Vertical Figure 1: Cross sections through the Wearality Sky Panorama Lenses Single Lens Field of View Single-eye partial view angles are readily determined from the measured dimensions using the right triangle identity, θ = tan 1 (r/x), as shown in Figure 2. Resulting primary view angles are shown in Figure 4. Inward horizontal field of view with r I = 21.2 mm and x I = 14.8 mm: θ I = arctan r I x I = arctan Outward horizontal field of view with r O = 34.4 mm and x O = 9.0 mm: θ O = arctan r O x O = arctan Upward vertical field of view with r U = 26.5 mm and x U = 12.9 mm: θ U = arctan r U x U = arctan Downward vertical field of view with r D = 23.6 mm and x D = 14.0 mm: θ D = arctan r D x D = arctan Single-eye total view angles combine the corresponding partial vew angles: Single-eye horizontal field of view spans inward and outward angles: θ H = θ I + θ O Single-eye vertical field of view spans upward and downward angles: θ V = θ U + θ D

3 3 Figure 2: Radial view angle Figure 3: Diagonal angle θ Figure 4: Single eye principal angles Figure 5: Single eye diagonal angle Diagonal field of view is the great circle angle between points at the corners of the visible range. This angle is defined by the spherical law of cosines, which expresses the great circle distance θ between Point 1 (ϕ1, λ1 ) and Point 2 (ϕ2, λ2 ) in terms of their latitude and longitude, as shown in Figure 3. θ = arccos (sin ϕ1 sin ϕ2 + cos ϕ1 cos ϕ2 cos λ1 λ2 ) The single-eye diagonal view angle is the arc from ( θd, θi ) to (θu, θo ), or for the less fortunate, from (θu, θi ) to ( θd, θo ) as highlighted in white in Figure 5. θ = arccos (sin θd sin θu + cos θd cos θu cos θi θo ) = arccos (sin θu sin θd + cos θu cos θd cos θi θo ) = arccos ( sinθu sin θd + cos θu cos θd cos θi θo )

4 4 Dual Lens Field of View With both eyes looking straight ahead to infinity, the total horizontal FOV is understood as the sum of the outer angles; left of the left eye and right of the right eye as detailed in Figures 6 and 7, with the corresponding diagonal field of view shown as the white sector in Figure 8. Total horizontal field of view spans left and right outward angles: θh = θo + θo Total vertical field of view spans upward and downward angles: θv = θu + θd Total diagonal field of view is the arc from ( θd, θo ) to (θu, θo ): θ = arccos (sin θd sin θu + cos θd cos θu cos θo θo ) Figure 6: Dual eye total horizontal angle Figure 7: Dual eye principal angles Figure 8: Dual eye diagonal angle

5 5 Variation The output field of view of Wearality Sky is influenced by human factors including interpupillary distance, eye rotation, and distance from eye to lens. As shown in Figure 9, nearer is wider and farther is narrower, though diagonal FOV remains greater than 150 out to an eyepoint offset of mm. Perceived FOV may also be limited by input-side factors of image size and formation. Figure 9: Total diagonal, horizontal, and Vertical FOV by offset (in mm) from design eyepoint Summary Wearality Sky single-eye partial output field of view exceeds: 75.3 outward and 55.0 inward horizontally 64.0 upward and 59.3 downward vertically Wearality Sky single-eye total output field of view exceeds: horizontally vertically diagonally Wearality Sky dual-eye total output field of view exceeds: horizontally vertically diagonally

6 6 Conclusion Wearality s unique Panorama Lens is a notable advance in the design and manufacture of optical systems for immersive applications. Figure 10 is a frame from time 4:44 in a customer video showing that the wide field of view optics of Wearality Sky significantly exceed the focus, chromatic aberration, and field of view qualities of well-known, expensive products of classical design. Figure 10: Customer comparison of common HMD lens (bottom) and Wearality Sky lens (top)