Wearality® Sky™ Field of View
Wearality Technical Staff
[email protected]
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
180°–190° 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
(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 rI = 21.2 mm and xI = 14.8 mm:
θI = arctan
rI
21.2
= arctan
≈ 55.0806°
xI
14.8
• Outward horizontal field of view with rO = 34.4 mm and xO = 9.0 mm:
θO = arctan
rO
34.4
= arctan
≈ 75.3385°
xO
9.0
• Upward vertical field of view with rU = 26.5 mm and xU = 12.9 mm:
θU = arctan
rU
26.5
= arctan
≈ 64.0435°
xU
12.9
• Downward vertical field of view with rD = 23.6 mm and xD = 14.0 mm:
θD = arctan
rD
23.6
= arctan
≈ 59.3227°
xD
14.0
Single-eye total view angles combine the corresponding partial vew angles:
• Single-eye horizontal field of view spans inward and outward angles:
θH = θI + θO ≈ 130.4191°
• Single-eye vertical field of view spans upward and downward angles:
θV = θU + θD ≈ 123.3663°
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 |)
≈ 156.6479°
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 ≈ 150.6769°
• Total vertical field of view spans upward and downward angles:
θV = θU + θD ≈ 123.3663°
• 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 |)
≈ 165.4652°
Figure 6: Dual eye total horizontal angle
Figure 7: Dual eye principal angles
Figure 8: Dual eye diagonal angle
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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 6.4891mm. 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:
• 130.3° horizontally
• 123.3° vertically
• 156.6° diagonally
Wearality Sky dual-eye total output field of view exceeds:
• 150.6° horizontally
• 123.3° vertically
• 165.4° diagonally
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)