Aspheric lens
An aspheric lens (also called an asphere) is a lens whose surface profile is not a portion of a sphere or a cylinder. The departure from a spherical shape lets a single element bring rays from across its aperture to a common focus, which reduces spherical aberration and several other optical aberrations that a simple spherical lens cannot correct on its own.[1][2] Because one asphere can do the aberration correction that would otherwise need three or four spherical elements, aspheric designs make optical systems shorter, lighter, and more efficient.[3]
In virtual reality (VR) and augmented reality (AR) headsets the aspheric lens is one of the main eyepiece design approaches used to magnify a microdisplay and place its image at a comfortable focus for the eye. It competes with the Fresnel lens and the pancake lens, each of which trades image quality against thickness, weight, and cost in a different way.[4]
How it works
A spherical surface is easy to grind and polish but is not the ideal shape for forming an image. Rays that pass through the outer part of a spherical lens are refracted more strongly than rays near the axis, so they cross the optical axis closer to the lens than the paraxial rays do. The result is spherical aberration, a blurring that grows with aperture. The underlying reason is that the law of refraction depends on the sine of the angle of incidence rather than the tangent, so a constant curvature cannot focus all rays to one point.[1]
An aspheric surface varies its local curvature from the center to the edge so that every ray, regardless of its distance from the axis, is bent toward the same focal point. With single spherical elements, spherical aberration rather than the diffraction limit sets the smallest achievable spot, whereas a single asphere can collimate or focus a monochromatic beam close to the diffraction limit.[3] Because the aberration is corrected by surface shape rather than by adding glass, the designer can hold high optical performance with fewer lenses.[1][3]
Most aspheres are rotationally symmetric. Their surface sag z(r), the displacement along the axis at radius r from the axis, is usually written as a conic term plus a polynomial:
z(r) = r^2 / ( R ( 1 + sqrt( 1 - (1 + k) r^2 / R^2 ) ) ) + a4 r^4 + a6 r^6 + ...
where R is the base radius of curvature, k is the conic constant, and the a-coefficients describe higher-order deformation. The conic constant selects the base shape: k = 0 gives a sphere, k = -1 a parabola, k < -1 a hyperbola, and intermediate negative values give ellipsoids.[2]
History
The idea of correcting aberration with a non-spherical surface is old. The 10th-century Persian mathematician Ibn Sahl analyzed surfaces that focus light with minimal aberration, and in the 1620s to 1670s René Descartes and Christiaan Huygens worked on aspheric designs, including the curve Descartes called the Cartesian oval. Francis Smethwick ground the first high-quality aspheric lenses and presented them to the Royal Society on 27 February 1668.[2]
Practical use grew with manufacturing. Moritz von Rohr designed the first aspheric eyeglass lenses for Zeiss (the Punktal line) in the early 1900s, and the first commercial mass-produced aspheric camera element was made by Elgeet in 1956 for the Golden Navitar 12 mm f/1.2 lens. Improved fabrication has since made aspheres common in cameras, optical disc pickups, eyeglasses, and laser collimation.[2]
Manufacturing
Small glass and plastic aspheres can be molded, which allows cheap mass production for consumer products. Larger or higher-precision aspheres are made by grinding and polishing, or by single-point diamond turning, in which a computer-controlled lathe with a diamond tip cuts the profile directly. Final figuring can use ion-beam finishing, abrasive water jets, or magnetorheological finishing, and composite aspheres can be made by depositing a shaped layer of optical resin onto a spherical glass blank.[2] Plastic aspheres molded from acrylic are about half as dense as N-BK7 glass, which makes them useful where weight matters.[5]
Use in VR and AR
Early consumer VR headsets used aspheric lenses. The Oculus Rift DK1 (2013) and DK2 (2014) development kits used standard aspheric lenses, with a single element per eye magnifying the panel.[6] For the consumer Rift (CV1) in 2016 Oculus switched to a custom hybrid Fresnel lens design because the aspheric eyepieces had a small region of sharpness, with the DK2 image sharp only near the center, while the Fresnel design gave a much wider sweet spot and avoided some of the aspheric design's uncorrectable chromatic aberration. The Fresnel approach also kept the lens thin and light enough for a comfortable headset, at the cost of god rays, the streaks of stray light produced by reflections off the concentric Fresnel rings.[6][4]
The same trade-offs explain why Fresnel optics became the standard for a generation of headsets: an aspheric eyepiece with a large eye box needs a relatively large, thick glass element, which adds weight and bulk, and precision manufacturing makes it costly. Fresnel lenses collapse most of that thickness while keeping cost low, which suited mass-market headsets despite their god rays.[7][4]
Aspheric optics did not disappear, and some headsets use more than one element to widen the corrected region. The Valve Index (2019) fused two lenses into a single dual-element package per eye, which Valve said improved clarity and reduced distortion across the lens; the trade-off was added weight and cost, and reviewers noted glare from the design.[8]
In the high-end PC VR market aspheric optics returned in glass form. Pimax describes the Pimax Crystal (2023) as the first VR headset with glass aspheric lenses, with the name Crystal referring to the glass optics, paired with a 2880 by 2880 pixel panel per eye.[9] Its successor, the Pimax Crystal Super, uses a swappable optical engine built around redesigned aspheric glass lenses, offered in versions that trade field of view against angular resolution, for example a 50 pixels-per-degree engine at roughly 126 degrees horizontal field of view and a 57 pixels-per-degree engine at a narrower field of view.[9][10]
By the mid-2020s many compact consumer headsets had moved instead to pancake lenses, which fold the light path between thin reflective surfaces for a much shorter eyepiece. Pancake optics are thin and largely free of the ring artifacts of Fresnel lenses, but they lose a large fraction of the light through their multiple internal reflections. Aspheric (especially glass aspheric) eyepieces remain the choice where image clarity and light throughput are valued over thinness, such as in simulation-focused PC VR headsets, while their weight, size, and cost keep them out of the slimmest consumer designs.[4][7]
See also
References
- ↑ 1.0 1.1 1.2 "Spherical Aberrations". https://www.rp-photonics.com/spherical_aberrations.html.
- ↑ 2.0 2.1 2.2 2.3 2.4 "Aspheric lens". https://en.wikipedia.org/wiki/Aspheric_lens.
- ↑ 3.0 3.1 3.2 "Molded Glass Aspheric Lenses: Uncoated". https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3809.
- ↑ 4.0 4.1 4.2 4.3 "VR Headset Lens Comparative Analysis: Aspheric vs Pancake vs Fresnel". https://pimax.com/blogs/blogs/aspheric-vs-pancake-vr-lenses-and-why-glass.
- ↑ "Molded Plastic Aspheric Lenses, Uncoated". https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=16.
- ↑ 6.0 6.1 Template:Cite news
- ↑ 7.0 7.1 "Lenses in VR glasses: Between sharpness, weight and optical side effects". https://www.heise.de/en/background/Lenses-in-VR-glasses-Between-sharpness-weight-and-optical-side-effects-10503349.html.
- ↑ Template:Cite news
- ↑ 9.0 9.1 "Pimax Crystal - VR headset with glass aspheric lenses". https://www.ces.tech/ces-innovation-awards/2024/pimax-crystal-vr-headset-with-glass-aspheric-lenses/.
- ↑ "First Look at Pimax Crystal Super's New 57 PPD Optical Engine". https://pimax.com/blogs/blogs/first-look-at-pimax-crystal-super-s-new-57-ppd-optical-engine.