Spherical aberration

Spherical aberration is an optical aberration in which rays that pass through a lens or mirror at different distances from the optical axis come to a focus at different points. Most lenses have spherical surfaces because those are the easiest to fabricate with high optical quality, but a spherical surface is not the ideal shape for imaging: its outer parts are too strongly curved, so rays entering near the edge cross the axis sooner than rays near the center. Instead of a sharp point, the image of a point source becomes a blur. The effect does not depend on wavelength, which makes it a monochromatic aberration, unlike chromatic aberration.

In virtual reality (VR) and augmented reality (AR), spherical aberration matters in two places. The magnifying eyepieces of a head-mounted display must control it to keep the virtual image sharp, and the optics of the human eye have their own spherical aberration, which changes with age and with accommodation. Vision researchers have also tested deliberately added spherical aberration as a way to extend depth of focus and ease the vergence-accommodation conflict in headsets.

Reviewed 11 October 2026. Checked every claim against the cited RP Photonics, LaValle, Wyant, NASA, Road to VR, BOE and Sunny Optics patent sources and the abstracts or full texts and metadata of all 14 cited papers. About review dates.

Definition and cause

For a point on the optical axis, rays that make an appreciable angle with the axis intersect it in front of or behind the paraxial focus. The point where rays from the edge of the aperture (the marginal rays) cross the axis is called the marginal focus; the point where rays from near the center of the aperture (the paraxial rays) cross it is the paraxial or Gaussian focus. Because the field position does not enter the expression for this aberration, its effect is constant over the field of the system.

RP Photonics illustrates the effect with a ball lens 10 mm in diameter made of N-BK7 glass (refractive index 1.515 at 633 nm): when it focuses parallel light, the outer rays cross the optical axis substantially sooner than the paraxial ones. The encyclopedia gives the underlying reason as the form of the law of refraction, which contains the sine of the angle rather than the tangent that would be needed to avoid spherical aberration. For the same reason, a flat plane-parallel plate such as a window also introduces spherical aberration when convergent or divergent light passes through it.

In his textbook on VR, Steven M. LaValle describes the result as incoming parallel rays focused at varying depths rather than at a single point, which produces blur that cannot be compensated for by moving the object, the lens or the image plane. Moving the observation plane does change the size of the blur. The smallest blur, the circle of least confusion, lies three-quarters of the way from the paraxial focus to the marginal focus, and its radius is one-quarter of the radius of the blur at the paraxial focus.

Description and measurement

Spherical aberration is one of the five third-order aberrations called Seidel aberrations after L. Seidel; the others are coma, astigmatism, field curvature and distortion. In wavefront terms, third-order spherical aberration grows with the fourth power of the normalized pupil radius, and James C. Wyant's course notes write it with the coefficient W₀₄₀. In the Zernike polynomial description used in vision science, primary and secondary spherical aberration are the fourth-order and sixth-order spherical terms.

The strength of the aberration is often quantified by plotting the longitudinal shift of the focus against the height at which a ray enters the lens. That shift may scale with the square of the ray height, although partly corrected systems can be well compensated at one height and less so at others. The aberration also depends on aperture: LaValle notes that the larger the aperture, the more the aberrations interfere with imaging, and the eye controls light in a similar way through its pupil.

Correction

The main ways to reduce spherical aberration are:

Method	How it works	Trade-off or note
Aperture stop	Blocks the outer zone of the lens, where the aberration is strongest	Less light passes through the system
Aspheric surface	A non-spherical profile designed so that rays from all heights meet at one focus	Other aberrations can remain
Combinations of spherical lenses	Elements whose spherical aberrations compensate each other, as in photographic objectives	Requires several elements
Lens shape and orientation	A thin lens can be bent for minimum spherical aberration; a plano-convex lens focusing a collimated beam should face the beam with its curved side, so both surfaces share the refraction	Simple, but only reduces the aberration
Conic surfaces at their foci	A conic used at its proper conjugates produces no spherical aberration; a paraboloidal mirror with one conjugate at infinity is free of it, while a spherical mirror used the same way is not	Works only for the design conjugates

RP Photonics notes that better fabrication methods for aspheric optics have increased their use and allow high-performance objectives with fewer lenses, which can also improve light throughput.

History

Seidel published explicit formulae for the third-order aberrations, spherical aberration among them, in 1856.

Spherical aberration was the flaw found in the Hubble Space Telescope. On 27 June 1990, two months after launch, NASA announced that the telescope was flawed: both of its imaging cameras, the Wide Field and Planetary Camera and the Faint Object Camera, showed spherical aberration. An investigation board found that the primary mirror was too flat near its outer edge, by an error 10 times larger than the specified tolerance. The cause was a spacing error of 1.3 mm in the null corrector used to test the mirror's shape during polishing. Light striking the outer edge came to different focal points than light from the rest of the mirror, which blurred the images. During the first servicing mission in December 1993, astronauts installed the COSTAR instrument and the Wide Field and Planetary Camera 2, which NASA had redesigned to include internal optics that brought the telescope's blurred data into focus.

In the human eye

The eye's optics have spherical aberration of their own. In a study of 200 eyes of 100 people, Thibos and colleagues found that the population averages of the Zernike coefficients were nearly zero for every higher-order mode except spherical aberration. The retinal image depends on the balance between the cornea and the internal optics. Artal and colleagues reported in 2001 that the anterior cornea and the internal optics each have more aberration than the complete eye, so they partly compensate for each other. Smith and colleagues estimated the spherical aberration of the crystalline lens in 26 subjects and found it to be negative in the relaxed lens. In 30 young subjects, Kelly, Mihashi and Howland found strong evidence that the internal optics compensate the cornea's spherical aberration, but the compensation was not scaled to each individual, which they read as a passive result of genetically determined physiology.

This balance changes with age. Measuring subjects aged 20 to 70, Artal, Berrio, Guirao and Piers found that the spherical aberration of the cornea was larger than that of the whole eye in younger subjects and smaller in older ones, and that the internal compensation present in most younger eyes was absent in older eyes. In a multinational sample of normal eyes, Kingston and Cox found that spherical aberration became more positive with increasing age and with a steeper (more powerful) anterior corneal surface, but did not correlate with the degree of refractive error. Spherical aberration also shifts during accommodation: calculations and wavefront measurements by López-Gil and Fernández-Sánchez indicate that primary spherical aberration decreases as the eye focuses closer while secondary spherical aberration increases, which affects the measured accommodation response.

Ophthalmic lens design uses these findings. Holladay and colleagues designed an intraocular lens with a prolate anterior surface and a fixed amount of negative spherical aberration to partly compensate for the average positive spherical aberration of the cornea in cataract patients.

Applications in VR and AR

Headset eyepieces

A basic VR headset places a convex lens between the eye and a nearby display so that the screen appears as a large, distant virtual image. LaValle points out that the optical aberrations of such lenses grow with distance from the optical axis. When a user rotates the eyes to look directly through the edge of the lens, spherical aberration can show up as a lack of focus in the periphery, along with visible chromatic aberration and errors in distortion correction. He adds that these edge problems cannot be fixed by a single correction function, because the pupil moves away from the optical axis as the eye rotates; a different, asymmetric correction would be needed for each eye orientation, which would require eye tracking.

Single-element eyepieces are especially limited. A BOE Technology Group patent on optimizing VR lenses describes an earlier single-lens VR design that uses a Fresnel lens mainly to correct field curvature and coma, and states that in that design spherical aberration cannot be completely corrected and becomes an important factor affecting imaging quality. The patented method treats spherical aberration and coma, along with field curvature, astigmatism, distortion and dispersion, as optimization targets when computing lens surface shapes, radii and thickness. A thin VR eyepiece patented by Zhejiang Sunny Optics combines a Fresnel surface on the eye side of a lens with an aspheric surface on the other side, and the patent states that the design can correct the spherical aberration of the optical system while meeting the size and weight needs of a VR eyepiece.

Research designs for folded pancake optics also use aspheric surfaces. Wei-Jei Peng and Tsung-Xian Lee described a two-element aspheric pancake design with a 106 degree field of view, to which they added a diffractive element to reduce lateral color. A 2024 Applied Optics design by Ching-Shun Yang and Jui-Wen Pan pairs a holographic optical element with pancake optics built around a coated 50/50 aspherical lens. See Aspheric lens for how aspheric eyepieces have been used in commercial headsets.

Spherical aberration also appears in hands-on evaluations of new lenses. In a 2017 look at a prototype thin Fresnel lens from Wearality, Road to VR wrote that, considering chromatic aberration, spherical aberration and other effects, the image did not seem worse than through the company's earlier Wearality Sky lens, although clarity still felt somewhat lacking.

Metasurface eyepieces

Flat metalenses are being studied as thinner alternatives to refractive eyepieces. In a 2018 Nature Communications paper, Gun-Yeal Lee and colleagues demonstrated a wide field of view near-eye AR display using a nanoimprinted see-through metalens; they wrote that because the metalens has lower spherical aberration than a conventional lens, the image is not much distorted near the edge despite the wide field of view. A 2025 paper by Anna Wirth-Singh, Arka Majumdar and colleagues notes that meta-optic doublets had been used to correct monochromatic aberrations such as spherical aberration, coma and astigmatism since 2016, but with entrance apertures under 1 mm; their own meta-optic doublet eyepiece reached a field of view greater than 60 degrees with a 2.1 cm entrance aperture at a design wavelength of 633 nm.

Extended depth of focus and the vergence-accommodation conflict

Because spherical aberration spreads focus along the axis, adding it can extend the eye's depth of focus. Adaptive optics studies have tested this as a way to weaken the fixed focus cue of a headset screen.

At the University of Rochester, Lyu, Yoon and colleagues used a binocular adaptive optics vision simulator to induce combined fourth- and sixth-order Zernike spherical aberration in nine subjects aged 21 to 34. At 3 diopters of convergence, the extended depth of focus condition was the most effective of the three tested conditions (aberration-free, monovision and extended depth of focus) at inducing accommodation. Visual acuity was worse with extended depth of focus, and stereo thresholds were worse than in the aberration-free condition but better than with monovision. The authors concluded that, despite some loss in visual performance, extending depth of focus could allow a more natural vergence-accommodation relationship in VR.

In a 2026 study at the University of Murcia, Sager, Prieto and Artal used a binocular simulator with motorized vergence control to test ten subjects with added spherical aberration of 0, -0.24 and -0.43 micrometers (4.5 mm pupil) at vergence-accommodation conflicts of -1.5, 0 and +1.5 diopters around a screen at 1.5 diopters. Added spherical aberration did not substantially improve stereo acuity, and it reduced discomfort for the negative conflict but increased it for the positive and zero-conflict conditions, so the authors' hypothesis that it would reduce the effects of the conflict was not supported. They suggested that an intermediate amount might even out discomfort across conflict conditions, and that such optics could be built into extended reality devices or worn as contact lenses, while calling for more research.

See also

• Optical aberration
• Chromatic aberration
• Astigmatism
• Lens distortion
• Aspheric lens
• Fresnel lens
• Pancake lenses
• Metalens
• Optics
• Vergence-accommodation conflict