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Astigmatism

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Astigmatism is an optical defect in which a lens or optical system does not bring light from a point to a single focus, but instead focuses it at two separate lines at right angles to each other. The term has two related uses. In eye care it names a common refractive error of the eye, caused when the cornea or crystalline lens has a different curvature, and so a different optical power, along different meridians.[1][2] In optical design it names one of the five third-order (Seidel) aberrations, which affects the image of points away from the optical axis.[3]

Both meanings matter for virtual reality (VR) and augmented reality (AR) hardware. A 2018 meta-analysis estimated that 40.4% of adults and 14.9% of children have astigmatism of more than 0.5 diopters, which makes it the most common refractive error in both groups.[4] Focus dials such as those on HTC's VIVE headsets correct nearsightedness but not astigmatism, so makers point astigmatic users to glasses or prescription lens inserts made with a cylinder correction.[5] As a lens aberration, astigmatism also affects the eyepieces and off-axis optics of near-eye displays, and several research displays correct the viewer's own astigmatism in software or with tunable optics.[6]

Reviewed 11 October 2026. Optics, prevalence, history (Young 1801, Airy 1827 and 1846 scans), device prescription statements and research-paper details checked against the cited sources. About review dates.

Astigmatism of the eye

Optics of the eye

In an astigmatic eye, parallel rays of light focus at two focal lines perpendicular to one another instead of at a single focal point, and vision is blurred. Kearney, Shah and Vlasak, in a 2025 review in Ophthalmic and Physiological Optics, state that it can result from variations in the curvature or refractive index of the eye's optical components, and that the most common cause is a difference in corneal curvature along the two principal meridians.[1] The American Academy of Ophthalmology (AAO) describes it as "an imperfection in the normal curvature of your eye's cornea or lens"; the risk is inherited, and astigmatism can also follow eye disease, injury or surgery.[2] The US National Eye Institute says astigmatism can make vision blurry or distorted, lists blurry vision, squinting, headaches, eye strain and trouble seeing at night as the most common symptoms, and states that doctors do not know what causes it.[7]

A regular astigmatic eye is often modeled as a toric (sphero-cylindrical) surface. In their 2010 NETRA paper, Vitor Pamplona and colleagues from the MIT Media Lab and the Federal University of Rio Grande do Sul give its refractive power along a meridian with direction θ as P(θ) = S + C sin2(α - θ), where S is the spherical power, C the cylindrical power and α the angle of the cylinder axis. The power is therefore lowest along one meridian and highest along the meridian at right angles to it.[8]

Astigmatism is classified by the orientation of these meridians. It is "with the rule" when the steeper axis is close to vertical, "against the rule" when it is close to horizontal, and oblique when the axes lie between 30 and 60 degrees or between 120 and 150 degrees. According to the 2025 review, astigmatism is common in infancy and declines in early childhood, stays stable through adolescence and early adulthood, and then increases with age; it is generally with the rule when young and becomes increasingly against the rule later in life. Astigmatism can arise from the corneal surface, mainly its front surface, or from the crystalline lens; in children, corneal astigmatism is the largest contributor to the total.[1]

Prevalence

The 2018 meta-analysis by Hassan Hashemi and colleagues pooled population studies published between 1990 and 2016. The 135 astigmatism studies used different cut points, most commonly a cylinder power of 0.5 diopters or more, or of more than 0.5 diopters; the meta-analysis used the most common cut point, more than 0.5 D, which applied to 82 of the 135 articles. On that basis they estimated a pooled prevalence of 14.9% in children (48 studies, 152,570 participants) and 40.4% in adults (34 studies, 122,436 participants). The estimates varied widely by World Health Organization region, from 9.8% (South-East Asia) to 27.2% (the Americas) in children and from 11.4% (Africa) to 45.6% (the Americas) in adults.[4] A 2023 paper on prescription-aware rendering for VR cites a figure of at least 33% for astigmatism among potential VR users.[9]

Prescription and correction

On a spectacle prescription, the cylinder (CYL) value gives the amount of astigmatism in diopters, and the axis, "written in degrees between 1 and 180," gives its orientation.[10] The National Eye Institute names glasses and contact lenses as the most common treatments, with surgery as another option.[7] The AAO lists toric soft contact lenses, rigid gas permeable lenses (which may suit more severe or irregular astigmatism) and refractive surgery such as LASIK, which reshapes the cornea.[2]

Astigmatism as a lens aberration

In lens design, astigmatism is one of the five Seidel aberrations, together with spherical aberration, coma, field curvature and distortion. Wyant and Creath's 1992 treatment of wavefront aberration theory describes it in terms of two planes through an off-axis object point: the tangential (meridional) plane, which contains the object point and the optical axis, and the sagittal plane, which contains the chief ray and is perpendicular to the tangential plane. For astigmatism there is no wavefront aberration in the sagittal plane, while the tangential section has an extra curvature that grows with the square of the field angle. The rays from the point therefore pass through two orthogonal line images, one in each plane, and between them the wavefront can be refocused to give a circle of least confusion. In the image of a spoked wheel, the rim is sharp at the tangential focus and the spokes are sharp at the sagittal focus.[3]

Because astigmatism and field curvature both depend on the square of the field height, they are often grouped together. Without astigmatism, the tangential and sagittal image surfaces coincide on the curved Petzval surface; with primary astigmatism both lie on the same side of it, the tangential surface three times as far from it as the sagittal surface.[3] The same term is applied to manufacturing errors: a surface that is slightly cylindrical instead of spherical gives a wavefront with different curvatures in two orthogonal directions, which is called astigmatic even though the error does not depend on field angle. In the Zernike polynomial ordering used in that chapter (the authors note that the ordering is not universal), terms 4 and 5 represent astigmatism at 0 and 45 degrees combined with focus.[3]

History

Thomas Young described astigmatism in his own eye in "On the Mechanism of the Eye", the Bakerian Lecture he read to the Royal Society on 27 November 1800 and published in the Philosophical Transactions in 1801. He reported that his relaxed eye focused rays diverging vertically from an object 10 inches away, but rays diverging horizontally from an object at 7 inches. He could see a small bright point as a point only by holding a concave lens tilted at a suitable angle, and he wrote that he had been told that many people held a concave glass obliquely in order to see distinctly. Young concluded that the difference was not in the cornea, because it remained when the effect of the cornea was removed, and attributed it to the oblique position of the crystalline lens.[11]

The astronomer George Biddell Airy designed a correcting lens for astigmatism in his own left eye. In a paper read to the Cambridge Philosophical Society on 21 February 1825 and printed in its Transactions in 1827, he described how a bright point appeared elliptical to his left eye and turned into a line at certain distances, showing that the eye refracted more strongly in a nearly vertical plane than in the plane at right angles. Since lenses with spherical surfaces could not correct this, he worked out a lens with one concave cylindrical surface and one concave spherical surface, and obtained one "from an artist named Fuller, of Ipswich", after which he could read the smallest print with that eye.[12] In a follow-up paper read on 25 May 1846, Airy wrote that the term "astigmatism" had been "very happily affixed" to the phenomenon by "the present Master of Trinity College"; the same volume of the Transactions lists William Whewell as Master of Trinity. Airy also gave the reciprocal difference of the two focal distances he had measured in 1825 (3.5 and 6.0 inches) as "a proper measure of the astigmatism", and reported that while his overall shortsightedness had changed, the amount of astigmatism had remained nearly the same.[13]

In VR and AR

Headsets and display glasses

Some head-mounted displays and display glasses include per-eye focus dials for nearsighted users. HTC's guidance for its VIVE headsets states that IPD and diopter adjustments "help with pupil alignment (IPD) and nearsightedness (diopter dials) but do not correct astigmatism", and that users with astigmatism or complex prescriptions may not benefit from the dials of the HTC Vive Flow. The HTC Vive XR Elite dials adjust up to about -6.0 diopters per eye.[5]

Makers of display glasses send astigmatic users to clip-on prescription frames. Viture states that its Luma glasses compensate myopia up to -6.0D and the Luma Pro and Luma Ultra up to -4.0D, and sells a magnetic prescription lens frame for Luma series glasses, recommended for Luma Pro and Luma Ultra users "with severe astigmatism or myopia-correcting prescriptions beyond -4.0D"; its ordering information lists a cylinder range of -6.00 to +6.00.[14] For the Viture Pro 2, whose knobs reach -5.00D, the company sells a frame with lenses fitted for prescriptions beyond that limit or needing "other customization (such as astigmatism correction)", accepting a cylinder of -6.00 to +6.00.[15] Xreal's order form for Xreal One Pro prescription lenses asks for a CYL value, described as the "strength of astigmatism correction", and an axis value to be entered only by users with astigmatism.[16]

Headset prescription inserts specify cylinder ranges in the same way as glasses. Meta states that the Zenni inserts for its Quest headsets accept a sphere of -10.00 to +6.00 and a cylinder of -6.00 to +6.00.[17] Apple states that Apple Vision Pro cannot be worn with eyeglasses, and that users who need prescription glasses, "including for astigmatism", may be able to order ZEISS Optical Inserts.[18] In smart glasses with a built-in display, the prescription is part of the lens itself: Meta says the Meta Ray-Ban Display supports myopia, hyperopia and astigmatism "up to a total power of -4.00 to +4.00D (defined as SPH+CYL) and up to 4D of CYL", in single-vision lenses only.[19]

Astigmatism handling in selected devices (as stated by the makers)
Device Built-in focus adjustment Route for astigmatism Stated cylinder range
HTC Vive XR Elite Diopter dials up to about -6.0 D per eye; "do not correct astigmatism" Glasses or third-party prescription inserts (general HTC guidance) Not stated[5]
Viture Luma Myopia dial up to -6.0D Magnetic prescription lens frame -6.00 to +6.00[14]
Viture Pro 2 Knobs up to -5.00D Prescription frame with lenses -6.00 to +6.00[15]
Meta Quest 3 None stated Zenni prescription inserts -6.00 to +6.00[17]
Apple Vision Pro None stated; glasses cannot be worn ZEISS Optical Inserts Not stated by Apple[18]
Meta Ray-Ban Display None stated Prescription lenses ordered with the glasses Up to 4 D, total SPH+CYL within -4.00 to +4.00 D[19]

Astigmatism in headset optics

Monochromatic Seidel aberrations, astigmatism among them, scale with aperture size and field angle, which makes high image quality hard to reach in optics that combine a large aperture with a wide field of view, as eyepieces for near-eye displays do. Anna Wirth-Singh and colleagues made this point in a 2025 Light: Science & Applications paper on a meta-optic doublet eyepiece, noting that earlier metasurface doublets had corrected spherical aberration, coma and astigmatism but with apertures under 1 mm, too small for an eyepiece.[20] In the design of a 50-degree collimating lens for lightguide-based AR glasses (four plastic aspheric lenses for a 0.32-inch microdisplay), Wen-Shing Sun and colleagues reported that the modulation transfer function was affected by astigmatism at every field except the center, so the tangential and sagittal curves differed.[21] In a 2020 analysis of curved displays for VR, AR and MR headsets, Eduard Muslimov and colleagues noted that the shape of the image surface is set by the two Seidel sums for astigmatism and field curvature, and used this as the starting point for a refocusable projection system with a 90-degree field of view that they proposed for use in a VR headset.[22]

Off-axis optical layouts produce astigmatism directly. Microsoft Research's 2017 holographic near-eye display project proposed encoding corrections for the display optics in the hologram itself, which it said allows "arbitrary optical corrections on a per-pixel basis" and the use of simpler optics. It illustrated this with an optical see-through prototype in an off-axis configuration: without correction, "the off-axis optics result in severe astigmatism", so that no part of the image was in proper horizontal and vertical focus at once.[6][23]

Research on correcting the viewer's astigmatism

Several research systems aim to let astigmatic users see a sharp image without glasses:

  • Holographic correction. The same Microsoft Research project stated that holographic displays can correct near- and farsightedness as well as astigmatism, so that users could view the display without glasses. In a demonstration, a cylindrical lens placed in front of the camera simulated astigmatic vision, and with correction applied in the hologram the image looked "virtually the same" as with normal vision.[6][23] In 2021 Dongyeon Kim and colleagues at Seoul National University described a vision-correcting holographic display that combines a user's prescription with a physical model of the optics to correct on-axis and off-axis aberrations.[24]
  • Prescription-aware rendering. ChromaCorrect (Güzel, Beyazian, Chakravarthula and Akşit, 2023) optimizes rendered images with a differentiable model of the display and the viewer's refractive error, and accepts prescription values for myopia, hyperopia and astigmatism. The authors tested myopic and hyperopic astigmatism, and myopia combined with hyperopic astigmatism, using refractive errors of plus or minus 1.5 D, and reported better image-quality scores than a conventional method.[9]
  • Prescription-embedded AR optics. Jui-Yi Wu and Jonghyun Kim described in 2020 an AR display whose freeform image combiner is embedded inside a prescription lens; the design covers myopia, hyperopia, astigmatism and presbyopia, and a 169 g prototype showed a 40 by 20 degree virtual image.[25]
  • Tunable liquid crystal lenses. Researchers from Kent State University and Meta's Reality Labs described in 2023 a non-mechanical system of three liquid crystal cylindrical lenses whose optical power changes with applied voltage, intended to correct astigmatism and defocus, and named AR/VR and prescription eyeglasses among possible uses.[26]

Near-eye displays have also been used to measure astigmatism. NETRA, a 2010 system from the MIT Media Lab's Camera Culture group, placed a microlens array over a high-resolution display (the prototypes included mobile phones) held a few millimeters from the eye; the user aligned patterns on screen, and for astigmatism the system moved line segments along different meridians to find the power along each one. The authors noted that the granularity of the microlens array limits the accuracy of the cylinder axis.[8] The technology was later spun out into the startup EyeNetra.[27]

See also

References

  1. ↑ 1.0 1.1 1.2 Stephanie Kearney, Rakhee Shah, Natalia Vlasak (2025-10-30). "The role of astigmatism in myopia development, myopia progression and myopia control". Ophthalmic and Physiological Optics, vol. 45, no. 7. pp. 1946-1964. doi:10.1111/opo.70030. https://doi.org/10.1111/opo.70030. Retrieved 2026-10-11.
  2. ↑ 2.0 2.1 2.2 "What Is Astigmatism?". American Academy of Ophthalmology. https://www.aao.org/eye-health/diseases/what-is-astigmatism. Retrieved 2026-10-11.
  3. ↑ 3.0 3.1 3.2 3.3 James C. Wyant, Katherine Creath (1992). "Basic Wavefront Aberration Theory for Optical Metrology". Applied Optics and Optical Engineering, vol. XI, chapter 1. Academic Press. https://wp.optics.arizona.edu/jcwyant/wp-content/uploads/sites/13/2016/08/03-BasicAberrations_and_Optical_Testing.pdf. Retrieved 2026-10-11.
  4. ↑ 4.0 4.1 Hassan Hashemi, Akbar Fotouhi, Abbasali Yekta, Reza Pakzad, Hadi Ostadimoghaddam, Mehdi Khabazkhoob (2018). "Global and regional estimates of prevalence of refractive errors: Systematic review and meta-analysis". Journal of Current Ophthalmology, vol. 30, no. 1. pp. 3-22. doi:10.1016/j.joco.2017.08.009. https://pmc.ncbi.nlm.nih.gov/articles/PMC5859285/. Retrieved 2026-10-11.
  5. ↑ 5.0 5.1 5.2 VIVE Team (2025-07-22). "VR With Glasses: Using VIVE Headsets If You Wear Eyeglasses". VIVE Blog. HTC. https://blog.vive.com/us/can-you-use-a-vr-headset-with-glasses-learn-how-htc-vive-headsets-support-glasses-wearers-and-what-you-need-to-consider-for-comfort-in-virtual-reality/. Retrieved 2026-10-11.
  6. ↑ 6.0 6.1 6.2 "Holographic Near-Eye Displays for Virtual and Augmented Reality". Microsoft Research. Microsoft. https://www.microsoft.com/en-us/research/project/holographic-near-eye-displays-virtual-augmented-reality/. Retrieved 2026-10-11.
  7. ↑ 7.0 7.1 "Astigmatism". National Eye Institute. National Institutes of Health. 2024-12-04. https://www.nei.nih.gov/learn-about-eye-health/eye-conditions-and-diseases/astigmatism. Retrieved 2026-10-11.
  8. ↑ 8.0 8.1 Vitor F. Pamplona, Ankit Mohan, Manuel M. Oliveira, Ramesh Raskar (2010). "NETRA: Interactive Display for Estimating Refractive Errors and Focal Range". ACM Transactions on Graphics, vol. 29, no. 4 (SIGGRAPH 2010), article 77. doi:10.1145/1778765.1778814. https://www.inf.ufrgs.br/~oliveira/pubs_files/NETRA/NETRA_SIGRAPH1010.pdf. Retrieved 2026-10-11.
  9. ↑ 9.0 9.1 Ahmet H. Güzel, Jeanne Beyazian, Praneeth Chakravarthula, Kaan Akşit (2023). "ChromaCorrect: prescription correction in virtual reality headsets through perceptual guidance". Biomedical Optics Express, vol. 14, no. 5. pp. 2166-2180. doi:10.1364/BOE.485776. https://pmc.ncbi.nlm.nih.gov/articles/PMC10191670/. Retrieved 2026-10-11.
  10. ↑ Daniel Porter (2023-04-18). "Eyeglasses Prescription Terms". American Academy of Ophthalmology. https://www.aao.org/eye-health/glasses-contacts/how-to-read-eyeglasses-prescription. Retrieved 2026-10-11.
  11. ↑ Thomas Young (1801). "The Bakerian Lecture: On the Mechanism of the Eye". Philosophical Transactions of the Royal Society of London, vol. 91. Internet Archive (scan). pp. 23-88. doi:10.1098/rstl.1801.0004. https://archive.org/details/jstor-107085. Retrieved 2026-10-11.
  12. ↑ George Biddell Airy (1827). "On a peculiar Defect in the Eye, and a mode of correcting it". Transactions of the Cambridge Philosophical Society, vol. 2. Internet Archive (scan). pp. 267-271. https://archive.org/details/transactionsofca02camb. Retrieved 2026-10-11.
  13. ↑ George Biddell Airy. "On a Change in the State of an Eye affected with a Mal-formation". Transactions of the Cambridge Philosophical Society, vol. 8. Internet Archive (scan). pp. 361. https://archive.org/details/transactionsofca08camb. Retrieved 2026-10-11.
  14. ↑ 14.0 14.1 "VITURE Luma Prescription Lens Frame Without Lenses". VITURE. https://www.viture.com/en-US/product/viture-luma-prescription-lens-frame. Retrieved 2026-10-11.
  15. ↑ 15.0 15.1 "VITURE Pro 2 Prescription Lens Frame with Lenses". VITURE. https://www.viture.com/en-US/product/viture-pro-2-prescription-lens-frame-with-lenses. Retrieved 2026-10-11.
  16. ↑ "XREAL One Pro Prescription Lenses". XREAL Shop. XREAL. https://us.shop.xreal.com/products/xreal-one-pro-prescription-lens. Retrieved 2026-10-11.
  17. ↑ 17.0 17.1 "Zenni VR prescription lenses for Meta Quest". Meta Quest Help. Meta Platforms. https://www.meta.com/help/quest/1050152622641152/. Retrieved 2026-10-11.
  18. ↑ 18.0 18.1 "Using Apple Vision Pro with vision prescriptions and vision conditions". Apple Support. Apple. 2026-04-13. https://support.apple.com/en-us/120052. Retrieved 2026-10-11.
  19. ↑ 19.0 19.1 "Meta Ray-Ban Display: How to Buy & Why". Meta Quest Blog. Meta Platforms. 2025-10-02. https://www.meta.com/blog/meta-ray-ban-display-retail-faq/. Retrieved 2026-10-11.
  20. ↑ Anna Wirth-Singh, Johannes E. Fröch, Fan Yang, Louis Martin, et al. (2025-01-02). "Wide field of view large aperture meta-doublet eyepiece". Light: Science & Applications, vol. 14, article 17. doi:10.1038/s41377-024-01674-0. https://doi.org/10.1038/s41377-024-01674-0. Retrieved 2026-10-11.
  21. ↑ Wen-Shing Sun, Yi-Lun Su, Ying-Shun Hsu, Chuen-Lin Tien, Nai-Jen Cheng, Ching-Cherng Sun (2025-10-30). "Compact Design of a 50° Field of View Collimating Lens for Lightguide-Based Augmented Reality Glasses". Micromachines, vol. 16, no. 11, article 1234. doi:10.3390/mi16111234. https://doi.org/10.3390/mi16111234. Retrieved 2026-10-11.
  22. ↑ Eduard Muslimov, Thibault Behaghel, Emmanuel Hugot, Kelly Joaquina, Ilya Guskov (2020). "Variable Curvature Displays: Optical Designs and Applications for VR/AR/MR Headsets". Applied Sciences, vol. 10, no. 2, article 712. doi:10.3390/app10020712, arXiv:2001.07132. https://arxiv.org/abs/2001.07132. Retrieved 2026-10-11.
  23. ↑ 23.0 23.1 Andrew Maimone, Andreas Georgiou, Joel S. Kollin (2017-07-20). "Holographic near-eye displays for virtual and augmented reality". ACM Transactions on Graphics, vol. 36, no. 4 (SIGGRAPH 2017). doi:10.1145/3072959.3073624. https://doi.org/10.1145/3072959.3073624. Retrieved 2026-10-11.
  24. ↑ Dongyeon Kim, Seung-Woo Nam, Kiseung Bang, Byounghyo Lee, Seungjae Lee, Youngmo Jeong, Jong-Mo Seo, Byoungho Lee (2021). "Vision-correcting holographic display: evaluation of aberration correcting hologram". Biomedical Optics Express, vol. 12, no. 8. pp. 5179-5195. doi:10.1364/BOE.433919. https://doi.org/10.1364/BOE.433919. Retrieved 2026-10-11.
  25. ↑ Jui-Yi Wu, Jonghyun Kim (2020). "Prescription AR: a fully-customized prescription-embedded augmented reality display". Optics Express, vol. 28, no. 5. pp. 6225-6241. doi:10.1364/OE.380945. https://doi.org/10.1364/OE.380945. Retrieved 2026-10-11.
  26. ↑ Amit K. Bhowmick, Afsoon Jamali, Douglas Bryant, Sandro Pintz, Philip J. Bos (2023-07-12). "Design, fabrication, and characterization of a liquid crystal-based large area electrically tunable lens for correction of astigmatism and defocus". Optical Engineering, vol. 62, no. 7, article 075103. SPIE. doi:10.1117/1.OE.62.7.075103. https://doi.org/10.1117/1.OE.62.7.075103. Retrieved 2026-10-11.
  27. ↑ "A low-cost mobile diagnostic tool for self-evaluation of eye refractive disorders". Deshpande Center for Technological Innovation. Massachusetts Institute of Technology. https://deshpande.mit.edu/projects/a-low-cost-mobile-diagnostic-tool-for-self-evaluation-of-eye-refractive-disorders. Retrieved 2026-10-11.
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