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Maxwellian view

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The Maxwellian view is an optical viewing arrangement in which a lens forms an image of a small light source in the plane of the observer's pupil, so that the light enters the eye through a small region of the pupil, instead of the observer looking directly at the source or at an illuminated surface (the ordinary arrangement, called Newtonian view).[1][2] It is named after the physicist James Clerk Maxwell, whose 1860 colour-matching experiments used the arrangement.[3][4] The method has long been used in vision science to control the light reaching the retina, and it is the basis of a family of near-eye displays for augmented reality, called Maxwellian displays or retinal projection displays.[5][6]

In a Maxwellian display the image-forming beam passes through only a small part of the pupil, which acts like a pinhole and greatly extends the depth of field. The picture on the retina therefore stays sharp largely regardless of the eye's focus or refractive error, which is why such displays are described as "always in focus", "focus-free" or "accommodation-free" and are studied as a way around the vergence-accommodation conflict.[1][7][8] The main drawback is a very small eye box: if the pupil moves off the point where the light converges, the image disappears.[3]

Reviewed 15 October 2026. Bibliographic metadata of all cited papers checked via Crossref; definitions, numbers and study results checked against full texts or abstracts (Europe PMC, OpenAlex), QD Laser press releases (2018-2020) and the Maxwell 1860 abstract scan. About review dates.

How it works

In Newtonian view the eye looks directly at a source or a lit target. In Maxwellian view a lens collects light from a small source and focuses it to an image inside the pupil; the eye then sees the outline of the lens uniformly illuminated, even if the source itself is irregular.[2][4] When the image of the source is smaller than the pupil, all of the collected light enters the eye.[4] Zhan and colleagues, citing Gerald Westheimer's 1966 review of the method, note that this minimizes the effect of the eye's optical aberrations and makes the quantity of light entering the eye independent of pupil size.[1][9] Vision researchers value the arrangement because properties of the target, such as focus, size and shape, can be set independently of retinal illuminance.[2]

For displays, the target is an image. Chang and colleagues describe the principle as follows: the chief rays from the display panel converge at the eye pupil and then form an image on the retina, and because the beam entering the eye is a narrow pencil, the effective pupil is small and the depth of field becomes very large.[7] Xiong and colleagues give the same account: a point light source is imaged in the eye pupil, the beam is modulated to carry the picture, and because the source image is much smaller than the pupil, the retinal image is always in focus irrespective of the focus of the eye lens.[3] In this geometry the display plane and the retina form a pair of conjugate planes, with the eye treated as part of the optical system.[6]

The depth of focus is large but not unlimited. In a 2025 analysis, Westheimer showed that the defocused retinal image in Maxwellian view results from two superimposed wavefront components in the pupil (the diffraction pattern produced when the source that transilluminates the target is imaged in the eye's entrance pupil, and the wavefront error from defocus), so there is no general theory of defocus degradation comparable with the optical transfer function used for ordinary retinal imaging. He concluded that depth of focus is nonetheless always better in Maxwellian view because the light does not fill the pupil fully and uniformly.[10]

History

Maxwell's instrument for his colour-matching experiments, reported to the Royal Society in 1860, was a long dark box in which light passed through a slit, a lens and two prisms to form a spectrum; three adjustable slits selected spectral colours, and their mixture was "seen by an eye placed at the slit in the shorter arm of the instrument".[11] The full paper appeared in the Philosophical Transactions of the Royal Society the same year.[12] J. S. Reid's pages on Maxwell's legacy, hosted by the University of Aberdeen, describe this "colour box" as incorporating, without Maxwell drawing attention to it, the lens configuration now known as the Maxwell view, and note that the same principle later spread into projector condenser design, where the source is imaged into the projection lens.[4] Parimi and colleagues summarize Maxwell's observation that a lens imaging a slit onto his pupil appeared uniformly filled with light.[2]

Westheimer's 1966 article "The Maxwellian view" in Vision Research is cited for the principle by later display papers, including the 2021 display review by Xiong and colleagues and the 2019 holographic display paper by Chang and colleagues.[9][7][3] In visual science the method is used to present stimuli for eye examinations, for example to analyse the optical density of the lens and macular pigment, colour appearance, cone function and light adaptation.[5] Recent examples include a five-primary Maxwellian-view display built at Queensland University of Technology for silent-substitution studies of melanopsin, rod and cone responses, which uses a 2 mm artificial pupil to keep retinal illumination independent of the natural pupil, and potential vision testers at Indiana University that present acuity targets in Maxwellian view through a 3 mm pupil.[13][14][2] The QUT system holds the head still with temple bars, a head restraint and a chinrest (a bite bar is suggested as an alternative), because head movement can defocus the image and change retinal illumination.[13]

Laser displays that draw an image directly on the retina followed from the same idea. Stöhr and colleagues trace the line from a 1981 scanning-laser-ophthalmoscope experiment that projected optotypes onto the retina, through work by Thomas Furness and colleagues on direct retinal projection with a low-energy laser, to modern eyewear that sends thin laser beams through the centre of the eye's lens in Maxwellian view.[15] The scanned-beam approach is covered in Virtual retinal display.

Use in near-eye displays

Xiong and colleagues' 2021 review treats Maxwellian-type systems as one type of free-space AR combiner. The point source is usually a laser with narrow angular and spectral bandwidths, though LEDs can be used if an angular filter is added. The combiner is usually a holographic optical element (HOE) rather than a half-mirror, because an HOE allows an off-axis layout in an eyeglass-like position and reflects less ambient light; the strong chromatic dispersion of HOEs is itself one reason these systems use lasers.[3] The image can be formed by a spatial light modulator such as LCoS or a DMD in the beam path, or by laser beam scanning (LBS), where the laser diode itself is modulated.[3]

The review lists high light efficiency (nearly all the light goes into the eye) and a large field of view (about 80 degrees horizontal, set by the f-number of the combiner) as advantages, and the tiny exit pupil as the major weakness.[3] For VR headsets, the same review notes that Maxwellian-view and holographic displays need a very different optical architecture from current headsets and are therefore better suited to AR.[3]

Several research approaches build on the basic arrangement:

  • Holographic Maxwellian view. Takaki and Fujimoto (2018) generated a wavefront converging on the pupil with a holographic display; the convergence point can be moved electrically to follow the pupil, the beam width in the pupil can be changed to control depth of field, and eye aberrations such as astigmatism can be corrected.[16] Maimone, Georgiou and Kollin showed holographic near-eye prototypes that, per Xiong's review, can run either as a large-depth-of-field Maxwellian view or as a computer-generated hologram with per-pixel focus.[3][17]
  • Pupil-tracked light fields. Jang and colleagues' "Retinal 3D" display (2017) projected a pupil-tracked light field onto the retina through an HOE combiner, using laser beams shaped for a large depth of field to supply focus cues and a "dynamic eye-box".[18]
  • Foveated designs. The Foveated AR prototype from NVIDIA researchers and co-authors (2019) paired a high-resolution foveal display with a projector-based Maxwellian-view peripheral display whose nodal point was moved by a traveling HOE to follow the pupil; the authors reported a net 85 x 78 degree field of view per eye.[19]
  • Pin-light displays. Xiong's review describes pin-light displays as closely related: each pin-light source acts as a Maxwellian view with a large depth of field, and an array of them tiles small elemental views into a wider field.[3]

Eye box limitation and expansion

Because all image light passes through one small point, a slight shift of the eye pupil from that viewpoint makes the image vanish completely; Xiong and colleagues describe expanding the eye box as one of the most important challenges for Maxwellian-type systems.[3] A single viewpoint gives an eye box of about 2 to 4 mm by their estimate.[3] Two broad strategies exist. Pupil duplication creates several viewpoints at once, spaced more widely than the eye pupil so that only one enters the eye at a time; it divides the light among the viewpoints. Pupil steering moves a single viewpoint to follow the tracked pupil.[3][7] Chang and colleagues frame the same split as temporal multiplexing (rapidly moving the viewpoint with LED arrays or tilting mirrors, which trades frame rate against eye box size) versus spatial multiplexing (creating shifted pupils simultaneously with HOEs or computer-generated holograms).[7] Ratnam and colleagues proposed a taxonomy of pupil-steered architectures and an optical model with a wide-field schematic eye to simulate retinal image quality under imperfect steering.[20]

Work Approach Reported result
Kim and Park, Optics Letters (2018) Several concave mirrors multiplexed into one see-through HOE (pupil duplication) Always-focused images over the real scene with a 9.2 x 5.2 degree field of view and a 9 mm x 3 mm eye box[21]
Hedili, Soner, Ulusoy and Urey, Optics Express (2019) Transmissive LCD lit by an LED backlight whose light is focused into the pupil (a "pinhole display"); LED array with real-time pupil tracker (pupil steering) 37 degree field of view, 360 cd/m2 from LEDs totalling 0.42 lumens, 11 ms motion-to-photon latency[22]
Do, Kim and Min, Applied Optics (2019) Pinhole projector imaged near the eye by a retroreflector film and beam splitter Focus-free behaviour analysed and tested at accommodation distances of 0.25, 0.5 and 1 m[23]
Shrestha et al., Research (2019) Pixel beam scanning with viewpoints replicated by a beam-splitter array 3D AR prototype with a 36 degree field of view; the authors report comfortable viewing without nausea or eyestrain[8]
Chang, Cui, Park and Gao, Scientific Reports (2019) Computer-generated hologram multiplexed with several off-axis plane waves, shown on an amplitude-only display Duplicated pupils from one active component (an LCD or DLP panel)[7]
Lin, Zhan, Zou, Fan and Wu, Optics Express (2020) Thin-film two-dimensional beam deflector made of multi-twist broadband Pancharatnam-Berry deflectors (eye box replication) Full-colour always-focused images within a 9 mm x 9 mm eye box[24]
Xiong, Li, Li and Wu, Optics Letters (2021) Pupil steering by switching between cholesteric liquid crystal holographic lenses with polarization Steering without the aberrations caused by changing the incident angle on a single lens coupler[25]
Jiang et al., Advanced Science (2025) Photo-aligned liquid crystal Dammann grating with switchable viewpoints, a light selector and eye tracking 49 viewpoints spaced 0.532 mm apart over a 36 mm2 range; the light selector lets light from only one viewpoint reach the eye[6]

Commercial retinal projection eyewear

The Japanese laser maker QD Laser launched retinal-scanning eyewear under the RETISSA name in 2018, built on its "VISIRIUM" technology: weak light from red, green and blue semiconductor lasers is scanned by a MEMS mirror onto the retina.[26] Peer-reviewed studies describe the optics as a Maxwellian view system.[5][15] QD Laser's January 2018 announcement explains that the laser light converges once at the centre of the pupil before reaching the retina, so the image is little affected by the wearer's vision (focusing ability) or focus position and can be seen without blur even without glasses or contact lenses, and that the AR overlay in principle has no focus mismatch with the real background.[26] The company began taking in-store orders for the first RETISSA Display on 25 October 2018, with deliveries expected from December 2018; its listed specifications included a horizontal viewing angle of about 26 degrees in the centre of one eye's field, a 16:9 aspect ratio, 1024 x 600 projection resolution, a 60 Hz refresh rate and an eyewear unit of about 60 g.[27] The RETISSA Display II followed in February 2020, with the same 26 degree horizontal angle and a projection resolution equivalent to 720p (1,280 x 720) at 60 Hz.[28] Studies using the eyewear report that its laser is classified as Class 1 under IEC 60825-1,[15][29] and QD Laser's product announcements state that the products are not medical devices.[26][30] In June 2019 the company showed two prototypes at Laser World of Photonics in Munich, including the RETISSA Handy, which combined a commercial pico-projector with "a unique Maxwell optics system" for a 40 degree horizontal viewing angle.[30]

Research on perception and clinical use

Clinical studies have tested whether the focus-free property holds in practice. Stöhr and colleagues at University Hospital Essen tested QD Laser's eyewear in 20 healthy subjects with myopia, hyperopia, astigmatism or presbyopia and found no significant correlation between refraction and visual acuity with the device (r = 0.17), consistent with independence from refractive error; acuity with the device was lower than uncorrected acuity overall (0.50 versus 0.40 logMAR), and only myopic subjects saw significantly better with it.[15] At Keio University, Iyama and colleagues used the eyewear with a wide-angle camera lens to enlarge the visual field of healthy volunteers wearing pinhole attachments that simulated tunnel vision.[5]

Whether the eye stops accommodating is a separate question. Hirota and colleagues at Teikyo University (two co-authors were from QD Laser) had 22 young adults view an AR target through a RETISSA Display II, whose laser beams are 0.6 mm wide at the cornea, while a real target was placed at 5.0, 0.5, 0.33 or 0.2 m. Accommodative and pupillary responses still occurred and depended on the distance of the real object, and the authors concluded that the Maxwellian display "does not completely eliminate accommodation in real space".[29]

See also

References

  1. ↑ 1.0 1.1 1.2 Tao Zhan, Kun Yin, Jianghao Xiong, Ziqian He, Shin-Tson Wu (2020). "Augmented Reality and Virtual Reality Displays: Perspectives and Challenges". iScience, vol. 23, no. 8, article 101397. https://doi.org/10.1016/j.isci.2020.101397. Retrieved 2026-10-15.
  2. ↑ 2.0 2.1 2.2 2.3 2.4 Vamsi Parimi, Ann E. Elsner, Stephen A. Burns, Thomas J. Gast (2025). "Potential vision tester using Maxwellian view, small pupil, and different levels of wavefront correction with adaptive optics". Biomedical Optics Express, vol. 16, no. 6, pp. 2528 ff.. https://doi.org/10.1364/BOE.559475. Retrieved 2026-10-15.
  3. ↑ 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 Jianghao Xiong, En-Lin Hsiang, Ziqian He, Tao Zhan, Shin-Tson Wu (2021). "Augmented reality and virtual reality displays: emerging technologies and future perspectives". Light: Science & Applications, vol. 10, article 216. https://doi.org/10.1038/s41377-021-00658-8. Retrieved 2026-10-15.
  4. ↑ 4.0 4.1 4.2 4.3 J. S. Reid (2016). "Maxwell's legacy: Maxwell View and Maxwell's Optical Theorems". University of Aberdeen, Maxwell legacy pages. https://homepages.abdn.ac.uk/j.s.reid/pages/Maxwell/Legacy/MaxView.html. Retrieved 2026-10-15.
  5. ↑ 5.0 5.1 5.2 5.3 Chigusa Iyama, Yuta Shigeno, Eri Hirano, et al. (2019). "QD laser eyewear as a visual field aid in a visual field defect model". Scientific Reports, vol. 9, article 1010. https://doi.org/10.1038/s41598-018-37744-8. Retrieved 2026-10-15.
  6. ↑ 6.0 6.1 6.2 Haonan Jiang, Yuechu Cheng, Zhibo Sun, et al. (2025). "Pupil-Adaptive Retina Projection Augment Reality Displays With Switchable Ultra-Dense Viewpoints". Advanced Science, vol. 12, no. 18, article 2416961. https://doi.org/10.1002/advs.202416961. Retrieved 2026-10-15.
  7. ↑ 7.0 7.1 7.2 7.3 7.4 7.5 Chenliang Chang, Wei Cui, Jongchan Park, Liang Gao (2019). "Computational holographic Maxwellian near-eye display with an expanded eyebox". Scientific Reports, vol. 9, article 18749. https://doi.org/10.1038/s41598-019-55346-w. Retrieved 2026-10-15.
  8. ↑ 8.0 8.1 Pawan K. Shrestha, Matt J. Pryn, Jia Jia, Jhen-Si Chen, Hector Navarro Fructuoso, Atanas Boev, Qing Zhang, Daping Chu (2019). "Accommodation-Free Head Mounted Display with Comfortable 3D Perception and an Enlarged Eye-box". Research, vol. 2019, article 9273723. https://doi.org/10.34133/2019/9273723. Retrieved 2026-10-15.
  9. ↑ 9.0 9.1 Gerald Westheimer (1966). "The Maxwellian view". Vision Research, vol. 6, no. 11-12, pp. 669-682. https://doi.org/10.1016/0042-6989(66)90078-2. Retrieved 2026-10-15.
  10. ↑ Gerald Westheimer (2025-04-28). "Defocus degradation of retinal images in the Maxwellian view". Journal of the Optical Society of America A, vol. 42, no. 6, p. C1. https://doi.org/10.1364/JOSAA.559298. Retrieved 2026-10-15.
  11. ↑ James Clerk Maxwell (1860). "On the Theory of Compound Colours, and the Relations of the Colours of the Spectrum (abstract)". Proceedings of the Royal Society of London, vol. 10, pp. 404-409 (read 22 March 1860). Royal Society (scan at Internet Archive). https://archive.org/details/philtrans03559101. Retrieved 2026-10-15.
  12. ↑ James Clerk Maxwell (1860). "On the theory of compound colours, and the relations of the colours of the spectrum". Philosophical Transactions of the Royal Society of London, vol. 150, pp. 57-84. https://doi.org/10.1098/rstl.1860.0005. Retrieved 2026-10-15.
  13. ↑ 13.0 13.1 Thomas W. Nugent, Andrew J. Zele (2022). "A five-primary Maxwellian-view display for independent control of melanopsin, rhodopsin, and three-cone opsins on a fine spatial scale". Journal of Vision, vol. 22, no. 12, article 20. https://doi.org/10.1167/jov.22.12.20. Retrieved 2026-10-15.
  14. ↑ Ann E. Elsner, Joel A. Papay, Vamsi Parimi, Hae Won Jung, Christopher A. Clark, Stephen A. Burns, Thomas J. Gast (2023). "Potential vision tester using adaptive optics, Maxwellian view, and small pupil". Biomedical Optics Express, vol. 14, no. 12, pp. 6397-6409. https://doi.org/10.1364/BOE.502340. Retrieved 2026-10-15.
  15. ↑ 15.0 15.1 15.2 15.3 Mareile Stöhr, Dirk Dekowski, Nikolaos Bechrakis, Joachim Esser, Anja Eckstein, Michael Oeverhaus (2020). "First Evaluation of a Retinal Imaging Laser Eyewear System Based Low Vision Aid". Clinical Ophthalmology, vol. 14, pp. 4115-4123. https://doi.org/10.2147/OPTH.S273810. Retrieved 2026-10-15.
  16. ↑ Yasuhiro Takaki, Naohiro Fujimoto (2018). "Flexible retinal image formation by holographic Maxwellian-view display". Optics Express, vol. 26, no. 18, pp. 22985-22999. https://doi.org/10.1364/OE.26.022985. Retrieved 2026-10-15.
  17. ↑ Andrew Maimone, Andreas Georgiou, Joel S. Kollin (2017). "Holographic near-eye displays for virtual and augmented reality". ACM Transactions on Graphics, vol. 36, no. 4, article 85 (SIGGRAPH 2017). https://doi.org/10.1145/3072959.3073624. Retrieved 2026-10-15.
  18. ↑ Changwon Jang, Kiseung Bang, Seokil Moon, Jonghyun Kim, Seungjae Lee, Byoungho Lee (2017). "Retinal 3D: augmented reality near-eye display via pupil-tracked light field projection on retina". ACM Transactions on Graphics, vol. 36, no. 6, article 190. https://doi.org/10.1145/3130800.3130889. Retrieved 2026-10-15.
  19. ↑ Jonghyun Kim, Youngmo Jeong, Michael Stengel, et al. (2019). "Foveated AR: Dynamically-Foveated Augmented Reality Display". ACM Transactions on Graphics, vol. 38, no. 4 (SIGGRAPH 2019). https://doi.org/10.1145/3306346.3322987. Retrieved 2026-10-15.
  20. ↑ Kavitha Ratnam, Robert Konrad, Douglas Lanman, Marina Zannoli (2019). "Retinal image quality in near-eye pupil-steered systems". Optics Express, vol. 27, no. 26, pp. 38289-38311. https://doi.org/10.1364/OE.27.038289. Retrieved 2026-10-15.
  21. ↑ Seong-Bok Kim, Jae-Hyeung Park (2018). "Optical see-through Maxwellian near-to-eye display with an enlarged eyebox". Optics Letters, vol. 43, no. 4, pp. 767-770. https://doi.org/10.1364/OL.43.000767. Retrieved 2026-10-15.
  22. ↑ M. Kivanc Hedili, Burak Soner, Erdem Ulusoy, Hakan Urey (2019). "Light-efficient augmented reality display with steerable eyebox". Optics Express, vol. 27, no. 9, pp. 12572-12581. https://doi.org/10.1364/OE.27.012572. Retrieved 2026-10-15.
  23. ↑ Hyeongkyu Do, Young Min Kim, Sung-Wook Min (2019). "Focus-free head-mounted display based on Maxwellian view using retroreflector film". Applied Optics, vol. 58, no. 11, pp. 2882-2889. https://doi.org/10.1364/AO.58.002882. Retrieved 2026-10-15.
  24. ↑ Tiegang Lin, Tao Zhan, Junyu Zou, Fan Fan, Shin-Tson Wu (2020). "Maxwellian near-eye display with an expanded eyebox". Optics Express, vol. 28, no. 26, pp. 38616-38625. https://doi.org/10.1364/OE.413471. Retrieved 2026-10-15.
  25. ↑ Jianghao Xiong, Yannanqi Li, Kun Li, Shin-Tson Wu (2021). "Aberration-free pupil steerable Maxwellian display for augmented reality with cholesteric liquid crystal holographic lenses". Optics Letters, vol. 46, no. 7, pp. 1760-1763. https://doi.org/10.1364/OL.422559. Retrieved 2026-10-15.
  26. ↑ 26.0 26.1 26.2 "Retinal scanning laser eyewear RETISSA Display to go on sale this summer (press release, Japanese)". QD Laser. 2018-01-04. https://www.qdlaser.com/uploads/2018/01/180104-RETISSA-Display.pdf. Retrieved 2026-10-15.
  27. ↑ "RETISSA Display: in-store orders begin (press release, Japanese)". QD Laser. 2018-10-25. https://www.qdlaser.com/uploads/2018/10/press181025.pdf. Retrieved 2026-10-15.
  28. ↑ "QD Laser signs RETISSA series distribution agreement with Fujitsu Electronics (press release, Japanese)". QD Laser. 2020-10-07. https://www.qdlaser.com/uploads/2020/10/201007_1.pdf. Retrieved 2026-10-15.
  29. ↑ 29.0 29.1 Masakazu Hirota, Kakeru Sasaki, Kanako Kato, et al. (2024). "Ocular Accommodative and Pupillary Responses During Fixation on Augmented Reality With a Maxwellian Display". Investigative Ophthalmology & Visual Science, vol. 65, no. 11, article 30. https://doi.org/10.1167/iovs.65.11.30. Retrieved 2026-10-15.
  30. ↑ 30.0 30.1 "Development of New Types of Retinal Scanning Laser Displays with Lower Cost and Smaller Size". QD Laser. 2019-06-20. https://qdlaser.com/uploads/2019/06/PressRelease20190620RETISSAHandy-FlexPeriscope-EN2.pdf. Retrieved 2026-10-15.
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