Diffraction

Diffraction is the set of wave effects that occur when light, or any other wave, meets a structure that changes its amplitude or phase, such as an edge, a slit, an aperture or a periodic pattern. Behind the structure the wave spreads and interferes with itself, so that, for example, light passing through a small circular aperture forms a spot with a fuzzy edge surrounded by rings instead of a sharp-edged spot. The effect depends on wavelength: in the RP Photonics Encyclopedia's single-slit example, longer wavelengths produce a broader central peak and side peaks at larger angles.

Diffraction matters to virtual reality and augmented reality hardware in two opposite ways. It is a working principle: the gratings in diffractive waveguide combiners, holographic optical elements and holographic displays all steer light by diffraction. It is also a limit: diffraction at the eye's pupil bounds visual acuity, the finite pixel pitch of a spatial light modulator bounds the field of view and eye box of a holographic display, and unwanted diffraction of room light by waveguide gratings produces the "rainbow" artifacts seen in some AR glasses.

This article covers the physical phenomenon and its consequences for XR devices. The engineering of components built on it (diffractive optical elements, surface relief and volume gratings, their fabrication and the coupler technologies of commercial waveguides) is covered in Diffractive optics and Waveguide display.

Reviewed 6 October 2026. Checked every physics, history and XR claim against the cited RP Photonics and OpenStax pages, the Diffraction Grating Handbook, the Linda Hall Library post, the Meta blog, UploadVR, and the full texts or Crossref records of the Kogelnik, Levola, Gondran, Donnelly-Roorda, Maimone, Xiong, Kress-Pace, Tseng, Gopakumar and Choi papers. About review dates.

How it works

Diffraction is usually explained with the Huygens-Fresnel principle: every point of a wavefront acts as a source of secondary waves, and the field at a distant point is the interference of all of those contributions. For that reason there is no sharp boundary between diffraction and interference. By convention, the spreading of light through a single narrow slit is called diffraction, while the fringes behind a double slit are called interference, but the same principle describes both.

Two regimes are treated with different mathematics. Fraunhofer diffraction describes the far field, the pattern observed a long way from the diffracting structure, and corresponds to Fresnel numbers well below 1. Fresnel diffraction, with large Fresnel numbers, applies to the near field. Diffraction also occurs in reflection, and with polychromatic light the patterns differ between wavelengths, so a white beam can split into colors.

Gratings

A diffraction grating is a structure that periodically changes the intensity or phase of light, through a variable absorbance, refractive index or surface height. Light leaving a grating is split into discrete beams called diffraction orders. For a transmission grating with slit spacing d, the bright maxima appear at angles θ that satisfy the grating equation d sin θ = mλ, where λ is the wavelength and m = 0, ±1, ±2 and so on. The direction of every order except the zero order depends on wavelength, which is why gratings are used in spectrometers; with white light, the central maximum stays white while the higher orders spread into a rainbow of colors. The same effect, produced by regular microstructures, gives the iridescence of hummingbird feathers and butterfly wings.

When the periodic modulation extends through a thick volume rather than sitting on a surface, the process is called Bragg diffraction, and typically only one diffracted order is phase-matched. Herwig Kogelnik's 1969 coupled wave theory, published in the Bell System Technical Journal, analyzed this Bragg diffraction of light by thick hologram gratings and gave formulas for their diffraction efficiencies and for their angular and wavelength sensitivities. In a 2022 review written while they were at Microsoft's HoloLens team, Bernard Kress and Maria Pace note that the angular and spectral Bragg selectivity of volume holograms in AR waveguides can be modeled with this coupled wave theory, while numerical solvers handle other structures: finite-difference time-domain (FDTD) methods for non-periodic nanostructures and rigorous coupled-wave analysis (RCWA) for quasi-periodic ones.

The diffraction limit

Light passing through a circular aperture does not form a sharp spot. It forms a central bright disk with a fuzzy edge, surrounded by rings. Diffraction limits the resolution of any system that has a lens or mirror, and any light beam of limited width also spreads by diffraction as it propagates. For a circular aperture of diameter D, the first minimum of the pattern lies at an angle θ = 1.22 λ/D (in radians). Under the Rayleigh criterion, developed by Lord Rayleigh in the nineteenth century, two point sources are just resolvable when the center of one pattern falls on the first minimum of the other, so this angle is also called the diffraction limit. RP Photonics summarizes the practical rule: the angular resolution of an instrument such as a telescope is roughly the wavelength divided by the aperture diameter, and conventional optical microscopes are limited to resolutions of the order of half the optical wavelength.

History

Francesco Maria Grimaldi described diffraction in his Physico-mathesis de lumine, published posthumously in 1665. The Linda Hall Library's history of science consultant William B. Ashworth Jr. describes it as the effect "whereby light, after passing by an obstacle such as a slit or pinhole, spreads out more than expected, to produce thin colored fringes". According to the Diffraction Grating Handbook published by MKS Instruments, the first diffraction grating was made by the American astronomer David Rittenhouse in 1785, a half-inch wide grating with fifty-three apertures that he did not develop further.

Thomas Young's double-slit experiment of the early nineteenth century used a third narrow slit in front of the two slits to obtain spatially coherent illumination, since no laser was available. In 1818 Augustin-Jean Fresnel answered a French Academy competition on diffraction with a mathematical wave theory in which the fringes arise from interference of waves issued by each point of the screen, a generalization of Huygens' principle. Siméon Denis Poisson, a member of the jury, deduced from Fresnel's theory that the center of the shadow of a circular opaque disk should be bright, which he considered a refutation. François Arago soon verified the spot experimentally, Fresnel won the competition, and the result helped the wave theory of light displace Newton's corpuscular theory.

Joseph von Fraunhofer began working on diffraction gratings in 1821 and made gratings good enough to measure the absorption lines of the solar spectrum, now called Fraunhofer lines, and derived the equations for the dispersive behavior of gratings. According to the handbook, the 1882 work of Henry A. Rowland, a physics professor at Johns Hopkins University, established the grating as the primary optical element of spectroscopic technology.

Tapani Levola's 2006 paper "Diffractive optics for virtual reality displays" presented a study of how diffractive optical elements on planar waveguides could miniaturize the optics of near-to-eye displays. Kress and Pace describe the grating-based waveguide combiners of the Microsoft HoloLens (HoloLens 1, which they date to 2015) and the Magic Leap One (2018).

Applications and limits in VR and AR

The eye's own diffraction limit

The acuity of human vision is limited in part by diffraction, because light enters the eye through the pupil, a circular aperture. Diffraction and the eye's optical aberrations pull in opposite directions as the pupil changes size: a larger pupil reduces diffraction blur but admits more aberration. William Donnelly and Austin Roorda, reviewing this trade-off in the Journal of the Optical Society of America A, note that Campbell and Gubisch found the pupil size giving the best lateral resolution to be typically between 2 and 3 mm in diameter.

Visual acuity also gives headset displays a common resolution target. Xiong and colleagues note that 20/20 visual acuity corresponds to an angular resolution of 1 arcminute, or 60 pixels per degree, "which is considered as a common goal for AR and VR displays". See Retinal resolution for how close current headsets come to that figure.

Diffractive waveguide combiners

In a diffractive waveguide, an input grating diffracts light from a small projector into a glass plate at an angle steep enough for total internal reflection, and an output grating, usually with the same period, diffracts it back out toward the eye a little at a time across the eye box. Kress and Pace give typical periods for these grating couplers in the visible spectrum as below 500 nm, and stress that the total internal reflection angle is set by the refractive index of the waveguide, not by the index of the coupler nanostructures. From a k-vector analysis of the gratings, Xiong et al. conclude that the theoretical upper limit of a diffractive waveguide's field of view is determined by the waveguide's refractive index; at the time of their 2021 review, diffractive waveguide combiners generally reached a field of view of about 50 degrees.

Because the in-coupler and out-coupler apply opposite grating vectors, their dispersions cancel, and the output image generally shows no color dispersion even with a broadband LED source. The difficulty with color is instead uniformity and field of view: when red and blue share one in-coupler, red light propagates inside the plate at a larger angle than blue, so designs usually stack two or three waveguide layers with different grating pitches. Kress and Pace add that this spectral spread matters most with broadband LED illumination, and name the laser MEMS display engine of the HoloLens 2 as an exception among the waveguide devices of the time.

Xiong et al. name a higher-index waveguide as the straightforward way to widen the field of view. In a March 2025 blog post, Meta said that the silicon carbide used for the waveguides of its Orion prototype has a refractive index of 2.7, which AR waveguides tech lead Giuseppe Calafiore called "the highest refractive index known for an optical application", and that Orion's field of view is approximately 70 degrees. Research groups have also used diffraction-engineered metasurfaces as couplers: a 2024 Nature paper by researchers at Stanford University (in Gordon Wetzstein's group), the University of Hong Kong and NVIDIA used inverse-designed full-color metasurface gratings that must steer broadband visible light to high diffraction angles to achieve total internal reflection, and reported that the very large diffraction angle of red light made its efficiency the hardest to improve.

Rainbows, eye glow and ghosts

A grating placed in front of the eye diffracts light from the outside world as well as light from the display. Xiong et al. list three resulting artifacts of diffractive waveguides. Light leakage is guided light diffracted outward toward the environment, which reduces efficiency, gives the wearer an unnatural "bright-eye" appearance and raises a privacy issue. See-through ghosts form when real-world light is coupled in and out again by the out-coupler grating, and they are worse with higher-efficiency out-couplers. The rainbow "is caused by the diffraction of environment light into user's eye", with color dispersion because, unlike the display path, nothing cancels the grating's dispersion. A higher-index substrate pushes the unwanted diffracted light out of the see-through field of view, and optimized grating structures can suppress the unwanted diffraction directly.

Kress and Pace note that world-side leakage is commonly called "eye glow", and estimate it, as a share of the eye-side leakage, at about 50% for binary surface relief gratings, about 40% for slanted ones and about 8-10% for holographic grating couplers, compared with 5% for reflective waveguides without anti-reflection coating and under 1% with it. Meta has described the rainbow problem in its own development work: optical scientist Pasqual Rivera said that wearing prototypes with glass-based, multi-plate waveguides "felt like you were in a disco. There were rainbows everywhere", and Barry Silverstein, director of research science, said that silicon carbide "gets rid of those rainbows". Geometric (reflective) waveguides use mirrors instead of gratings, usually with a prism in-coupler to avoid unnecessary color dispersion; Xiong et al. note that they usually give better image sharpness and color uniformity than diffractive ones. Kress and Pace cite the dielectric partial mirrors of the Lumus LOE as an example of this approach.

Lenses and small apertures in headsets

Diffraction also affects conventional VR optics. Xiong et al. note that the grooves of Fresnel lenses cause diffraction artifacts and stray light that degrade image quality, and that pancake lenses, with smooth surfaces, have far fewer diffraction artifacts and stray light. Replacing refractive lenses with a single thin diffractive lens is, in the same review's words, "tempting", but "the diffractive nature of such a lens will result in serious color aberrations". The underlying cause is the wavelength dependence of diffraction angles.

Designs that rely on very small optical features hit the diffraction limit directly. In pin-mirror AR displays, the tiny mirrors cannot be made too small without losing resolution to diffraction, and a pin-light display design that placed an LCD panel directly in front of the eye suffered from diffraction of background light by the panel.

Holographic displays

Holographic displays form images by using a spatial light modulator (SLM) to modulate the wavefront of a coherent light beam, an approach covered in Computer-generated holography and Holography. In a 2017 paper in ACM Transactions on Graphics, Andrew Maimone, Andreas Georgiou and Joel Kollin presented VR and AR near-eye display designs based on phase-only holographic projection, including compact, eyeglasses-like prototypes with fields of view of 80 degrees.

The SLM's pixel pitch caps how far it can diffract light. Xiong et al. explain that the micron-scale pitch sets a maximum diffraction angle which, multiplied by the SLM size, equals the system's étendue, so a larger exit pupil comes at the cost of a smaller field of view. A 2024 Nature Communications paper by researchers from Princeton University, Meta Reality Labs Research, POSTECH and KAUST states the relation explicitly: the maximum diffraction angle is θ = sin^-1(λ/2Δ) for an SLM of pixel pitch Δ, and the étendue is 4A sin²θ for display area A. The authors placed a learned static optical element with a finer pixel pitch in front of the SLM and reported a 64-fold étendue expansion for natural images in full color.

Suyeon Choi, Changwon Jang, Douglas Lanman and Gordon Wetzstein called this limited space-bandwidth product, or étendue, of current SLMs "a fundamental problem of all digital holographic displays", since it limits how large the field of view and the eye box can be at the same time. Their 2025 Nature Photonics prototype used volume Bragg grating waveguide couplers and a MEMS mirror that steers the illumination, creating a synthetic eye box of 9 x 8 mm with a 38 degree diagonal field of view in an optical stack less than 3 mm thick. Its SLM had an 8 μm pixel pitch; the authors note that higher diffraction orders lowered contrast, and that a pitch below 4.8 μm would separate those orders for 3 mm pupils. In its coverage of the work, UploadVR noted that the 38 degree diagonal field of view is far narrower than the roughly 115 degrees of the Meta Quest 3.

See also

• Diffractive optics
• Waveguide display
• Holographic optical element
• Holography
• Computer-generated holography
• Eye box
• Exit pupil
• Pixels per degree
• Metasurface
• Optical combiner