Speckle
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Speckle is the grainy, random intensity pattern produced when coherent light, such as laser light, is scattered by a rough surface and is then detected by an intensity detector with a finite aperture, such as a camera or the human eye. The many scattered wavelets reach each point of the detector with random relative phases; where they interfere constructively the point is bright, and where they interfere destructively it is dark.[1] The pattern is also called a speckle pattern, laser speckle or, when it degrades an image, speckle noise.[2]
Speckle matters for virtual reality and augmented reality because several display technologies proposed for headsets and glasses use lasers or other highly coherent light. A 2020 review of holographic near-eye displays in Optica notes that holographic displays commonly use lasers because the technique requires coherent light, and that the lasers produce speckle noise, "a grainy intensity pattern superimposed on the image".[3] Researchers at Stanford University and NVIDIA wrote in 2021 that image quality and eye safety of holographic displays "are fundamentally limited by the speckle introduced by coherent light sources".[4] The same physics is also put to use: some depth sensors and eye-tracking designs deliberately project or observe laser speckle.[5][6]
Physics
How speckle forms
In a laser projection display, the rough surface is the screen. Jahja Trisnadi of Silicon Light Machines described the effect in 2002: the image on the screen appears to be broken into small areas the size of the detector's resolution spot, and the intensity of each spot varies randomly from darkest, when the contributions of the scattering points inside it interfere destructively, to brightest, when they interfere constructively. Because of this, the characteristic grain size of the speckle equals the size of the detector's resolution spot.[1] Measured speckle therefore depends on the detecting optics as well as on the light source and the surface: the speckle contrast recorded by a camera changes with its pixel size, focal length, f-number and integration time.[7]
In holographic displays the cause is the same interference, produced inside the display rather than on a screen. Computer-generated holograms often add a random phase to the object information to spread it across the hologram plane; Pi, Liu and Wang explain that the phase differences then cause unwanted interference between adjacent pixels, "which are known as the speckle noise".[2] Lee and colleagues at Seoul National University note that in holographic near-eye displays speckle "is inevitably generated at the observer's retina".[8]
Statistics and speckle contrast
In his 1976 paper "Some fundamental properties of speckle" in the Journal of the Optical Society of America, Joseph W. Goodman of Stanford University modeled speckle in polarized, monochromatic light as a random walk in the complex plane. The model gives negative-exponential statistics for the intensity, with a contrast of one.[9] Goodman's later book Speckle Phenomena in Optics: Theory and Applications appeared in a second edition from SPIE in 2020.[10]
The standard measure is the speckle contrast C, the standard deviation of the intensity divided by its mean; its value lies between 0 and 1.[1] The signal-to-noise ratio is the inverse, mean divided by standard deviation. For fully developed speckle the standard deviation equals the mean, so C = 1 and the signal-to-noise ratio is also 1, which Lee and colleagues describe as "a severe noise".[8]
History
The granular appearance of laser light scattered from a surface was noticed soon after visible lasers became available; Trisnadi called speckle an obstacle "well-known since the invention of visible laser".[1] Early analyses were published in 1963, among them B. M. Oliver's "Sparkling spots and random diffraction" in Proceedings of the IEEE[11] and L. Allen and D. G. C. Jones's "An analysis of the granularity of scattered optical maser light" in Physics Letters.[12] Goodman's 1976 paper summarized the basic statistics of speckle and the diversity needed to reduce it, and Trisnadi's 2002 analysis of laser projection displays builds on that work.[9][1]
Speckle is a practical concern for laser projectors and laser cinema.[1][7] In 2016 the International Electrotechnical Commission published IEC 62906-5-2, "Laser display devices - Part 5-2: Optical measuring methods of speckle contrast", which specifies standard conditions and methods for measuring the monochromatic speckle contrast of laser display devices, including hybrid devices that combine lasers with LEDs.[13]
Perception
Measured speckle contrast depends on the camera's pixel size, focal length, f-number and integration time, so values from different studies can only be compared when the measurement procedure is disclosed.[7] A 2015 study in Scientific Reports by researchers from Vrije Universiteit Brussel, KU Leuven, iMinds and the projection division of Barco tested speckle tolerance with 186 participants in a movie theatre fitted with a prototype laser projector. Its camera setup was matched to typical characteristics of the human eye, with a 3.2 mm clear aperture.[7]
| Viewing condition | Red (639 nm) | Green (532 nm) | Blue (465 nm) | Source |
|---|---|---|---|---|
| Still images, speckle detection limit (earlier study by the same group) | 3.6% | 3.2% | 4.4% | [7] |
| Moving images (movie trailers), speckle disturbance limit | (6.9 ± 0.3)% | (6.0 ± 0.3)% | (4.8 ± 0.9)% | [7] |
The authors reported that speckle perception depends strongly on image content as well as on the measured speckle contrast, and that the disturbance limit for movies is "substantially larger than that for still images". They also cited earlier studies that estimated a detection threshold of about 3% for still images, while noting that those reports did not fully describe how speckle was measured.[7]
Speckle has also been described as a safety concern for near-eye holography. Lee and colleagues write that because speckle intensity is random, it might reach a hazardous intensity level for the human visual system, and Peng and colleagues call it "a potential safety hazard for the user".[8][4]
Reduction methods
The diversity principle
Goodman showed that reducing speckle contrast requires "diversity in polarization, space, frequency, or time". Adding M uncorrelated speckle patterns on an intensity basis lowers the contrast by a factor of 1/√M, while adding them as complex amplitudes gives no reduction.[9] Trisnadi applied this to laser projection: independent speckle patterns can be produced by varying the angle, polarization or wavelength of the illumination, and they must be averaged within the spatial and temporal resolution of the eye, whose integration time he put at about 50 ms.[1]
- Angle diversity: the projection optics illuminate several uncorrelated sub-areas within one resolution spot of the eye in sequence, for example with a time-varying diffuser.[1]
- Polarization diversity: a depolarizing screen splits the scattered light into two independent, orthogonally polarized patterns, giving a reduction of √2; Trisnadi reported that full polarization diversity, using two lasers or one laser with an optical path delay longer than its coherence length, can give a factor of 2.[1]
- Wavelength diversity: several lasers with sufficiently different wavelengths, a broadband laser, or a pulsed laser produce uncorrelated patterns.[1]
Trisnadi warned that combined methods do not automatically multiply: illumination from two angles with two wavelengths only yields four independent patterns if each wavelength is itself angle-diversified. With a Hadamard diffuser on a Grating Light Valve laser projector, his group reported a residual speckle contrast of 8%.[1]
Methods used in holographic displays
The 2020 Optica review groups speckle suppression for holographic near-eye displays into three strategies: superposition, spatial coherence construction, and temporal coherence destruction.[3] Later work added architectures that combine several sources.[14]
| Method | How it reduces speckle | Reported drawbacks |
|---|---|---|
| Time-multiplexed holograms | A series of holograms of the same object with statistically independent random phases is shown within the eye's response time, so the summed speckle has lower contrast[3] | Needs a spatial light modulator with a high frame rate, which makes dynamic display difficult[2]; consumes temporal bandwidth that may be needed elsewhere[14] |
| Rotating or vibrating diffuser | Speckle patterns are averaged within the modulator's frame time[3] | Larger form factor[3] |
| Complex amplitude modulation (smooth phase) | Uses a smooth phase map so that overlapping image points interfere constructively instead of randomly[3] | Requires a low-frequency wavefront and a small numerical aperture, which increases depth of field and weakens the focus cue[3]; non-uniform eye box[14] |
| Partially coherent sources (LEDs, superluminescent LEDs) | Reduced temporal or spatial coherence superimposes many independent speckle patterns[3][8] | Loss of resolution and depth of field[8]; LEDs add blur and are dimmer[4] |
| Multisource holography | An array of mutually incoherent sources and two spatial light modulators create differently speckled versions of the image that average at the image plane[14] | Demonstrated on a benchtop prototype[14] |
Applications in VR and AR
Holographic near-eye displays
Computer-generated holography can give each part of an image its own focal distance, which is why it is studied for VR and AR headsets, but the coherent light sources used by virtually all holographic displays produce speckle.[3][4] Several research groups have treated speckle as a central design constraint:
- Seoul National University (2020). Lee and colleagues built theoretical models of how a partially coherent source's angle and wavelength diversity trade speckle contrast against resolution, and used them to choose optimal sources for benchtop prototypes. Their optimal laser diode reduced speckle contrast by an average of 44.0% in experiment (47.5% predicted), and their optimal LED by 54.0% (51.5% predicted). They concluded that some loss of depth of field or resolution is "inevitable for considerable speckle reduction".[8]
- Stanford University and NVIDIA (2021). Yifan Peng, Suyeon Choi, Jonghyun Kim and Gordon Wetzstein modeled LEDs and superluminescent LEDs (SLEDs) inside a hologram optimization with camera-in-the-loop calibration. SLEDs are spatially coherent but temporally incoherent. In their tests the laser gave the strongest speckle and the LED the weakest but blurriest image, and the SLED gave "the best trade-off" between sharpness, contrast, brightness and speckle. In a 3D experiment they reported a peak signal-to-noise ratio of 21.94 dB for the SLED against 20.95 dB for the laser.[4]
- Reality Labs Research at Meta (2023). Grace Kuo, Florian Schiffers, Douglas Lanman, Oliver Cossairt and Nathan Matsuda proposed "multisource holography", which uses an array of sources and two spatial light modulators to suppress speckle in a single frame without sacrificing resolution. They reported up to a 10 dB increase in peak signal-to-noise ratio over an equivalent single-source system and validated the idea with a benchtop prototype.[14]
On the commercial side, VividQ announced in July 2021, alongside version 5.0.1 of its software development kit, a patent-pending optical design for speckle reduction offered as a licensable design; its announcement noted that holographic systems using coherent laser light "tend to suffer from the so-called 'speckle' (or laser noise)".[15]
Laser-illuminated AR optics
Lasers are also used outside holography in AR displays. In laser beam scanning, red, green and blue laser beams are combined and steered by a MEMS mirror to draw the image, which a waveguide then displays to the eye.[16] Patents from AR optics companies describe speckle countermeasures for laser-illuminated near-eye displays:
- A Magic Leap patent application by Pierre St. Hilaire (US 2019/0011722 A1, filed 5 July 2018 with a July 2017 provisional priority date) states that speckle "may severely degrade the image quality of projection displays that include laser light sources". It describes a diffusing element near a diode laser that reflects part of the beam back into the laser; together with a modulated drive current, the feedback drives the laser into a chaotic regime and broadens its emission spectrum to roughly 3 to 10 nm. The family includes US 11,009,718 B2, granted 18 May 2021.[17]
- A Lumus patent, US 10,969,590 B1 ("Near-eye display with laser diode illumination", granted 6 April 2021, priority 6 September 2018), notes that the coherence of laser-diode light "tends to give rise to interference-related artefacts". For a light-guide display whose output is coupled out by parallel partially reflective surfaces, it describes driving the laser diode at a power level that keeps the coherence length below twice the spacing between adjacent surfaces, which the patent says typically eliminates speckle or reduces it to an acceptable level.[18]
These patents describe proposed techniques; they do not by themselves show which shipping products use them.
Speckle as a sensing signal
Projected laser patterns are used for depth sensing. Describing the original Microsoft Kinect, Kourosh Khoshelham and Sander Oude Elberink wrote in 2012 that its laser beam is split by a diffraction grating "to create a constant pattern of speckles projected onto the scene"; the infrared camera's image is correlated against a stored reference pattern, and shifts of each speckle along the baseline give depth by triangulation.[5] They also observed that in strong light the projected speckles appear with low contrast, which can cause gaps and outliers in the point cloud.[5] An earlier PrimeSense patent application (WO 2007/043036, priority 11 October 2005, inventors Zeev Zalevsky, Alexander Shpunt, Aviad Maizels and Javier Garcia) describes reconstructing 3D surfaces by projecting "a laser random speckle pattern" onto an object and measuring its shifts against a reference image.[19] See Structured light for the wider technique.
Speckle has also been proposed for eye tracking in head-mounted displays. A DigiLens patent, "Apparatus for eye tracking" (US 9,456,744 B2, priority May 2012, granted 4 October 2016, with Jonathan Waldern among the inventors), tracks laser light reflected from the eye as speckle.[20] An Avegant patent, "Relative position based eye-tracking system" (US 10,884,492 B2, priority July 2018, granted 5 January 2021), illuminates a small area of the eye with a laser diode or an LED; when a laser diode is used, its reflection from the eye's surface forms a speckle pattern, and an optical sensor tracks eye features through optical flow. The patent names use in a head-mounted display.[6]
See also
References
- ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 Jahja I. Trisnadi (2002). "Speckle contrast reduction in laser projection displays". Proceedings of SPIE, vol. 4657 (Projection Displays VIII). Silicon Light Machines. https://www.siliconlight.com/wp-content/themes/siliconlight/pdf/speckle-spie.pdf. Retrieved 2026-10-15.
- ↑ 2.0 2.1 2.2 Dapu Pi, Juan Liu, Yongtian Wang (2022-07-26). "Review of computer-generated hologram algorithms for color dynamic holographic three-dimensional display". Light: Science & Applications, vol. 11, article 231. https://doi.org/10.1038/s41377-022-00916-3. Retrieved 2026-10-15.
- ↑ 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Chenliang Chang, Kiseung Bang, Gordon Wetzstein, Byoungho Lee, Liang Gao (2020-11). "Toward the next-generation VR/AR optics: a review of holographic near-eye displays from a human-centric perspective". Optica, vol. 7, no. 11, pp. 1563-1578. https://doi.org/10.1364/OPTICA.406004. Retrieved 2026-10-15.
- ↑ 4.0 4.1 4.2 4.3 4.4 Yifan Peng, Suyeon Choi, Jonghyun Kim, Gordon Wetzstein (2021-11-12). "Speckle-free holography with partially coherent light sources and camera-in-the-loop calibration". Science Advances, vol. 7, no. 46, article eabg5040. https://doi.org/10.1126/sciadv.abg5040. Retrieved 2026-10-15.
- ↑ 5.0 5.1 5.2 Kourosh Khoshelham, Sander Oude Elberink (2012-02-01). "Accuracy and Resolution of Kinect Depth Data for Indoor Mapping Applications". Sensors, vol. 12, no. 2, pp. 1437-1454. https://doi.org/10.3390/s120201437. Retrieved 2026-10-15.
- ↑ 6.0 6.1 Aaron Matthew Eash et al. (2021-01-05). "US10884492B2 - Relative position based eye-tracking system". Google Patents. Avegant Corp.. https://patents.google.com/patent/US10884492B2/en. Retrieved 2026-10-15.
- ↑ 7.0 7.1 7.2 7.3 7.4 7.5 7.6 Guy Verschaffelt, Stijn Roelandt, Youri Meuret, Wendy Van den Broeck, Katriina Kilpi, Bram Lievens, An Jacobs, Peter Janssens, Hugo Thienpont (2015-09-15). "Speckle disturbance limit in laser-based cinema projection systems". Scientific Reports, vol. 5, article 14105. https://doi.org/10.1038/srep14105. Retrieved 2026-10-15.
- ↑ 8.0 8.1 8.2 8.3 8.4 8.5 Seungjae Lee, Dongyeon Kim, Seung-Woo Nam, Byounghyo Lee, Jaebum Cho, Byoungho Lee (2020-11-02). "Light source optimization for partially coherent holographic displays with consideration of speckle contrast, resolution, and depth of field". Scientific Reports, vol. 10, article 18832. https://doi.org/10.1038/s41598-020-75947-0. Retrieved 2026-10-15.
- ↑ 9.0 9.1 9.2 J. W. Goodman (1976-11-01). "Some fundamental properties of speckle". Journal of the Optical Society of America, vol. 66, no. 11, pp. 1145-1150. https://doi.org/10.1364/JOSA.66.001145. Retrieved 2026-10-15.
- ↑ Joseph W. Goodman (2020). "Speckle Phenomena in Optics: Theory and Applications, Second Edition". SPIE Press. SPIE. https://doi.org/10.1117/3.2548484. Retrieved 2026-10-15.
- ↑ B. M. Oliver (1963). "Sparkling spots and random diffraction". Proceedings of the IEEE, vol. 51, no. 1, pp. 220-221. https://doi.org/10.1109/PROC.1963.1686. Retrieved 2026-10-15.
- ↑ L. Allen, D. G. C. Jones (1963-12). "An analysis of the granularity of scattered optical maser light". Physics Letters, vol. 7, no. 5, pp. 321-323. https://doi.org/10.1016/0031-9163(63)90054-4. Retrieved 2026-10-15.
- ↑ "IEC 62906-5-2:2016 Laser display devices - Part 5-2: Optical measuring methods of speckle contrast". IEC Webstore. International Electrotechnical Commission. 2016-06-07. https://webstore.iec.ch/publication/25037. Retrieved 2026-10-15.
- ↑ 14.0 14.1 14.2 14.3 14.4 14.5 Grace Kuo, Florian Schiffers, Douglas Lanman, Oliver Cossairt, Nathan Matsuda (2023-12-05). "Multisource Holography". ACM Transactions on Graphics, vol. 42, no. 6 (SIGGRAPH Asia 2023). https://doi.org/10.1145/3618380. Retrieved 2026-10-15.
- ↑ "VividQ Reveals New Solutions for High-Quality Holographic Display Development". VividQ. 2021-07-22. https://www.vividq.com/news/vividq-reveals-new-solutions-for-high-quality-holographic-display-development. Retrieved 2026-10-15.
- ↑ Ulrich Hofmann (2023-11-29). "Solve Augmented-Reality Display Challenges with Laser Beam Scanning". Electronic Design. https://www.electronicdesign.com/technologies/industrial/displays/ar-vr/article/21278142/oqmented-solve-augmented-reality-display-challenges-with-laser-beam-scanning. Retrieved 2026-10-15.
- ↑ Pierre St. Hilaire (2019-01-10). "US20190011722A1 - Speckle-reduction in virtual and augmented reality systems and methods". Google Patents. Magic Leap, Inc.. https://patents.google.com/patent/US20190011722A1/en. Retrieved 2026-10-15.
- ↑ Yochay Danziger, Ronen Chriki, Nitzan Livneh (2021-04-06). "US10969590B1 - Near-eye display with laser diode illumination". Google Patents. Lumus Ltd.. https://patents.google.com/patent/US10969590/en. Retrieved 2026-10-15.
- ↑ Zeev Zalevsky, Alexander Shpunt, Aviad Maizels, Javier Garcia (2007-04-19). "WO2007043036A1 - Method and system for object reconstruction". Google Patents. Prime Sense Ltd.. https://patents.google.com/patent/WO2007043036A1/en. Retrieved 2026-10-15.
- ↑ Milan Momcilo Popovich, Jonathan David Waldern, Alastair John Grant (2016-10-04). "US9456744B2 - Apparatus for eye tracking". Google Patents. DigiLens Inc.. https://patents.google.com/patent/US9456744B2/en. Retrieved 2026-10-15.