Shack-Hartmann wavefront sensor

A Shack-Hartmann wavefront sensor (also written Hartmann-Shack wavefront sensor) is an optical instrument that measures the shape of a wavefront of light with an array of small lenses placed in front of an image sensor. Each lenslet focuses its own portion of the incoming light to a spot. The position of the spot depends on the average slope of the wavefront over that lenslet, so the pattern of spot displacements can be converted into local slopes and then numerically integrated into a map of the whole wavefront.

The sensor was developed in the late 1960s at the Optical Sciences Center of the University of Arizona by Roland Shack and his graduate student Ben Platt, who replaced the holes of the Hartmann screen test (devised by the astronomer Johannes Hartmann in 1900) with lenslets. It became a standard tool in adaptive optics for astronomy, in measuring the aberrations of the human eye, and in testing optics and laser beams.

In virtual reality (VR) and augmented reality (AR) research, Shack-Hartmann sensors are used to measure how a viewer's eye focuses while looking at a head-mounted display, which is needed to study the vergence-accommodation conflict and displays that try to solve it. Oculus Research built one into its 2017 multifocal display testbed, patents assigned to Meta and Apple describe headsets with a built-in Shack-Hartmann sensor, and the same sensor appears in head-mounted vision simulators and in tools for aligning headset optics.

Reviewed 13 October 2026. Checked principle, history (Hartmann test, Shack-Platt lenslets, Wilson, Bille, Rochester), the Oculus testbed paper and blog, Meta and Apple patents, the Murcia headset simulator, Axiom note and KAIST/BGU papers against the cited sources. About review dates.

How it works

A Shack-Hartmann sensor has two main parts: a microlens array and an image sensor placed at the focal plane of the lenslets. The array divides the incoming wavefront into many small sub-apertures. Within each sub-aperture the wavefront is treated as a tilted plane wave, and the lenslet focuses it to a spot whose position corresponds to the average slope of the wavefront across that lenslet. Measuring how far each spot has moved from its reference position gives the local slope. Go and colleagues describe the same chain: the displacement of the spot pattern is related to the incident wavefront angle, and in turn to the optical phase gradient, and a two-dimensional phase map is obtained by numerically integrating that gradient.

Turning a grid of slope measurements into a wavefront is a reconstruction problem. In a 1980 paper in the Journal of the Optical Society of America, W. H. Southwell of Rockwell International treated it as least-squares fitting, introduced a zonal estimation model, compared zonal and modal estimation, and analyzed how noise in the slope measurements propagates into the reconstructed wavefront. In their 1994 measurements of the human eye, Liang and colleagues reconstructed the wavefront from the measured slopes with Zernike polynomials and derived the eye's aberrations from the estimated coefficients.

The design is simple and works in a single camera exposure. Go and colleagues contrast it with interferometric methods, which need bulky set-ups with a reference arm and are sensitive to small wavelength-scale fluctuations. Its performance is limited by the lenslets themselves. To avoid cross-talk between neighboring lenslets, the incoming light must stay within an angular range set mainly by the lenslet's numerical aperture, and shortening the focal length widens that range at the cost of angular resolution. According to the same paper, the minimum feature size and maximum curvature that conventional fabrication can produce keep lenslets at about 100 micrometers with a low numerical aperture, which limits the sampling density to around 100 per square millimeter and the maximum measurable angle to around 1 degree. The size of each focal spot also limits how precisely its displacement, and therefore the local slope, can be measured.

History

Hartmann screen test

Johannes Hartmann (1865-1936) was a German astrophysicist who worked at Potsdam on the "Great Refractor", an 80 cm refracting telescope whose optics were not good enough for usable photographic images. To find the fault, he placed a screen with a series of holes over the telescope's aperture and exposed photographic plates on either side of focus. Each hole passed a separate bundle of rays, and by connecting corresponding spots on the two plates he could see where the rays from different parts of the aperture crossed the axis. The test showed that the problem was in the main lens, which was then refigured. The University of Arizona dates the screen test to 1900.

Shack and Platt's lenslet array

According to Jim Schwiegerling and Daniel Neal, the Shack-Hartmann sensor came out of a Cold War project. The US Air Force wanted to image satellites from ground-based telescopes despite atmospheric turbulence and approached Aden Meinel and the Optical Sciences Center (OSC) at the University of Arizona. Meinel suggested diverting part of the incoming light to a Hartmann test so that the atmospheric aberrations could be recorded at the moment each image was taken, and Roland Shack was asked to find out whether this was feasible.

A satellite sends little light to the ground, and a Hartmann screen blocks all of it except what passes through the holes. Shack's first change was to put a lens in each hole, concentrating the light into a focal spot that was easier to record. His second was to drop the screen and let the lenses grow until their edges met, so that every photon reaching the array ended up in a spot. Commercial lenslet arrays existed but did not have suitable dimensions, so Shack and Ben Platt, then a graduate student, made their own. They ground and polished 50 grooves across a disk of Cer-Vit glass with a concave cylindrical rod, cut two square pieces from the grooved area, and thermally pressed a square of Plexiglas between the two pieces, oriented at 90 degrees to each other; Platt did the heating in his home kitchen oven. The result was an array of crossed cylindrical lenslets. Schwiegerling and Neal give the lenslet aperture as 1 mm and note that at that size the crossed cylinders behave like spherical lenses. The finished sensor was delivered to the Air Force satellite-tracking telescope at Cloudcroft, New Mexico, but was never used, and its fate is unknown.

In a short piece titled "Lenticular Hartmann Screen" in the March 1971 Optical Sciences Center newsletter, Platt and Shack described the technique as "a modification of the very old Hartmann test", and Brian Bauman, a 2003 doctoral graduate of the center, has written that the spring 1971 meeting of the Optical Society of America was probably the first time the lenslets were presented to the optics community. In 2001 Platt and Shack published their own account of the sensor's history in the Journal of Refractive Surgery.

Lasers, telescopes and adaptive optics

Through the 1970s and 1980s the Department of Defense needed wavefront sensors to correct mirrors that distorted under the heat of high-energy lasers. Much of that work was classified. Dale Neal, program manager for several of these projects, recalled in remarks quoted by Schwiegerling and Neal that Julius Feinleib, then at Itek, built one of the first Shack-Hartmann sensors around 1977.

Astronomers were slow to take up the idea. Shack handed out lenslet arrays to visiting astronomers in the early and mid-1970s, but the potential was not recognized until Ray Wilson of the European Southern Observatory (ESO) visited the OSC in 1976. After a second visit in 1977, Wilson took one of the original lenslet arrays back with him and used it to demonstrate active correction of a 1 m mirror. CCD cameras, which allowed the spot patterns to be captured and analyzed quickly, were the other technology that made such systems practical. ESO's 3.58 m New Technology Telescope, whose flexible main mirror is reshaped by actuators during observations, saw first light on 23 March 1989. Writing in 2005, Schwiegerling and Neal described the Shack-Hartmann method as "by far the most actively used technology" for correcting astronomical telescopes. Shortly after receiving the 2010 Kavli Prize in Astrophysics, Wilson wrote that in a just world he would share the prize with Roland Shack, among others, "for inventing the Shack-Hartmann detector", without which he would have had no suitable detector for his active optics. In adaptive optics the sensor is paired with a correcting element such as a deformable mirror.

Ophthalmology and vision science

In the mid-1980s Shack visited Josef Bille at the University of Heidelberg, and Bille's group became the first to apply the technique to the eye, first to measure the shape of the cornea and later to measure the aberrations of the whole eye. In a 1994 paper, Junzhong Liang, Bernhard Grimm, Stefan Goelz and Bille measured the light reflected from a spot focused on the fovea and concluded that the method gave a fast, precise and objective measurement of the eye's aberrations.

At the University of Rochester, Liang, David Williams and Donald Miller combined a Hartmann-Shack sensor with a deformable mirror to correct the eye's monochromatic aberrations. Their 1997 paper reported that the correction gave normal eyes better than normal optical quality, raised observers' contrast sensitivity to fine patterns, and allowed a fundus camera to resolve structures the size of single cells in the living human retina. Laser Focus World reported that the system's sensor used a hexagonal array of 217 lenslets and that its mirror had 37 lead zirconate-lead titanate actuators. Schwiegerling and Neal wrote in 2005 that the Shack-Hartmann sensor had become the most widespread and well-known technology for customized refractive correction.

Applications in VR and AR

Measuring accommodation in display research

Most head-mounted displays show images on a single fixed focal plane, so the eye's focusing (accommodation) and the eyes' convergence (vergence) can receive conflicting cues. Varifocal and multifocal displays try to remove this conflict, and testing them requires measuring how the eye actually focuses. A Shack-Hartmann sensor does this objectively by measuring the defocus of light returning from the retina, the same principle Liang and colleagues used in 1994.

In January 2018, Oculus described how its research division built a "perceptual testbed" for this purpose. The project began when optical scientist Yusufu Sulai, whose earlier research had centered on high-resolution retinal imaging systems, started building a Shack-Hartmann wavefront sensor; the finished system combined a wavefront sensor, a multi-planar display and an eye tracker. Kevin MacKenzie said the team wanted to improve its ability to measure the accommodation response accurately.

The testbed was described in a SIGGRAPH Asia 2017 paper by Olivier Mercier, Sulai, Douglas Lanman and colleagues at Oculus Research, Université de Montréal and McGill University. It measured the accommodation of the viewer's left eye at 67 Hz. Near-infrared light from a superluminescent diode was coupled into the eye with a weakly reflecting beam splitter, and light reflected from the retina was separated from the display path by a hot mirror and relayed to an Imagine Optic HASO wavefront sensing camera with a 34 by 34 microlens array, giving a 294 micrometer pitch at the system's entrance pupil. The testbed also included eye tracking cameras running at 250 Hz.

In a pilot study, four observers watched a target that moved sinusoidally in depth between 0.6 and 1.8 diopters at 0.1 Hz, viewed with one eye so that only retinal blur could drive focusing. Both scene decomposition methods tested drove changes in accommodation. Linear blending produced an accommodative gain of about 0.61, consistent with earlier studies, while the authors' optimized decomposition produced a significantly lower gain of 0.28.

Headset designs in patents

Several patents describe building the sensor into a headset. US patent 10,656,707, "Wavefront sensing in a head mounted display", filed on 10 April 2018 and granted on 19 May 2020 with Robin Sharma, Marina Zannoli and Kevin James MacKenzie as inventors, was assigned to Facebook Technologies and is now held by Meta Platforms Technologies. It describes an eye sensor with a tunable lens that has a micro-lens state, in which the lens acts as a lenslet array and the sensor works as a Shack-Hartmann accommodation sensor measuring the eye's focusing state, which depends on the shape of the crystalline lens, and a neutral state, in which the same sensor is used for eye tracking.

US patent 11,874,530, "Head-mounted display device with vision correction", assigned to Apple (priority date 17 May 2017, granted 16 January 2024), describes a Shack-Hartmann sensor inside a head-mounted device, one of several eye-measuring options it lists alongside Tscherning and ray-tracing aberrometers. Near-infrared light is routed to the user's eye through waveguides, the returning light reaches a two-dimensional lenslet array that forms a grid of spots on a camera, and control circuitry fits Zernike polynomials to the spot measurements to determine refractive errors. The patent describes obtaining spherical correction by changing the separation between the display and the eye, and cylindrical correction by tuning a tunable cylindrical lens. A patent describes a possible design and does not show that a product uses it.

Head-mounted vision simulators

Vision scientists have also miniaturized adaptive optics into a headset form. In 2024, Shoaib Soomro, Pablo Artal and colleagues at Voptica and the Laboratorio de Óptica of the University of Murcia described a head-mounted adaptive optics visual simulator in Biomedical Optics Express. It combines a microdisplay for visual stimuli, a liquid crystal on silicon spatial light modulator for changing the wavefront, and a Hartmann-Shack sensor built from an off-the-shelf microlens array (3.17 mm focal length, 192 micrometer pitch) and a 3.1-megapixel CMOS camera. A 780 nm laser kept below 50 microwatts creates the reference spot on the retina. The device measures about 20 by 10 by 15 cm and weighs about 0.5 kg. In tests with an artificial eye it measured and compensated induced defocus, astigmatism and higher-order aberrations, reaching a post-correction resolution of up to 37.5 cycles per degree, and in subjective tests its defocus curves closely matched those of a commercial desktop simulator. The authors present portability and clinical access, rather than VR or AR, as the purpose of the design.

Alignment and testing of headset optics

Because the sensor measures wavefront curvature directly, it can also be used when aligning headset optics. In an application note on Imagine Optic's HASO sensors, Axiom Optics notes that AR and VR headsets image their screens to a virtual plane and that the broadband light of the display itself can be used for the measurement. It states that the short-wave infrared HASO model measures wavefront curvature with an accuracy of plus or minus 0.002 per meter (diopters) over the 900 to 1700 nm band, equivalent to a point source about 300 m away.

Research

Recent research aims to remove the limits set by conventional lenslets. In 2024, Gi-Hyun Go, Mooseok Jang and colleagues in the Department of Bio and Brain Engineering at KAIST replaced the lenslets with an array of metalenses 12.95 micrometers in diameter with a 30 micrometer focal length. Their "meta Shack-Hartmann" sensor reached a sampling density of 5,963 per square millimeter and an acceptance angle of up to plus or minus 8 degrees, which the authors report is an order of magnitude better than a traditional sensor, and they used it for single-shot phase imaging of complex objects including biological tissue patterns. Researchers at Ben-Gurion University of the Negev replaced each lenslet with a coded phase mask and used coded aperture correlation holography to locate the shifted patterns; they reported a mean square wavefront error one order of magnitude lower than a regular Shack-Hartmann sensor.

See also

• Microlens array
• Adaptive optics
• Deformable mirror
• Optical aberration
• Vergence-accommodation conflict
• Varifocal display
• Eye