Exit pupil

The exit pupil of an optical system is the image of its aperture stop as seen from the image side, formed by the optical elements that follow the stop. In visual instruments such as binoculars, telescopes and microscopes, the exit pupil is where the observer's eye should be placed. In head-mounted displays and AR glasses, its size and position decide how far the eye can move before the image is clipped. The related eye box is the three-dimensional region in which the eye sees the whole image, and its volume depends strongly on the exit pupil size. In waveguide combiners, a technique called exit pupil expansion copies a small projector pupil many times across the lens so that the eye box becomes large enough for different wearers.

Reviewed 27 September 2026. Checked every definition, number and attribution against the cited SPIE, RP Photonics, Nikon, USAARL HMD guide, Xiong et al. 2021 review, Crossref records of the Nokia and Cakmakci papers, the Magic Leap patent, the Vuzix SEC exhibit and Display Daily. About review dates.

Definition

Every imaging system has an aperture stop, the opening that limits the cone of light passing through it. Seen from the object side through the elements in front of it, that stop appears as the entrance pupil; seen from the image side through the elements behind it, it appears as the exit pupil. The entrance and exit pupils lie in conjugate planes of the complete system. According to the RP Photonics Encyclopedia, the exit pupil may coincide with a physical aperture on the image side, or it may be a virtual image at almost any axial position, often behind the optical system.

The distance between the exit pupil and the last optical surface (or the end of the eyepiece) is the eye relief. A 2009 U.S. Army design guide for helmet-mounted displays notes that this classical definition, measured along the optical axis from the last surface to the exit pupil, can mislead in head-worn devices whose last surface is a tilted combiner. In those systems the actual clearance between the face and the nearest part of the optics may be much smaller.

Visual instruments

The eyepieces of telescopes and microscopes are normally designed so that their exit pupil coincides with the pupil of the observer's eye. If the exit pupil is larger than the eye's pupil, part of the light cannot enter the eye and the image is dimmer than it could be. If it is smaller, the eye's full angular resolution is not used.

For binoculars, the exit pupil can be seen as the bright circle in the centre of each eyepiece when the instrument is held about 30 cm from the face and pointed at a bright light. Nikon gives its diameter as the effective diameter of the objective lens divided by the magnification, so an 8x42 binocular has an exit pupil of 5.3 mm. The same guide states that the human pupil normally opens to about 2 mm in daylight and 7 mm in the dark.

Exit pupil in head-mounted displays

Pupil-forming and non-pupil-forming optics

Head-worn display optics fall into two design forms, pupil forming and non-pupil forming, a split used in Ozan Cakmakci and Jannick Rolland's 2006 review of head-worn displays. The U.S. Army guide describes the non-pupil-forming type as a simple magnifier: the easiest to design, the least expensive to make, and the lightest and smallest. A pupil-forming design works like a compound microscope, binoculars or a periscope. A first group of lenses forms an intermediate image of the image source, and a second group relays it and forms a pupil, "a hard image of the aperture stop".

The longer path of a pupil-forming design leaves room for mirrors that fold the optics around the head, and the extra lenses give more freedom to correct aberrations. The drawbacks are more weight, more cost, precise fitting, and no imagery at all outside the exit pupil. The same guide states that an exit pupil in the strict sense exists only in pupil-forming designs. For non-pupil-forming designs it prefers the term "viewing eyebox", because outside that region the image is vignetted or clipped but still partly visible. Among military systems it cites, the IHADSS and HIDSS helicopter displays are pupil-forming designs.

Size and eye relief

A larger exit pupil makes a head-mounted display more tolerant of the device moving on the head. For flight HMDs with pupil-forming optics, the U.S. Army guide gives 12 to 15 mm as an acceptable exit pupil, while noting that the operationally successful IHADSS has only a 10 mm exit pupil. The off-axis part of the exit pupil has an outsized effect on the size and weight of the optics, and the guide states that trimming it to 50 percent of the on-axis diameter reduces size and weight without significantly reducing performance. To leave room for spectacles, it gives a generally accepted minimum eye relief of 25 mm.

Relation to the eye box and field of view

In near-eye displays for VR and AR, Xiong and colleagues describe the exit pupil as the area where the ray bundles from the whole field of view intersect. They define the eye box as the region within which the full field of view can be seen without vignetting, a 3D volume that depends strongly on the exit pupil size. A larger eye box tolerates more variation in interpupillary distance and more headset movement.

In geometric optics the field of view and the eye box trade against each other because of the conservation of etendue (the optical invariant), and raising the system etendue requires larger optics. The exit pupil also affects brightness. For a fixed input luminous flux, the output luminance of an AR combiner depends on its field of view and exit pupil; Xiong et al. calculate that a lossless combiner with a 60 degree diagonal field of view and a 10 mm square exit pupil could reach about 17,000 nit per lumen. As an example of a free-space design, the same review cites a freeform total-internal-reflection prism combiner by Cheng et al. with a 54 degree diagonal field of view and an 8 mm exit pupil diameter.

At the other extreme, Maxwellian-view displays focus a point source into the eye pupil. Their main weakness is a very small exit pupil: if the eye pupil moves slightly away from the viewpoint, the image disappears. In holographic displays the etendue is set by the spatial light modulator, so a larger exit pupil comes at the cost of a smaller field of view.

Exit pupil expansion

A waveguide combiner traps light from a small projector inside a thin plate by total internal reflection. At each reflection, part of that light is coupled out toward the eye. The same image therefore leaves the plate at many points, which Xiong et al. call exit pupil expansion (EPE); they describe it as the distinctive feature of waveguide combiners because it "effectively enlarges the system etendue" and with it the effective eye box. The cost is brightness: the review notes that a larger eye box or field of view usually lowers image brightness, which is a problem for waveguide AR systems with EPE in strong ambient light.

Expansion in one direction produces a large eye box only if the projector's pupil is already large in the other direction, which is hard for the light engine. Practical designs therefore favour two-dimensional EPE, built from two one-dimensional stages. In a typical diffractive waveguide, a turning grating duplicates the light in one direction and redirects it, and the out-coupler then expands it in the other direction. A Magic Leap patent application by Robert D. Tekolste and Victor K. Liu, published in 2018, describes the same layout. An orthogonal pupil expander (OPE) region redirects part of the guided light toward an exit pupil expander (EPE) region, which sends it out of the eyepiece toward the viewer's eye. Reflective (geometric) waveguides use partial mirrors in place of gratings. Xiong et al. cite a design by Wang et al. with five partial mirrors, a 50 by 30 degree field of view and a 4 mm exit pupil with one-dimensional EPE.

History of diffractive exit pupil expanders

Researchers at Nokia Research Center in Finland published a series of papers on diffractive exit pupil expanders in the late 2000s. In a 2006 paper in the Journal of the Society for Information Display, Tapani Levola studied how diffractive optical elements on planar waveguides could shrink the optics of near-to-eye displays. An invited SID paper by Levola the same year described a biocular display using a diffractive planar waveguide as an EPE. The paper called the design ergonomically excellent but limited by low efficiency and uneven light distribution, and reported that deep slanted gratings could exceed 90 percent diffraction efficiency.

Later Nokia papers addressed wearability and field of view. In the 2008 "chevron" EPE of Levola and Viljakaisa Aaltonen, the in-coupling area was divided into two parts with opposite slant angles, so the plate could be cut into left and right halves and tilted into a chevron shape that follows the face like conventional eyeglasses. In 2009 Pekka Äyräs, Pasi Saarikko and Levola wrote that diffractive expanders of this type usually could not exceed a field of view of much more than 25 degrees. They demonstrated a two-plate stacked expander for green light with a field of view of more than 40 degrees.

On 21 October 2011, Vuzix announced a license from Nokia to develop and produce see-through waveguide optics for near-eye displays based on Nokia's exit pupil expanding (EPE) technology, which Nokia had developed and prototyped over about ten years. In 2015, Display Daily reported that Levola and Saarikko, the principal developers of Nokia's surface relief grating waveguides, had later joined Microsoft. It also wrote that one of their Microsoft patent filings, which used multiple waveguides for different colours, was "very likely" the display in the newly announced HoloLens.

See also

• Eye box
• Eye relief
• Field of view
• Waveguide display
• Diffractive waveguide
• Near-eye display
• Vignetting