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First insights about Apple Vision Pro optics

Apple Vision Pro (AVP) comes with custom catadioptric lenses. The catadioptric optics is known from telescopes where set of mirrors are folding optical path to reduce the size of the telescope. For the VR pancake lenses, the catadioptric approach is also used to fold optical path to allow very compact lenses modules. The difference is that telescope serves very narrow Field of View (FoV) such that mirrors are with reduced aperture and hole, while wide FoV pancake lens is having elements for light polarization manipulation. The pancake module could be based on single lens element (as it is implemented in PICO 4) or on a multiple lenses (as it is in Quest Pro) {we will add link about Quest Pro and Pico 4 optics} . For simplicity we will use schematic based on two lenses elements as shown on the figure below: 

pancake optics generic scheme by Hypervision LTD

The most challenging component in the scheme above is a retarder#2 (also known as quarter wave plate - QWP) that changes linear polarization to circular. The QWP couldn't be deformed and should stay flat that brings constraints to the pancake module design, since it is embedded between front and back lenses. Therefore, the solutions of pancake modules available on the market are limited to have at least one flat surface that is constraining optimizations in the VR optics design. However, this limitation was resolved in AVP optics.

By taking first glance on the 3-element of AVP pancake module it is strikes the eyes that two elements are having big difference in the vertical and horizontal sides thickness. As shown on the picture by (1), the near to display lens element side thickness is much bigger than the top thickness. An in opposite, the middle lens element has top thickness much bigger than the side thickness as shown by (2). Assuming that AVP optics has rotational symmetry - how that could be explained ? We knew the answer because being familiar with Facebook patent US20180120579A1.      

Reproduction of Apple Vision Pro pancake visual module by Hypervision LTD

Facebook patent US20180120579A1.   


The US20180120579A1 patent by Facebook teaches how to resolve the restriction for QWP (140) deformation. As could be seen on the figures above and Claim 6 from the right, the QWP 140 is embed between two cylindrical surfaces, such that flat QWP 140 thin film is cylindrically rolled between surfaces 404 and 416 Fig 4c (or between lenses 104 and 106). The cylindrical rolling of flat film is preserving it from deformation and therefore QWP 140 is preserving its linear to circular polarization conversion property.

Claim 6. The HMD of claim 1, wherein the back second surface of the back curved optical element has a concave cylindrical surface profile, and the front second surface of the front curved optical element has a convex cylindrical surface profile that coincides with the concave cylindrical surface profile of the back curved optical element, wherein the front second surface and the back second surface are coupled to each other with the adhesive element

Apple Vision Pro Optics 

Next thought was that Apple was delaying release of the MR headset for several years and must have applied for patents that are already published (it takes about 18 months for the pending patent to show-up on the web after the application). Indeed Apple applied several patents about the optical solution, with priority from Feb-2017 and the last application US20210132349A1 is well describing what was shown on the AVP release pictures. 

Apple Vision Pro pancake lens module vertical and horizontal cuts to show cylindric retarder reproduced by Hypervision LTD

The claims and figures inside the US20210132349A1 patent are bridging evidence that QWP 28 is cylindrically rolled between S6 and S7 surfaces of the lenses 26 and 32. Actually, the lenses 26 and 32 are creating single element lens with unique feature to convert polarized light. This way APV overcame the limitation of other pancake lenses requiring to have have flat surface for QWP lamination. 

Claim 7. The head-mounted display defined in claim 1, wherein the second surface is cylindrically concave and wherein the third surface is cylindrically convex


Claim 8, The head-mounted display defined in claim 1, wherein the second and third surfaces are mating cylindrical surfaces.

Field of View (FoV) Estimations

Disclaimer: the reported horizontal FoV of AVP is between 100° - 110°. In the modelling and analysis below, we show wishful implementation resulting in bigger FoV than reported.

The beauty of the AVP pancake optics is concave surface near the eye allowing to implement relatively compact optics with big FoV. By analyzing WEB pictures of lenses and uDisplay and approximately knowing the dimensions we did the following assumptions:

  1. Interpupillary distance (IPD) 65mm (default) and expected to be adjustable; according reviews there are 3 positions

  2. Eye Relief (ER) of 12mm. The face interface is wide, however, glasses can't be used, so ER is 12mm or less.

  3. There is some tilt between left and right visual modules - we assumed 5° (may be little more)

  4. uDisplay active area: 27.6 x 22.8 mm.

Considering assumptions above we did modeling as show on the picture below:

Modeling of Apple Vision Pro biocular optics for field of view calculation reproduced by Hypervision LTD

It is important to differentiate between peripheral FoV (measured for straight gazing eye) and rotational FoV (indicating maximal rotation of the eye for gazing on the off-center virtual stimulations). The comfort zone of eye rotation is +/-30° and they eye could reach 50° under enforcement. The peripheral FoV (shown for the left eye) is naturally larger than rotational (shown for the right eye) due to simple geometry, where pupil location is 8mm closer to the lens than center of eye rotation. So the horizontal rotational monocular FoV is: 42° (nasal) + 50° (temporal) = 92° and horizontal biocular FoV is twice temporal and therefore 2 x 50° = 100°. However, all marketing figures are talking about Peripheral FoV and that is shown in the next paragraph.


By doing measurements from the model above here are results for Peripheral FoV:

  • Horizontal: Nasal 50°+Temporal 60° => total: monocular horizontal 50+60° = 110°; biocular horizontal 2x60° = 120°;

  • Stereo overlap:  2x50° = 100°

  • Vertical: Top 45°+Bottom 45°; therefore Vertical FoV = 90°

Lets make rough verification of FoV based on aspect ratio of assumed display dimensions: 27.6 : 22.8​ = 1.21, while monocular horizontal : vertical is 110° : 90° = 1.22. Therefore, assumptions make sense.

To summarize, the assumed (and wishful) FoV (H x V) is 120° x 90°.

PPD Estimation

For PPD calculation the following assumptions will be made:

  1. Linear offset from the display center per angle of view 

  2. Pixel size of 7.395 um; based on assumed aspect ratio, square pitch, and given 23Mpx per two displays.


The assumption (2) and uDisplay dimensions resulting in resolution of 3,732 x  ​3083. Most probably the correct horizontal resolution is 3,840 that is double of standard 1,920. 

By sticking to the resolution + assumption (1) + assumed FoV, by using vertical FoV and resolution, the calculated PPD is 3,083 px / 90° ~ 34[ppd]. Considering that PPD could be non-linear the result for the central sweet spot could be +/- 10% different. Also, the actual FoV and resolution aspect-ratio could be different and for lower FoV and higher pixel count + non-linearity, the actual PPD could reach 40[ppd].

Ray Tracing and the the Eye-box 

One of the advantages of the well designed pancake lens is edge-to-edge clarity and AVP is expected to be such. Big eyebox provides possibility to misalign eye visual and optics central axes + different ER from nominal.  The pancake lens, in general, also provides bigger eyebox versus aspheric or Fresnel lenses. However, pancake lenses designed for uDisplay, where pixels are very small (7.4um like in AVP case) and magnification is very strong, there is no enough resource for the eyebox and therefore, visual and optical axes should be well aligned. According to the reviews there are 3 positions for IPD adjustment and that could be inferior over continuous regulation of IPD. 

Pancake optics based on fast LCDs are having x2 - x3 larger pixels and eyebox could be designed better correspondingly. To make more precise assumption about the eyebox, we may ray-trace the AVP lens later. Following ray-tracing we will compile material into Application note. Please leave your contact-info and comments to get it. 

Let us know what do you think:

Thanks for registration for AVP App.Note ! We'll get back to you once will be compiled.

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