Optical Terms Library for AR/VR/MR Systems – Distortion

Dear, friends

Sharing our experience as optical engineers specializing in #augmentedreality, me and my partners in JOYA Team want to create a common language, a database that can be shared and used by anyone who wishes to learn and understand the specifics of augmented &virtual reality systems – our optical terms library. If there is a term you want to learn about - leave a comment and we promise to give our interpretation of this term.


The next term is Distortion


Distortion is widely used term for optical systems quality. Distortion is a geometric image aberration, a ratio between a perfect rectangular projected image shape and the real image shape produced by the optical system. Distortion is the image point position deviation that depends on FOV (or object size), which expresses the change of magnification versus Field of View. In general, non-symmetric systems can produce non-symmetric image distortion. Symmetric systems can produce 2 types of Distortion:

  • Barrel Distortion (negative distortion) when the real image is smaller than perfect image

  • Pincushion Distortion (positive distortion) when the real image is larger than perfect image


Fig 1. Distortion of a rectangular grid.

(a) Undistorted grid, (b) Barrel Distortion, (c) Pincushion Distortion

[Published in IEEE Transactions on Consumer Electronics 2009 by Junhee Park, Seong-Chan Byun, Byung-Uk Lee]


Distortion is specified in % [percent]. In most systems the Distortion requirement is limited to the values that cannot be distinguished by human eye, otherwise image correction is required:

  • Distortion: residual distortion less than 3%

There are many kinds of optical aberrations that exist in optical systems, but most of them get little or no attention at all, while Distortion is almost always does. In every specification document there is a requirement for distortion, but is it justified? Is distortion really that important? In most cases, Distortion is one of the least important aberrations, it has no impact on image quality, it can be easily corrected electronically, it is very un-sensitive to optical elements and assembly tolerances, so it can be safely treated as on of the least important parameters.

Sometimes, Distortion can be incorporated by design to be used, for instance to increase the system FOV on expense of the peripheral FOV resolution, larger FOV can be “squeezed” on the edges – the toll of this is lower resolution. In this case, the nominal designed Distortion is non-zero.

Our addition to the Distortion specification:

  • The Distortion requirement shall be specified both before and after the distortion correction application. Distortion above certain limit cannot be corrected.

  • Distortion correction has some effect on the image resolution especially at the edge of FOV.

  • Unless specified otherwise, the Distortion requirements apply for a Maximum FOV, nominal Exit Pupil Distance for a given Spectrum and Measurement Pupil Size and at the Center of System Pupil.

  • Distortion shall be defined for a Nominal and Shifted Pupil Positions, since distortion correction is usually performed for one pupil position (usually nominal pupil position).

  • If the system nominal distortion is non-zero, Grid Distortion Image shall be provided in order to avoid sign issues or mistakes.

  • Distortion has impact on the Symbol Accuracy, so in case when this is important Symbol Accuracy may be a limiting factor constraining Distortion requirements (more on this will be detailed in a separate post dedicated to Symbol Accuracy)

The Distortion Requirements for AR systems or other visual systems would depend on the fact if the distortion correction can be applied to the projected image or not. A different case is if the intension is to design a system with non-zero Distortion, this parameter requirements for the optical design must be set as early as possible, since changing it in the design process may mean that the whole design would start over. Here are several different cases when system Distortion should be tailored to the use-case scenarios in order to create an optimal design:

  • In case of an augmented reality system, when the projected image is combined with direct scene view, and accurate symbol position on real world details is necessary, image distortion shall be limited as part on the symbol position accuracy error budget.

  • In case of a mixed reality system, when the projected image is combined with a direct viewing camera / night vision system, the two images’ distortion shall be close so that there is no perceivable shift between the two images that can impact the user experience.

  • In case of a virtual reality system, when a full video image is projected, the impact of distortion is much lower, when there is no comparison to the real-world objects. The human vision is highly comparative, so the image distortion can be as high as not to significantly distort familiar objects.

Our definition of Distortion:

  • Distortion for Maximum Diagonal FOV, Center System Pupil, Spectrum, Nominal Exit Pupil Distance @ Measurement Pupil: Positive (pincushion) ≤ 3%


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