AR Eye-Gaze Tracking with Moiré Lenses

• AR Eye-Gaze Tracking System is defined as a technology that embeds parallel micro-gratings in contact lenses to create moiré patterns, amplifying minute eye rotations with sub-degree precision.
• It employs a robust methodology using redundant grating pairs and Fourier-based phase extraction to reliably compute eye orientation independent of ambient lighting conditions.
• This approach is actively integrated in AR/VR applications to enable features such as foveated rendering and natural user interfaces, offering a passive, cost-effective, and scalable solution.

AR eye-gaze tracking systems utilizing moiré-pattern-functionalized contact lenses represent a novel, passive, and high-precision approach to eye orientation measurement, with significant implications for augmented reality (AR) and virtual reality (VR) interfaces. This technique departs from traditional infrared and camera-based methods by embedding superimposed micro-gratings within standard contact lenses, generating visually amplifiable moiré patterns that encode eye rotation with sub-degree accuracy.

1. Principle of Moiré Patterns for Eye Tracking

The core of this technology is the incorporation of two parallel micro-gratings within a soft contact lens, separated by a transparent gap (approximately 250 μm). When the overlapped gratings are viewed from an external camera, they generate large-scale moiré patterns—interference fringes whose phase shifts respond sensitively to small changes in relative grating orientation. As the user’s eye rotates, the lens turns correspondingly, causing a lateral displacement between the gratings due to the parallax effect, which in turn shifts the phase of the moiré fringes observed at the camera. Because the moiré effect dramatically amplifies micron-level translational shifts into millimeter-scale pattern movement (for instance, a few μm displacement mapping to a 0.5–1.1 mm moiré fringe period at typical grating parameters), high-precision extraction of eye orientation is enabled by simple image analysis.

A single contact lens may feature multiple grating pairs with distinct parameters to generate several non-overlapping moiré domains. This redundancy supports cross-validation and mitigates local defects or occlusions.

2. Technical Specifications and Measurement Model

The typical implementation employs a bottom grating (A) with period $P_A = 31.6\,\mu m$ and four independent top grating (B) segments with periods $P_{B1-4} = 29.7, 30.7, 32.5, 33.5\,\mu m$. The gratings are aligned parallel within the lens matrix and separated along the optical path by $H \approx 250\,\mu m$.

The measured intensity profile of each moiré segment is modeled as: $$I(x) \propto \cos\big(k(x - x_0)\big), \quad k = \frac{2\pi}{a_x}$$ where $a_x$ is the spatial moiré period and $x_0$ is the phase offset related to grating displacement.

The lens orientation angle, $\theta_{\text{lens}}$, is computed from the relative phase shifts between moiré regions: $$\tan\theta_{\text{lens}} = \frac{P_B}{H} \frac{x_4 - x_1}{a_1 + a_4} + C$$ with $x_1, x_4$ representing phase offsets in different moiré regions, $a_1, a_4$ their spatial periods, and $C$ a calibration constant.

These measurements are robust to external scale, translation, and lighting variations, as the method relies solely on relative moiré phase.

3. Experimental Validation and Measurement Precision

Testing involved mounting the contact lens on a model eye fixed to a rotation stage, which was then incrementally rotated through ±15° in 1° steps under a standard camera at a viewing distance of approximately 40 cm. Moiré phase extraction was performed via Fourier analysis of the captured intensity profile.

The root mean square error (RMSD) of angular measurement was found to be:

• $\sigma = 0.41^\circ$ for a single moiré pair,
• $\sigma = 0.28^\circ$ when averaged across redundant pairs,
• further improved to below 0.2° within ±10° from center.

This angular resolution—exceeding 0.3° per measurement—is well within typical requirements for gaze detection in AR/VR applications.

4. Advantages Compared to Traditional Eye-Tracking Approaches

The moiré-pattern contact lens approach is fundamentally passive:

• It requires no active illumination (no IR LEDs) or power source.
• It operates robustly across ambient lighting conditions (sunlight, shadow, etc.) since it exploits geometric phase, not intensity.
• There is no need for fiducial marks, color bars, or explicit perspective corrections—the measurement depends only on local moiré geometry.
• The sensors can be visualized using standard external cameras, such as those integrated into AR/VR headsets, with minimal system-level adjustment.
• Because the encoded information is both visually explicit and highly amplified, computational decoding is efficient, typically based on simple Fourier or filtering operations.
• The micro-grating structures are fully compatible with standard soft contact lens manufacturing processes and dimensions.

A key distinction is invariance to translation/scale in the captured image and insensitivity to lighting, which contrasts with current camera/IR-reflection-based systems that require careful calibration and may degrade under varying environmental conditions or fail in the presence of occlusion (e.g., eyelids, eyelashes).

5. Integration and Applications in AR/VR Systems

This platform is directly compatible with existing and emerging AR/VR systems:

• The moiré-functionalized contact lens can be worn alongside receiving AR/VR visual feeds, or combined with display-equipped “smart” contact lenses.
• Utilization of headset cameras (already integrated into AR/VR hardware) for moiré pattern capture eliminates the need for additional, protruding, or visible sensors.
• High-precision (<0.3°) gaze estimation supports foveated rendering, natural user interaction, real-time UI adaptation, objective behavioral analytics, and stabilization of in-lens displays in “smart” contact lens contexts.
• The passive module is comfortable and suited for daily wear, adopting the global prevalence of contact lens usage (>140 million users).
• Robustness to lighting and absence of scaling corrections makes the system especially suitable for mobile, all-day AR/VR operation across varied environments.

6. Prospects for Enhanced Precision and Future Improvements

Theoretical and practical enhancements can further boost performance:

• Reduction of grating period below 30 μm and increased inter-grating spacing could yield an order-of-magnitude improvement in angular sensitivity (approaching or surpassing 0.05°).
• Advanced image processing, including optimized windowing, denoising, and potentially machine learning-based phase readout, could enhance robustness and accuracy.
• Multi-pattern designs and combinatorial gratings may widen the unambiguous angular range or enable self-calibration and built-in reference checks.
• Integration with functional display contact lenses is feasible, permitting unified platforms capable of simultaneous gaze sensing and AR display.
• Manufacturing scalability and further miniaturization would serve mass adoption while maintaining optical clarity and comfort.
• The same moiré grating principle could be applied for additional biosensing modalities, health monitoring, or secure identity recognition embedded within wearable optics.

7. Summary Table: Characteristic Comparison

Feature	Moiré-Pattern Contact Lens
Angular Resolution	>0.3°, <0.2° with redundancy
Power Requirement	None (Passive, camera-readout only)
Lighting Sensitivity	Insensitive, robust to environment
Required Hardware Addition	None (uses standard cameras)
Computational Overhead	Low (Fourier/phase extraction)
Calibration/Scaling	None (phase-based, reference-free)
Suitability for AR/VR	High (precise, robust, seamless)
Future Potential	Sub-0.05° accuracy, smart lens fusion

Conclusion

Moiré-pattern-enabled contact lens eye tracking constitutes a passive, precise, and robust solution for AR/VR gaze-based interaction. By optically amplifying minute eye rotations through micro-grating structures and extracting rotation directly from moiré phase shifts, this technology addresses key limitations of existing camera and IR-based systems—removing power requirements, sensitivity to ambient conditions, and the need for explicit perspective calibration. The platform supports straightforward integration into current AR/VR architectures, offers significant manufacturing and user comfort advantages, and provides an expandable basis for next-generation smart eyewear and wearable biointerfaces. The foundational methodology and performance metrics reported by Fradkin et al. indicate considerable promise for both widespread adoption and further enhancement in measurement precision and system capabilities.