Spatial-chromatic encoding cosmetic contact lenses for enhanced natural eye tracking

Domain: physics
Published: 2026-02-03
Editorial outcome: major_revision

Abstract
Vision-based analysis of ocular features represents the predominant approach for eye tracking. However, these features are highly susceptible to interference from illumination, eyelid/eyelash occlusion, and individual variations, leading to low recognition rates and diminished tracking accuracy. To address these limitations, eye movement feature enhanced cosmetic contact lenses are proposed, implementing a spatial-chromatic encoding strategy. Employing a head-mounted eye tracker integrated with RGB cameras, this system enables accurate and robust gaze tracking in natural environments. Under challenging illumination, the lenses achieve a 93% feature recognition rate, significantly surpassing pupil recognition and tolerating highly off-axis camera placement. Eye movement model and human eye tracking demonstrate superior accuracy (<1°), gaze direction estimation, and continuous fixation positioning. Utilizing these lenses, diverse eye-tracking applications are demonstrated, including image identification, reading analysis, and outdoor interaction. This approach advances the development of lightweight, unobtrusive eye-tracking systems and facilitates broader application of gaze-based interaction technology in real-world settings.

Introduction
Eye tracking technology provides an objective, real-time window into human attention allocation, cognitive processing, and behavioral decision-making by recording and analyzing visual behaviors such as gaze point trajectories, pupillary movements, and blink frequency. Its significance stems from the central role of the visual system in human information processing - approximately 83% of external information is acquired visually. Within fundamental research, this technique serves as a critical tool for exploring perception, memory, language comprehension, and decision-making mechanisms, capable of revealing implicit cognitive processes often elusive to traditional behavioral experiments. At the applied level, eye tracking has found widespread use in human-computer interaction, user experience research, clinical medicine, educational psychology, and intelligent cockpit.

To date, researchers have proposed numerous technical approaches to achieve accurate, real-time eye tracking, including electrooculography, the scleral search coil technique, video/image-based methods, magnetic resonance-based methods, and electrostatic induction methods. Among these, video/image-based eye tracking currently represents the most dominant and widely adopted technology. It utilizes one or more cameras to capture images of the eye, subsequently employing image processing algorithms to identify eye movement-related ocular features. These features encompass intrinsic properties of the eyeball itself, such as the iris and pupil, as well as reflection-based features provided by the eye tracking system, such as near-infrared glints or patterns projected from the screen. Accurate identification of these eye movement features is fundamental to achieving eye tracking. However, robustly identifying these features within complex, naturalistic environments remains a significant challenge. On one hand, variable ambient light reflected from the corneal surface is captured by the camera, superimposing random environmental patterns onto the eye movement features. This complicates their automatic extraction using generic algorithms. On the other hand, user-specific factors can reduce the success rate of feature identification and tracking accuracy, including low iris-pupil contrast, occlusion by eyelids and eyelashes, indistinct iris boundaries, and pupil shape irregularities. Achieving lightweight and unobtrusive eye tracking in authentic, natural environments represents an important developmental goal. Yet, in such contexts, eye trackers often prove susceptible to interference. This vulnerability primarily stems from the highly limited and individually varied eye movement characteristics. Consequently, enhancing eye movement-related ocular features is key to realizing robust and high-performance eye tracking.

In recent years, advancements in flexible electronics and bioelectronics have driven flexible devices to revolutionize human-computer interaction. Among these, contact lenses conform to the corneal surface and move with the rotation of the eyeball. Integrating optoelectronic devices into contact lenses serves as an effective approach to enrich eye movement characteristics. For instance, our research team previously integrated inductive–capacitive resonators based on a frequency encoding strategy into contact lenses, achieving precise eye-tracking and eye-command recognition. Gan et al. incorporated magnetic materials into contact lenses and accurately identified eye orientations across 9 directions wirelessly by measuring magnetic field variations using an 8-channel teslameter. Fradkin et al. integrated a passive optical module within a contact lens, comprising two overlapping grating layers that form a moiré pattern sensitive to eye movement angles, achieving remarkably high angular resolution and strong resistance to ambient light interference. Khaldi et al. integrated a wirelessly powered near-infrared laser into contact lenses, where eye movement direction was indicated by the position of the near-infrared spot. Evidently, integrating devices with diverse physical properties into contact lenses can provide consistent eye movement characteristics. This consistency enhances interference-resistant eye-tracking, improves the usability of eye-tracking technology, and expands its applications scenarios, such as enabling eye-tracking during eye closure. However, at its current stage, eye-tracking contact lenses still need to focus on meeting the fundamental physicochemical properties of contact lenses, such as being lightweight, highly flexible, and exhibiting excellent surface wettability, before they can be widely adopted by broader populations.

To address the aforementioned challenges, cosmetic contact lenses, easily accessible daily items with high public acceptance, are employed to enhance eye movement features, enabling accurate and robust eye tracking in natural scenarios. Using an RGB (Red, Green, Blue) primary spatial-chromatic encoding strategy, these lenses print arrayed green solid circles and red dots circularly, endowing brightly colored and standard-shaped eye movement features while also readily meeting requirements for safety and comfort. By capturing lens images using the common, low-cost RGB camera and applying straightforward hue-space and morphological image processing algorithms, a significant enhancement in eye tracking performance is achieved. The proposed solution offers the following advantages: (a) superior overall recognition rate of 93% under challenging and complex lighting conditions, which is improved by 53% compared to the bare eye; (b) <1° eye tracking accuracy, gaze direction estimation, and full-frame continuous gaze point positioning; (c) support for highly off-axis camera placement, enabling unobtrusive eye tracking technology. Having all these features, the proposed eye movement feature enhanced (EMFE) cosmetic contact lens is expected to make eye trackers accessible, reduce the cost of eye tracking technology, and promote its widespread application in real-world, natural daily life scenarios.

Results
Design of eye movement feature enhanced (EMFE) cosmetic contact lens
Cosmetic contact lenses can integrate specific patterns with vivid colors within the lens material to decorate the eye. To achieve accurate and robust eye tracking, we designed the EMFE cosmetic contact lens based on an RGB color-coded strategy, as shown in Fig. 1a. The lens pattern features a peripheral blue ring adorned with 12 evenly spaced green solid circular elements, interspersed with red dots between the green elements. Red, green, and blue are located at 0°, 120°, and 240° in the hue domain, respectively, exhibiting significant chromatic differences. When imaging the eye wearing this lens with an RGB camera, the high color contrast and sharp pattern edges enable recognition algorithms to accurately identify these eye movement features. The peripheral pattern distribution avoids visual field obstruction while ensuring feature visibility even under highly off-axis camera angles. Compared to the single feature (e.g., pupil) in bare-eye images, the 12 uniformly distributed green solid circles significantly enhance pattern recognition robustness against complex lighting interference, eyelid occlusion, and eyelash obstruction. Accurate gaze tracking is achieved through a centroid-angle mapping function that calculates gaze angles from the green solid circles’ centroids. Furthermore, a greater number of green solid circles enhances the accuracy of gaze angle measurement. During dynamic eye movements, motion blur often occurs in images captured by low-frame-rate cameras. Here, the red dots streak into red trajectories. Due to the small diameter of the red dots, the direction of the red trajectories aligns with that of the eye movement. By identifying these red trajectories and combining them with eye movement angles calculated from adjacent static frames, full-frame continuous gaze point positioning can be extracted. This spatio-temporal feature-enhanced tracking method enables eye tracking technology applications in natural environments. Furthermore, the green solid circles are standard shapes with known diameters. Combined with the camera’s imaging parameters, they enable the estimation of the pose information of the green solid circles in the camera coordinate system. This capability aids in determining the spatial position of the EMFE cosmetic contact lens, thereby supporting more advanced eye-tracking functionalities such as gaze direction estimation and camera slippage compensation.

The EMFE cosmetic contact lens pattern, created using commercial cosmetic dyes, is transferred from a flat design to the spherical lens surface via pad printing technology. A sandwich fabrication process embeds the pattern layer within the lens body. Steam autoclave sterilization ensure the lenses are safe and sterile. As shown in Fig. 1b, the lenses exhibit cornea-matched curvature and diameter. An ultra-thin 80-μm thickness ensures stable adhesion to the corneal surface, enabling the lenses to move precisely with the eye. The EMFE contact lens has a measured oxygen permeability (Dk) of 18.2×10−11 (cm2/s) [mL·O2/(mL·hPa)] and an oxygen transmissibility (Dk/t) of 19.8×10−9 (cm/s) [mL·O2/(mL·hPa)]. The water content of the EMFE contact lens is 56%. The lens has excellent surface wettability. As shown in Supplementary Fig. 1, the droplet rapidly spread across the lens surface without maintaining a spherical shape. This behavior indicates that the interaction energy between the water and the lens surface significantly exceeds the cohesive energy of the water itself. The standardized pattern design and fabrication process allow the EMFE lenses to be easily mass-produced at extremely low cost while maintaining excellent pattern consistency. To verify the cytotoxicity of the EMFE cosmetic contact lens, the viability of cells from human corneas (HCE-T) was measured. Extracts of the lens were prepared by immersing the lens in the cell culture medium for 24 h. After culturing the cells using extracts for 24 h and then adding CCK-8 reagent, the absorbance was measured to record the viability of the cells. More details are provided in the Methods. As shown in Supplementary Fig. 2, the cell viability using extracts of the EMFE cosmetic contact lens remained above 95% after 24 h of incubation with no notable differences among the controls, and it is significantly superior to commercial contact lenses. This suggests that the EMFE cosmetic contact lens was non-cytotoxic over long-term wear and would pose little risk of corneal inflammation. The micrographs of HCE-T after 24-hour culture are demonstrated in Supplementary Fig. 3. The cell distribution density incubated in different extracts was similar, indicating low biotoxicity. Besides, a 6-h-long dye leakage test was conducted under tear-mimicking conditions. Two EMFE contact lenses were immersed in phosphate-buffered saline (PBS) and incubated in a water bath maintained at 35°C for 6 h. As shown in Supplementary Fig. 4, the PBS solution remained clear and colorless after immersion, and no observable changes in color or pattern were detected on the EMFE contact lenses, indicating great biosafety and stability.

Figure 1c shows a participant wearing the EMFE contact lens and the head-mounted eye tracker. The head-mounted eye tracker incorporates two off-axis eye-facing cameras for imaging the eyes and one scene camera capturing the forward view. The three video streams are transmitted via the Universal Serial Bus (USB) protocol, combined using a USB hub onto a single cable connected to the image signal processing terminal, such as a laptop. This system enables real-time acquisition and transmission of three channels of 30-fps eye movement RGB video. Furthermore, cosmetic contact lenses inherently possess vision correction functionality while weighing only approximately 20 mg. This eliminates the need for additional bulky lenses (which weigh approximately 10 g), a critical advantage for weight-sensitive eye-tracking technology applications in emerging fields such as virtual reality (VR) and augmented reality (AR).

Recognition rate characterization of eye movement feature
Accurate identification of eye movement-related features is the prerequisite for eye movement tracking. Complex and random environmental lighting interference poses a significant challenge to eye movement feature recognition in natural environments. Especially when using RGB cameras, lighting interference is far more severe compared to cameras equipped with narrowband near-infrared filters. We setup three distinct lighting environments: indoor artificial lighting, outdoor natural lighting, and window-side natural lighting. Under these three lighting conditions, we captured a total of 700 eye images of the volunteer wearing EMFE cosmetic contact lenses, and captured naked eyes using the same RGB camera. Then, the images were analyzed using MATLAB R2020b, and the recognition accuracy of the target recognition algorithm was compared. For eye images with cosmetic contact lenses, the green solid circles serve as the feature pattern for eye movement tracking. Thank to the strong color contrast between the green solid circles and the surrounding blue area, as well as the sharp edges of the pattern, we initially extracted the green region in the image using the HSV threshold method. However, due to lighting conditions and the scene context, some pixels in the eye images may be misidentified, such as highlights and projections of natural objects. Additionally, highlights, eyelids, and eyelashes may overlap with or obscure the green solid circles. Nevertheless, since the green solid circle pattern, created using a transfer printing process, is a consistent standard circle, it often appears elliptical under different eye movement angles when projected by the camera. The aforementioned interferences typically produce irregular patterns. Therefore, by applying threshold screening to the area, eccentricity, and solidity of connected regions, we can achieve high-accuracy recognition of the green solid circle pattern in cosmetic contact lenses. The top row of images in Fig. 2a illustrates representative eye images with cosmetic contact lenses under the three lighting conditions. The algorithm-identified green solid circles are outlined with red lines. Some small or overly flattened green solid circles are actively excluded by the algorithm. Furthermore, in outdoor scenes, green tree projections on the surface of the cosmetic contact lenses are not mistakenly identified as green solid circles, demonstrating the robustness of the recognition algorithm. For naked eye images, due to their sharp edges, pupils are commonly used as features for eye movement tracking. We employed the ElSe, ExCuSe, PuRe, PuReST, Swirski2D algorithms in PupilEXT, and the Gradient algorithm proposed by Fabian Timm et al. to identify pupil regions in the images. The centroids of the identified regions are marked with different symbols in the images, as shown in the bottom row of Fig. 2a. The absence of a marker indicates algorithm failure due to excessive centroid deviation or undetected pupil. Additionally, the low contrast between the iris and pupil colors, as well as lighting and scene projections on the cornea, significantly interferes with pupil recognition accuracy. By manually annotating the green solid circles in cosmetic contact lenses and pupil regions in the naked eye as ground truth, we compared these with the eye movement features identified by the algorithms. If the algorithm-identified region’s centroid lies within the ground truth region, the recognition is considered successful, and the pixel deviation between the centroid and the ground truth region’s centroid is calculated. Figure 2b, c compares the recognition rate differences between green solid circle recognition in cosmetic contact lenses and pupil recognition in naked eyes, as well as the cumulative probability of centroid pixel deviations for these eye movement features. Under indoor artificial lighting, outdoor natural lighting, and window-side natural lighting scenarios, the recognition rates for green solid circles in cosmetic contact lenses were 96.6%, 83.3%, and 99.0%, respectively, while the pupil recognition rates for bare eyes using different algorithms were all below 55%. The significant improvement in recognition rates is attributed to two factors: the strong color contrast and consistent morphological standards of the cosmetic contact lens patterns, and the increased number of feature patterns. This demonstrates the robustness of using EMFE cosmetic contact lenses for eye movement feature recognition in complex and random natural environments. The overall recognition rate for green solid circles was 93%, with 90% of centroid deviations being less than 12 pixels, while pupil centroids exhibited significantly larger pixel deviations. The distribution of centroid deviations of the green solid circles is shown in Supplementary Fig. 5. In subsequent applications, using the centroid of the green solid circles to map gaze angles via the gaze angle mapping function, the more precise recognition of green solid circle centroids can enhance the accuracy of eye movement angle calculations.

At present, to avoid obstructing the line of sight and construct a natural, unobtrusive head-mounted eye-tracking device, the camera position must deviate from the eyeball’s optical axis when looking straight ahead. The camera must capture the eye region at a large tilt angle, which makes it highly susceptible to losing the eye movement feature and causing tracking failures under large eye movement angles. The two-dimensional rotation range of human eye movement is ±40° horizontally and ±30° vertically. Gaze points are set at 10° intervals, and volunteers are guided to sequentially fixate on each point. The camera is placed below and in front of the eyeball, with different pitch angles set to keep the eyeball centered in the image. Eye movement feature recognition is analyzed under different gaze angles for both cases: wearing EMFE cosmetic contact lenses and without lenses. As shown in Fig. 2d, for the image with lenses, the aforementioned feature recognition algorithm is used to identify the green solid circles, with their edges marked in red. For the image without lenses, manual annotation is used. However, due to the large off-axis camera angles and eye movement angles, combined with the objective physiological structure of the pupil being inside the eyeball, the pupil is often occluded, leading to the loss of the feature. The lower image in Fig. 2d demonstrates a representative occluded pupil image when the camera pitch angle is 80°, and the eyeball rotates to a yaw angle of 0° and a pitch angle of 30°. As the camera pitch angle increases from 50° to 80°, the feature recognition algorithm can accurately identify the green solid circle pattern across the full range of eye movements for images with EMFE cosmetic contact lenses. In comparison, for images without lenses, the camera pitch angles of 50° and 60° can capture the pupil region across the full range of eye movements. However, at pitch angles of 70° and 80°, 14% and 18% of the eye movement range, respectively, lose pupil features. Furthermore, even when the volunteer squints to different degrees, the camera is still able to easily capture the green circular pattern, as shown in Supplementary Fig. 6. This demonstrates that wearing EMFE cosmetic contact lenses enables a high off-axis camera placement, facilitating a more natural and unobtrusive eye-tracking technology.

Eye tracking characterization using the eye movement model
A two-dimensional rotation platform (as shown in Fig. 3a) can precisely control the horizontal yaw angle and vertical pitch angle of the model eye, aiding in the characterization of the accuracy of eye tracking technology based on EMFE cosmetic contact lenses. Referencing the rotation range of the human eyeball, the model eye’s two-dimensional rotation range was set to horizontal ±40° and pitch ±30°, with intervals of 10°. Images of the model eye were captured at each eye movement angle. Using the HSV threshold method and connected domain morphological threshold method, the green solid circles on the EMFE cosmetic contact lens were identified, and the centroids of the green solid circles were extracted. Subsequently, a polynomial fitting method is used to construct the mapping function between the green solid circles’ centroids and the gaze angle, enabling gaze angle calculation. As shown in Fig. 3b, the set values of the two-dimensional gaze angles (gray squares) and the calculated results (yellow circles) obtained through feature recognition and mapping function calculations are compared. If all 63 gaze angle data points are used for polynomial parameter fitting, it implies a complex and time-consuming calibration process for the user. Therefore, to simplify the calibration process, we selected 9 gaze angles from a 3×3 array as calibration data for polynomial parameter fitting to construct the mapping function. The remaining 54 eye movement angle images are used as test data, with the calculated eye movement angle results shown as red points in Fig. 3b. It can be seen that whether all data or 9-point calibration is used, the calculated eye movement angles align well with the set values. The specific angular errors are statistically shown in Fig. 3c. The eye movement angle calculation error using the 9-point calibration method is 0.82°±0.58° (mean±S.D.), while using all 63 eye movement angle data points results in an error of 0.74°±0.40°. This indicates that the 9-point calibration method maintains high accuracy in eye tracking while significantly simplifying the calibration process. Besides, a more detailed accuracy characterization was conducted with intervals of 1° under the eye rotation range. As shown in Supplementary Fig. 7, the computed gaze angles exhibit minimal errors in the central region of the eye movement range, while larger errors occur mainly at the four corners, corresponding to more extreme gaze angles. These residual errors stem from the reduced number of detectable feature patterns at extreme angles and the inherent limitations of polynomial-based fitting under large-angle rotations. The overall angular error was 0.29°±0.21°. To quantitatively evaluate the accuracy of the EMFE contact lens-based eye tracking technique under various environmental conditions, the eye tracking characterization was also conducted beside a window (with a light intensity of 322 lux) and outdoors (with a light intensity of 25100 lux). The gaze angle map and error statistic under different illumination scenarios are shown in Supplementary Fig. 8. The tracking accuracy was 0.95°±0.61° beside a window and 0.96°±0.67° outdoors. The slightly higher angular errors observed in the window-side and outdoors scenarios are attributed to more complex lighting conditions in those environments, which introduced interference in identifying the centroid coordinates of the green solid circles. Due to the human eye’s attention mechanism, the brain primarily analyzes visual information within a 1–2° field of view corresponding to the fovea. Therefore, a gaze angle error of less than 1° is sufficient to accurately determine the gaze point and analyze the regions of visual attention. Additionally, the gaze accuracy based on a 4-green-solid-circle EMFE cosmetic contact lens is characterized with the angle error of 1.20°±0.72°, as shown in Supplementary Fig. 9. The 12-green-solid-circle lens exhibits superior eye-tracking accuracy, which can be attributed to the camera’s ability to identify at least three green solid circles across various gaze angles. After averaging the computed gaze angles, the system mitigates the effects of centroid deviations caused by environmental light interference and pattern distortion due to eyelid occlusion. The results indicate that a greater number of green solid circle features can improve the eye tracking accuracy of EMFE contact lens-based systems.

Using a mapping function for eye tracking compensates for errors introduced by the individual variation in the angle between the visual axis and optical axis, enabling precise gaze angle tracking. However, this method requires a calibration process to obtain polynomial parameters. Alternatively, EMFE cosmetic contact lenses can achieve gaze direction estimation directly. As shown in Fig. 3d, due to the structural consistency of the green circular patterns, the pose information (i.e., the 3D coordinates of the circle center and the normal vector of the circular plane) of each green solid circle in the camera coordinate system can be calculated using the known diameter of the green solid circles and the intrinsic camera parameters. Using the pose information from multiple green solid circles, the intersection between the full frame and the static frame was analyzed. Inset: eye movement velocity was calculated frame-by-frame. The intersection of their normal vectors gives the center coordinates of the cosmetic lens sphere, and the normal vector of the plane fitted to the 3D coordinates of the circle centers represent the direction of the eye’s optical axis (indicated by the green line in the figure). Supplementary Fig. 10 presents the estimated gaze directions across the full eye movement range (yaw: ±40°, pitch: ±30°) at 10° steps. A comparison between these set gaze directions and the calculated results is shown in Supplementary Fig. 11. The gaze angle estimation error was 3.08°±1.54°.

Human eye movement modes, such as fixation, smooth pursuit, and saccades, exhibit distinct characteristics in terms of eye movement speed. During static fixation or slow eye movements, cameras can capture clear eye images. However, during dynamic eye movements, motion blur makes it difficult for cameras to recognize eye movement features, leading to the loss of gaze point data. Thank to the design of eye movement feature enhancement patterns, common cameras are able to achieve full-frame-rate gaze point localization. For static eye movement images, the green solid circles are used as the eye movement feature for calculation. For dynamic eye movement images, the red trajectories formed by red points in motion blur are used as the eye movement feature, as shown in Fig. 3e. Similarly, the HSV threshold method and connected domain morphological threshold method were used to identify the red trajectory, followed by extracting the skeleton of the red trajectory region as the motion trajectory during the dynamic eye movements. Since dynamic image frames are always preceded and followed by static image frames, by combining the centroid coordinates and eye movement angles of the red points in the preceding and succeeding static image frames with the red point trajectory in the dynamic frame, the gaze point coordinates of the dynamic frame can be calculated. Figure 3f demonstrates the eye movement trace simulated by a two-dimensional eye movement model, where the red curve represents the continuous gaze angle positioning analyzed from static and dynamic images, while the gray curve represents the gaze angle positioning analyzed solely from static images. The inset in Fig. 3f calculates the eye rotation speed for each frame in this eye movement trajectory. If only static images are analyzed, the true sampling rate of the eye-tracking technology will drop to 65% of the video’s full sampling rate, and break the continuity of gaze points. This is of great importance in revealing cognitive processing mechanisms, assessing neurological function, and aiding clinical diagnoses. In addition, the eye movement trace results from the low-frame-rate system with the EMFE contact lens are compared with those obtained with a Pico Neo 3 Pro eye tracker, which samples at 90 fps. Supplementary Fig. 12 shows the time-series plots of the yaw and pitch angles obtained from both methods, indicating a highly consistent gaze angle trace.

Head movements or slippage of the head-mounted eye tracker cause displacement between the camera and the eyeball, altering the mapping relationship and reducing the accuracy of long-term eye tracking. This is a common challenge in eye-tracking technology. To mitigate gaze angle errors induced by camera slippage, a compensational algorithm has been developed. Based on the three-dimensional coordinates of three or more green solid circle centers, the spatial position of the eye can be calculated. Changes in the eye’s spatial position reflect the displacement of the camera relative to the eyeball. After calculating the displacement, spatial compensation is applied to the green solid circles (i.e., subtracting the displacement vector), as shown in Supplementary Fig. 13. The compensated circles are projected back to the image plane to update their centroid coordinates, which are then input to the mapping function to obtain the corrected gaze angle. Here, the camera was calibrated to achieve the mapping function (Position 1), moved upward by 2.5 mm (Position 2), and then away from the eyeball by 2.5 mm (Position 3) in off-axis photography conditions to verify the effect of the compensation algorithm, as shown in Fig. 3g. Supplementary Fig. 14a, b shows the distributions and error statistic of gaze angles when the camera is at the Position 1, indicating strong agreement between the estimated and target gaze coordinates. Due to the slippage of the camera, noticeable pixel-level shifts in the green solid circle centroids occurred. Since these shifts did not originate from actual eye rotation, directly inputting the shifted centroid coordinates into the mapping function led to large gaze errors. The comparisons of the gaze angle map and error statistic with and without compensation at Position 2 and Position 3 are shown in Supplementary Fig. 14c, d and Fig. 3h, i, respectively. The yellow points represent the gaze angle results without compensation, exhibiting a distinct trapezoidal distortion. At Position 3, the overall gaze error reached 17.14°±1.88°. After applying the compensation algorithm, the resulting gaze angles, shown as red points, were significantly closer to the targets. As shown in Fig. 3i, the overall gaze error was reduced to 2.03°±0.65°, indicating that 88% of the original error was successfully compensated for. The residual error after compensation mainly stems from inaccuracies in calculating the 3D positions of the green solid circles and the eye.

Eye tracking characterization of human eyes wearing EMFE cosmetic contact lenses
EMFE cosmetic contact lenses were prepared using a sandwich process and undergo steam high-temperature sterilization to ensure safety and sterility. Volunteers wore EMFE lenses and a head-mounted eye tracker, with an off-axis camera integrated into the device, capturing eye images. Volunteers faced a display screen or whiteboard at a distance of 60 cm. Setup gazing points with known screen coordinates were marked on the screen or the whiteboard to guide volunteers to fixate, thereby testing the performance of eye-tracking based on EMFE contact lenses (as shown in Fig. 4a). This human experiment was approved by the Ethical Committee of the First Affiliated Hospital of Nanjing Medical University, Jiangsu Provincial People’s Hospital, with an ethical approval number of 2025-SR-023. Figure 4b shows photographs of volunteers wearing EMFE lenses while gazing in different directions.

To test the accuracy of eye-tracking based on EMFE contact lenses, four volunteers (two males and two females) with different ocular features (in Supplementary Table 1) were instructed to observe a whiteboard positioned 60 cm away. A two-dimensional array of gaze targets was arranged on the whiteboard. While the human eye is capable of a wider range of rotational movement, it generally prefers head turning for horizontal angles beyond approximately 16°. Therefore, the target points were confined within a range of ±16° in yaw and ±16° in pitch, spaced at 4° intervals, forming a 9×9 grid comprising 81 gaze targets. The volunteers were guided to fixate on each of these points sequentially, and six frames of eye images were captured per gaze point. The green solid circles were identified using MATLAB R2020b, and a mapping function was derived to calculate the gaze angle coordinates. Figure 4c displays the set values (gray squares) and calculated values (red dots) of the gaze angle. Eye-tracking performance is commonly described by accuracy and precision. Accuracy is defined as the average error between the actual and calculated positions of the gaze angle. Precision is defined as the dispersion of the eye-tracking device when recording the same fixation point. Figure 4d, e statistically show the accuracy and precision of eye-tracking based on EMFE lenses, with values of 0.70°±0.38° and 0.22°±0.13°, respectively. The distributions of gaze angles, along with the calculated accuracy and precision for all four volunteers, are shown in Supplementary Fig. 15. The specific accuracy and precision values for each volunteer (A–D) are summarized in Supplementary Table 2. All four volunteers achieved eye-tracking accuracy and precision better than 1°, demonstrating that the EMFE-based eye-tracking technique can avoid the interference caused by ocular individual differences. Similarly, an eye movement angle error of less than 1° is sufficient to accurately determine the gaze point and analyze the regions of visual attention. Besides, the long-term stability was evaluated by wearing the EMFE contact lens continuously for 6 h. As shown in Supplementary Fig. 16, the eye-tracking accuracy and precision with the EMFE contact lens were 0.61°±0.34° and 0.28°±0.18°, respectively, after long-term wearing and showed no significant difference from the initial wearing state. After removal of the lens, no blurring or deformation of the feature patterns was observed (in Supplementary Fig. 17), confirming the stability of the EMFE contact lens for long-term eye-tracking applications.

Blinking-induced eyelid occlusion poses a common challenge for eye tracking by significantly lowering the success rate of ocular feature identification. To quantify this effect, volunteers wore an EMFE contact lens on the left eye while blinking naturally. A frame-by-frame analysis correlated the detectability of the enhanced eye movement feature with the degree of eyelid occlusion. Simultaneously, an infrared camera tracked the right eye via pupil recognition for comparison. As shown in Supplementary Fig. 18a, the number of detectable green solid circles decreased with increasing occlusion. At occlusion levels exceeding 80%, pattern recognition failed completely, resulting in approximately 66 ms of data loss with the EMFE contact lens method. In contrast, pupil-based tracking experienced longer interruptions (approximately 231 ms) due to more frequent and complete pupil occlusion. A similar trend was observed during the prolonged, heavy blink (Supplementary Fig. 18b), where data loss extended to about 198 ms (EMFE contact lens-based) versus 330 ms (pupil-based). In summary, while eyelid occlusion above 80% leads to temporary tracking failure, the EMFE contact lens-based method exhibits significantly shorter failure durations and resumes immediately upon eye reopening, demonstrating superior robustness compared to pupil-based tracking during blinks. However, due to the dynamic interaction between the eyelid and the lens, a slight gaze angle error occurs during the moment of blinking. As shown in Supplementary Fig. 19, during eye reopening, tangential eyelid forces caused vertical lens slippage, introducing a pitch angle error of approximately 2–4° with no notable horizontal displacement. This vertical shift self-corrected rapidly after the eye reopened, and the resulting gaze error was eliminated within 0.3–0.7 s.

Additionally, a red dot moving along a 20 cm × 20 cm rectangular path at different speeds (0.5 s, 0.75 s, and 1 s per side length) is displayed on the screen to guide the volunteer to perform eye movements of varying speeds. The gaze point trajectories of the volunteer are shown in Fig. 4f. As the speed of the guided gaze point increases, the density of the participant’s gaze points along the movement path becomes sparser, yet continuous gaze point localization is maintained, demonstrating the capability to track dynamic eye movement traces. Figure 4g displays the corresponding eye movement speeds. The colored regions in the figure correspond to the process where the volunteers’ gaze points follow the moving red dot, while the uncolored regions correspond to moments when the red dot is stationary. This demonstrates that enhancing eye movement feature through EMFE lens patterns enables spatially accurate and temporally continuous eye tracking.

Eye tracking in multiple indoor and outdoor scenarios
Based on the eye-brain consistency hypothesis, the human brain primarily analyzes visual information at the fixation point. By tracking users’ eye movements, we can identify regions of interest, infer user intentions, and achieve efficient human-computer interaction. As shown in Fig. 5a, the volunteer was asked to find the image containing a bicycle among nine images. To enable interaction between the eye movement and the screen, the volunteer first underwent a 9-point calibration process. The volunteer was guided to look at each of the nine calibration points on the screen in sequence, with five frames of eye images captured at each calibration point. A mapping function was then constructed based on feature patterns. As shown in Fig. 5b, the upper part illustrates the calibration point settings and calculated fixation point coordinates, while the lower part provides statistics on the fixation point error distribution, with an accuracy of approximately 0.74 cm±0.39 cm. Subsequently, the volunteer freely observed the images on the screen for a period of time, during which a head-mounted eye tracker recorded the eye images of the volunteer wearing EMFE cosmetic contact lenses and identified eye movement features to calculate fixation point coordinates. Considering precision errors of the eye-tracking system, the algorithm performed a gradient score on pixels at varying distances from the calculated fixation point, with the highest score at the fixation point and a decreasing score as the distance increases. During the observation of images, the score accumulated frame by frame. After processing, the score distribution formed a heatmap of regions of interest, as shown in Fig. 5c. The image containing a bicycle clearly had a higher interest score. Combining the pixel display areas of each image, the interest scores calculated for each region are shown in Fig. 5d, which also demonstrates that the user paid more attention to the bicycle image. The entire process of region of interest recognition is shown in Supplementary Video 1.

The analysis of fixation points during reading represents one of the core applications of eye-tracking technology. It provides an indirect yet objective mean to reveal the reader’s internal, real-time cognitive processing. By analyzing fixation points, insights can be gained into the difficulty and depth of cognitive processing, as well as into reasoning patterns and individual differences among readers. A text segment is displayed on the screen, and the user reads it. The head-mounted eye tracker recorded the eye images of the volunteer wearing EMFE cosmetic contact lenses and calculated the user’s fixation point coordinates frame by frame. As shown in Fig. 5e, the eye movement trace during reading consisted of static fixation points and dynamic eye movements. The blue circles in the figure mark the coordinates of the volunteer’s fixation points in sequence, and the color changes in the trajectory curve represent variations in the speed of eye movements. Additionally, the trajectory clearly shows reading details such as regressions and re-fixations. The eye movement trace obtained from a 180-fps high-speed RGB camera is shown in Supplementary Fig. 20. As shown in Fig. 5f, this figure specifically illustrates the speed changes during the eye movement process. The entire process of eye tracking when reading is shown in Supplementary Video 2.

Eye tracking in the wild is a crucial functional module for future lightweight mixed reality, enabling dynamic fusion between virtual objects and the real world. However, achieving robust eye tracking faces challenges due to randomly varying outdoor lighting conditions and complex scene changes. The volunteer wearing EMFE contact lenses and a head-mounted eye tracker was tested across multiple scenarios from afternoon till dusk, including beside a shopping mall, along a tree-shaded road, in a square, by a lakeside, and in front of a large electronic screen, as illustrated in Fig. 5g. The volunteer held a red dot marker, moving it to different angles within their field of view while continuously fixating on the dot. During outdoor eye tracking experiments, ambient lighting shifted from intense direct sunlight during the day to soft oblique sunlight at dusk. Despite random scenes projecting interference patterns onto the contact lens surface, eye movement features on the lens were consistently identified, enabling continuous tracking. This process is shown in Supplementary Video 3.

Methods
Pattern design and fabrication of the EMFE cosmetic contact lens
The eye-tracking feature pattern of the EMFE cosmetic contact lens is designed based on an RGB primary color strategy. The annular pattern is positioned peripherally on the lens, featuring an outer diameter of 13 mm and an inner diameter of 8 mm to ensure an unobstructed visual window. Considering camera parameters and the precision of transfer printing technology, the blue ring incorporates 12 uniformly distributed green solid circles (1.5 mm diameter) for static image eye feature enhancement and 12 red dots (0.3 mm diameter) for dynamic eye movement trajectory tracking.

The EMFE cosmetic contact lens, fabricated from HEMA hydrogel material, employs a sandwich-like multi-layer preparation process to integrate the eye-tracking pattern within the lens body by a manufacturer of cosmetic contact lenses with a registration certificate for a medical device. As the pattern comprises three colors, corresponding steel plates were sequentially prepared for the red, green, and blue elements. Lens pigment was applied to fill the engraved patterns on the plates. Using an elastic silicone transfer printing process, the patterns were transferred from the two-dimensional steel plates onto the three-dimensional spherical surface of the lens. To compensate for the distortion inherent in transferring from a flat surface to a spherical substrate, the plate patterns underwent radial pre-calibration. Furthermore, areas corresponding to the green solid circles and red dots within the blue ring were hollowed out on the plate to ensure color fidelity in the final product. The encapsulated pigment is sealed within the lens interior and is vulnerable to steam sterilization, ensuring biocompatibility.

Cytotoxicity tests
Human corneal epithelial cell lines (Cellosaurus CVCL_1272, obtained from Shanghai Zhong Qiao Xin Zhou Biotechnology Co. Ltd.) were employed to test cytotoxicity. HCE-T were maintained in HCE-T complete medium (ZM1003, obtained from Shanghai Zhong Qiao Xin Zhou Biotechnology Co. Ltd.) at 37°C in a humidified atmosphere of 5% CO2. After several passages, these cells were harvested and plated at a density of 5000 cells per well. The cells were incubated in complete medium for 24 h.

Before the extracts were prepared by immersing both the EMFE cosmetic contact lenses and commercial contact lenses (Clariti, Coopervision) in complete medium at 37°C for 24 h. In addition, complete medium was used as a control group. Extracts of the EMFE cosmetic contact lenses and extracts of commercial contact lenses were used as the comparisons. The extracts were prepared with a contact lens of 0.2 g in a complete medium of 1 ml according to ISO 10993-5. After the cells were cultured using extracts for 24 h, a cell viability test (n=5) was performed. The cytotoxicity was assessed by a cell counting kit-8 assay (C0038, Beyotime Biotech Inc). The absorbance was read at 450 nm using a multimode plate reader. The absorbance values were converted into percentage values relative to the absorbance obtained from only the cell growth media.

Head-mounted eye tracker
The head-mounted eye tracker comprises two eye-tracking cameras targeting the eyes and one forward-facing scene camera, as shown in Supplementary Fig. 21. Detailed specifications for both camera types are provided in Supplementary Table 4. The two eye-tracking cameras are integrated into the inferior-anterior region of both eyeballs, positioned approximately 30 mm from the ocular surface. Each camera is pitched upward at 50° to capture eye images. Video streams from all three cameras are consolidated via a USB hub, enabling communication with a host computer through a single USB cable. The head-mounted eye tracker has a total weight of 96 g, supporting prolonged wear and continuous acquisition of the user’s eye movement.

Eye movement feature recognition algorithm
The eye movement features on the cosmetic contact lens consist of two types of patterns: green solid circles and red dots. These patterns exhibit standardized, consistent color and structure, with a peripheral blue ring providing strong color contrast. Consequently, these characteristic patterns can be accurately identified using a simple HSV threshold and a connected component morphological threshold. The recognition results of the algorithm at key stages are illustrated in Supplementary Fig. 22.

To prevent misidentification of similarly colored patterns outside the eye, the algorithm first identifies the eye region before detecting features like the green solid circles and red dots within this region. For green solid circle identification: The algorithm applies an HSV threshold within the eye region to select pixel areas exhibiting reasonable saturation and brightness within the green color range. While illumination reflections, scene object projections, and eyelashes in the image are prone to misidentification, these regions exhibit significant morphological differences compared to the green solid circle. Therefore, filtering based on the area, eccentricity, and solidity of connected components effectively recognizes the green solid circle regions. This step also removes green solid circles severely occluded by eyelids. Due to complex and random lighting environments, reflection artifacts may superimpose on the green solid circle, causing centroid deviation. The algorithm assesses the interference level by calculating the Intersection over Union (IoU) between the connected component and its fitted ellipse. Setting an appropriate IoU threshold filters out green solid circles excessively affected by lighting interference. For red dots or their motion blur identification, similarly, the algorithm uses an HSV threshold to select red regions within the eye area. In static images, red regions appear circular, while in dynamic images, they manifest as linear blurs. Consequently, the algorithm filters based on the area of connected components. Finally, the skeleton of the connected component is extracted, enabling the calculation of either the centroid for the red dot or the trajectory for the motion blur.

Eye movement angle calculation algorithm
The eye tracking characterization, both on the eye movement model and the human eye, experiences two phases: the calibration phase and the tracking phase.

During the calibration phase, the eye movement model is rotated to a set of setup angles, and the volunteers are guided to fixate sequentially on a set of visual targets at known positions (e.g., specified gaze angles or screen coordinates). The eye tracker captures images of the eye at each target. The regions of the green solid circles are identified in each image, and their respective centroid pixel coordinates are computed. A polynomial mapping function is then fitted for each green solid circle, relating its centroid coordinates to the corresponding known gaze directions, thereby concluding the calibration phase.

During the eye-tracking phase, the eye tracker continuously captures eye images. The centroids of the detectable green solid circles are computed, and their corresponding mapping functions are applied to estimate the gaze angle. When multiple green solid circles are detected in both calibration and tracking, multiple mapping functions are constructed and applied. The final gaze direction is obtained by averaging the individual estimates from all available circles.

Safety assurance for human eye movement tracking
To evaluate key performance metrics such as recognition rate and accuracy of the eye-tracking technology during practical application, healthy participants (2 males and 2 females) were selected to wear these commercial cosmetic contact lenses. Ages of the participants are between 22 and 29 years old. This study was approved by the Ethics Committee of the First Affiliated Hospital of Nanjing Medical University (2025-SR-023). All data measurements on the bodies of participants are performed with their full, informed consent. The public disclosure of all individual data has been approved by the participants. Participants were required to be free from ocular pathologies such as dry eye syndrome or ocular surface inflammation. Before wearing the EMFE contact lens, intact packaging was verified, and participants were instructed to wash their hands thoroughly prior to lens application. During the experiments, the head-mounted eye tracker employed no close-range eye illumination. The wearing time of the cosmetic lens did not exceed 6 h. Collectively, these measures ensured the safety of the experimental procedures.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In the manuscript entitled “Spatial-chromatic encoding cosmetic contact lenses for enhanced natural eye tracking,” the\nauthors present an eye-tracking system that is integrated into cosmetic contact lenses that leverages spatial-chromatic\npatterns for enhanced performance. The main contributions of this work include: (1) the design of eye movement feature\nenhanced (EMFE) contact lenses; (2) the demonstration of highly accurate eye movement recognition under complex\nlighting conditions and off-axis camera placements; and (3) the validation of <1° tracking accuracy and calibration-free gaze\nestimation in both model eyes and human subjects across indoor and outdoor environments. This study offers a promising\nand practical approach to achieve accurate eye-tracking technology. However, from my point of view, there are several\ncritical issues that need further supplementation and clarification in the current version of the manuscript. Therefore, I\nsuggest the publication of this manuscript in Nature Communications after addressing the major issues listed below.\nFirstly, there are fundamental errors in some explanations and experimental setup.\n1. On page 9, the authors state that common cameras, due to their low frame rate, result in motion blur during saccades and\nlead to loss of critical information about rapid eye movement trajectories. However, commodity HMD eye trackers frequently\noperate at ≥ 60–120 Hz (e.g., Pico Neo3 Pro: 60/90 fps; HTC Vive Pro Eye: 120 Hz), while the head-mounted eye tracker\nused in this study records at only 30 fps. Therefore, to substantiate claims about “rapid eye movement trajectories,” the\nauthors should acquire data using head-mounted eye tracker with cameras at ≥ 60–120 fps.\n2. At the current sampling frequency, a typical saccade of ~60 ms would be sampled at only ~2 time points, which is\ninsufficient to reconstruct a rapid trajectory or estimate reliable velocity profiles. Therefore, the authors should increase the\nsampling frequency (e.g., ≥5–10 samples per saccade) for reliable recordings. Otherwise, the authors should drop these\nclaims, and any conclusions based on 30 fps restricted to regimes where it is adequate.\nSecondly, the manuscript provides limited evaluation and insufficient explanation of the key characteristics of the EMFE\ncontact lenses.\n1. The authors claim that specific patterns with vivid colors enable accurate and robust eye tracking. However, the\nmanuscript lacks an explanation of how key design parameters—such as the number, size, shape, and color of the green\ncircles or red dots—were optimized. To support this claim, the authors are encouraged to describe the design rationale and\nprovide experimental evidence comparing different pattern configurations. For example, it would be helpful to show whether\nincreasing the number of dots enhances tracking accuracy, or to include comparative results for different colors, shapes, and\narrangements.\n2. Since the contact lens remains in continuous contact with tears, it would be advisable to assess the potential leakage of\ncosmetic dye from the lens under tear-mimicking conditions. In particular, the authors are recommended to investigate\nwhether prolonged exposure to artificial tears or phosphate-buffered saline (PBS) at physiological temperature leads to dye\nleakage or color changes.\nThirdly, additional experiments and descriptions are required to enhance the completeness of the manuscript.\n1. The authors report that the system achieves an accuracy of <1° based on tracking experiments. However, this value\nreflects tracking error from relatively coarse target spacing rather than the system’s actual resolving capacity. Therefore, the\nauthors are recommended to rigorously evaluate the system’s angular resolution by testing point arrays of 1° or sub-degree\nspacing to more precisely quantify the minimum resolvable angular separation.\n2. The authors demonstrated that the system recognizes targets under various environmental conditions, such as outdoors,\nindoors, and near windows, suggesting robust recognition performance. However, these results are largely qualitative. A\nmore quantitative evaluation of accuracy would better substantiate the reliability of the system. For example, analyzing how\naccuracy varies with light intensity or light color would provide more rigorous validation. The authors are therefore\nencouraged to include such additional analyses to enhance the reliability of the system.\n3. Although the authors claim to have addressed common challenges of vision-based eye tracking under individual\nvariation, these aspects are not sufficiently demonstrated in the current manuscript. In particular, the robustness of the\nsystem should be validated under conditions that reflect inter-individual differences such as pupil size, eyelid coverage, and\nblinking. The authors are encouraged to provide experimental data from multiple subjects with diverse ocular characteristics\nto substantiate the claimed advantages of the proposed method.\nLastly, the following statements require appropriate references to support the claims.\n1. “Additionally, due to the human eye's attention mechanism, the brain primarily analyzes visual information within a 1-2°\nfield of view corresponding to the fovea.”\n2. “Similarly, an eye movement angle error of less than 1° is sufficient to accurately determine the gaze point and analyze the\nregions of visual attention.”", "reviewer_2": "The manuscript, “Spatial-Chromatic Encoding Cosmetic Contact Lenses for Enhanced Natural Eye Tracking” introduces an\ninnovative and practical approach to enhance eye tracking in natural scenes by designing spatially and chromatically\nencoded cosmetic contact lenses (EMFE lenses). It cleverly utilizes widely available and highly acceptable cosmetic contact\nproducts, avoiding the challenges associated with integrating complex electronic components into contact lenses. The\nexperimental validation is rigorous and comprehensive, demonstrating high accuracy (<1°) and excellent recognition rates\n(93%) across a range of tests, from model eye verification to human trials. Furthermore, demonstrations in diverse\napplication scenarios underscore the method's significant advantages in enhancing the\nrobustness of eye movement feature recognition, tracking accuracy, and overall system\napplicability. However, several specific aspects require further scrutiny,\nas detailed below.\n1. The manuscript establishes a crucial foundation by demonstrating the biosafety of the EMFE lens materials through\ncytotoxicity tests. However, for a device intended for prolonged ocular surface wear, biocompatibility is a multifaceted\ncharacteristic. Currently, the study lacks the characterization of two key physicochemical properties that are indispensable\nfor evaluating any contact lens material: surface wettability and oxygen permeability. These\nproperties are directly correlated with wearing comfort and ocular health and should be\ncomprehensively assessed.\n2. The manuscript currently assumes the stability of the encoding pattern during wear. However, contact lenses are subject\nto constant movement on the ocular surface during blinking and are exposed to the complex tear film environment. A critical\nconcern is whether the pattern could experience wear, deformation, or blurring due to mechanical friction against the eyelid,\ntear permeation, or protein deposition. Such degradation could significantly impact the pattern's optical performance and the\nstability of eye tracking recognition.\n3. While this study introduces a novel eye-tracking method leveraging encoded-pattern cosmetic lenses and reports key\nperformance metrics, it lacks a systematic comparison against state-of-the-art academic solutions and commercially\navailable devices. To more effectively articulate the unique contributions and overarching value of this research, it is\nrecommended to supplement a comparative analysis. This comparison should specifically address critical system\nparameters such as accuracy, robustness, and sampling rate, positioning the proposed method within the existing\nlandscape of eye-tracking technologies.\n4. The natural blinking reflex, occurring 10-20 times per minute with durations of approximately 100-400 milliseconds each,\nleads to the complete or partial occlusion of the cornea by the eyelid. This transient obscuration of the EMFE lens pattern\npresents a significant challenge. The manuscript should clarify how the proposed algorithm effectively handles the sudden\nabsence of tracking features during blinks. Specifically, it is crucial to address whether this phenomenon can result in\ntracking signal interruption or lead to anomalous output generation.\n5. The scope of eye movement tested during human trials should be detailed, specifically the maximum tested eye\nmovement angle. Large-angle eye movements can potentially induce contact lens displacement, leading to measurement\nerrors. Moreover, the dynamic interaction between the eyelid and the lens during blinking, involving rotational and\ntranslational forces, can cause instantaneous, albeit minor, displacements, even with good lens-cornea adhesion. It is\ncritical to investigate the impact of such displacements on absolute pattern position, and on the geometry-based 3D pose\nestimation. Furthermore, the time required for the algorithm to regain stable tracking after a blink needs to be quantified.\n6. The manuscript validates the system's accuracy under an ideal fixed configuration. In practical scenarios, factors such as\nvariations in head-mounted device tightness, positioning, and frame pitch and roll angles during donning and doffing can\nalter the relative pose between the camera and the eyeball. This variability can significantly affect the accuracy of the\ncalibrated mapping function or geometric model. The manuscript should address whether these real-world deployment\nchallenges could lead to degraded accuracy in practical applications.\n7. The manuscript utilizes 12 uniformly distributed green circles as the core static tracking features. However, the rationale\nfor selecting this specific number of feature points is not sufficiently elaborated. It is unclear whether a different number of\nfeature points could achieve comparable or superior performance. The authors should clarify whether this choice was\nempirically determined or derived through systematic optimization. Providing the relevant design rationale or experimental\nvalidation for the feature point selection would significantly strengthen the manuscript.\n8. In this article, the authors spend considerable space introducing bioelectronics eye tracking technology. We suggest that\nthe authors add some important research in the field of bioelectronics (see the following references: DOI: 10.1038/s41467-023-39315-6; 10.1038/s41528-025-00458-9; 10.1126/sciadv.abl8379).", "reviewer_3": "The paper describes a new method for implementing camera-based eye trackers using contact lenses. The system consists\nof two parts. First a contact lens with a blue peripheral ring dotted with green and red dots spaced at regular intervals. The\nsecond part is the spectacle frame equipped with RGB cameras.\nThe working principle consists in taking images of the lens, use the high colour contrast of the large green dots on the blue\nring to compute the centroid of the detected green dots (called circle in the article, I do not think it is the correct word), thereby\nyielding the gaze direction. Likewise, the red dots (much smaller than the green ones) generate streaks than are used to\nextract eye movements.\nThe proposed new eye tracker implementation is interesting since it is using “classic” contact lens, the contact lens remains\npassive (no power), does not require high quality camera and is not prone to parasite light interference.\nOverall, I find the paper well written with very interesting results in the field of eye tracking. Still, there are some issues that\nneeds to be addressed. I’m listing some below.\nThe state-of-the art analysis is missing a recently published method which is similar to the one presented in the sense that it\nuses passive contact lens with specific features that can be detected using a camera to determine the gaze (F I. M. Fradkin,\net al., \"Contact lens with moiré labels for precise eye tracking,\" Proc. SPIE 13414, Optical Architectures for Displays and\nSensing in Augmented, Virtual, and Mixed Reality (AR, VR, MR) VI, 134141W (21 March 2025);\nhttps://doi.org/10.1117/12.3058057).\nI don’t think that embedding optolectronic devices on lens compromise transparency and raises biosafety as claimed in the\nintroduction if proper precautions are taken as describes in the references. I agree that it is easier to meet these\nrequirements using the proposed methods.\nOne thing that should be better explained. Based on the description, if the camera is significantly off centred with the eye,\ne.g. positioned below the eye as in Fig. 2., the camera sees more green dots at the bottom of the eye, even though the\nperson looks straight ahead. So computing the centroid, would indicated the person is looking down rather than straight\nahead. That does not seem correct.\nI do not understand why it would not possible to use the green discs to obtain trajectories? Why the need to use tiny\n(compared to the green dots) red dots?\nYou have not explained how the various algorithms are implemented. What hardware/software platform is used? Is it\nembedded in the spectacle frame shown in Fig .1? You show outdoor experimentations, are computation done in real or\ndiffered time?\nIt would also be interesting to better described your experiments, how many lens were tested, how many persons involved,\netc were done to measure accuracy.\nAlso, in Fig2 would be nice to have a short description of the experimental set up used to produce the results. You give a\nrecognition rate but you don’t say how many tests were done, on how many persons.\nFig 2 and Fig 2 caption refer to CCL, better use EMFE as defined in the main text.\nThe human eye can have a wide rotation eye movement, but usually above 16° horizontally, one prefers turning the head.\nSo steps of 10° seems a bit too large to assess accuracy, shouldn’t you have reduce the study between -16°and +16° using\nsmaller steps?\nThe abstract claims that no calibration is required. Yet, in section Eye tracking Characterization a 9-point calibration is used.\nThis needs to be clarified, calibration or not calibration?"}, "author_response": "Response to Reviewer 1 Comments\nComments:\nIn the manuscript entitled “Spatial-chromatic encoding cosmetic contact lenses for enhanced\nnatural eye tracking,” the authors present an eye-tracking system that is integrated into\ncosmetic contact lenses that leverages spatial-chromatic patterns for enhanced performance.\nThemaincontributionsofthisworkinclude:(1)thedesignofeyemovementfeature\nenhanced (EMFE) contact lenses; (2) the demonstration of highly accurate eye movement recognition\nunder complex lighting conditions and off-axis camera placements; and (3) the validation of\n<1° tracking accuracy and calibration-free gaze estimation in both model eyes and human\nsubjects across indoor and outdoor environments. This study offers a promising and practical\napproach to achieve accurate eye-tracking technology. However, from my point of view,there\nare several critical issues that need further supplementation and clarification in the current\nversion of the manuscript. Therefore, I suggest the publication of this manuscript in Nature\nCommunicationsafteraddressingthemajorissueslistedbelow.\nReply:Wesincerelyappreciatethereviewer’spositiveassessmentoftheapplicationpotential\nand practical value of our eye-tracking technique based on spatial-chromatic encoding\ncosmetic contact lenses.At the same time, the reviewer’s insightful comments have played a\ncritical role in enhancing the quality of this paper. In response to the major issues raised, we\nhaveconductedadditionalexperimentstothebestofourabilityandsupplementedtherevised\nmanuscript with essential data. Below are our point-by-point responses to the reviewer’s\ncomments.\nFirstly,therearefundamentalerrorsinsomeexplanationsandexperimentalsetup.\n1. On page 9, the authors state that common cameras, due to their low frame rate, result in\nmotionblurduringsaccadesandleadtolossof critical informationabout rapideye movement\ntrajectories. However, commodity HMD eye trackers frequently operate at ≥ 60-120 Hz (e.g.,\nPico Neo3 Pro: 60/90 fps; HTC Vive Pro Eye: 120 Hz), while the head-mounted eye tracker\nused in this study records at only 30 fps. Therefore, to substantiate claims about “rapid eye movementtrajectories,”theauthorsshouldacquiredatausing head-mountedeye trackerwith\ncamerasat≥60-120fps.\nReply: We sincerely thank the reviewer for their valuable feedback from a professional\nperspective, which has been crucial in enhancing the scientific rigor of our manuscript. The\nreviewer correctly noted that our setup, using a 30-fps eye tracker, does not strictly support\nclaims of capturing \"rapid eye movement trajectories.\" To address this, we compared the\neye-trackingresultsfromthelow-frame-ratesystemwiththeEMFE contactlensagainst those\nobtained with a Pico Neo3 Pro eye tracker, which samples at 90 fps.As shown in Figure 1a,\nwe mounted an EMFE contact lens on the left eye of a model eye and captured images at 30\nfps, while simultaneously recording the right eye with the Pico Neo3 Pro eye tracker and\ncollecting its output data. Figure 1b shows the time-series plots of the yaw and pitch angles\nobtainedfromboththePicoNeo3ProandtheEMFEcontactlensmethods.Thedatafromthe\nPico Neo3 Pro eye tracker, which captured eye movement speeds exceeding 200°/s during\nthis segment, show a highly consistent gaze trajectory with the EMFE method. In detail, the\nPico Neo3 Pro data exhibit higher-frequency trajectory components. Accordingly, in the “Eye\nTracking Characterization using Eye Movement Model” of the revised manuscript, we have\nreplaced the expression \"rapid eye movement trajectories\" with \"continuous gaze angle\npositioning\" to more accurately describe the capability of the EMFE contact lens-based eye\ntrackingtechnique.\nFigure 1. Comparison between the 30-fps eye tracking system based on the EMFE\ncontactlensandthe90-fpseyetrackingsystembasedonthePicoNeo3Proeyetracker.\na Photograph of the model eye employed to generate synchronous eye movements. b\nTime-series plots of the yaw and pitch angles obtained from both the Pico Neo3 Pro and the\nEMFEcontactlensmethods.\n2.Atthecurrentsamplingfrequency,atypicalsaccadeof~60mswouldbesampledatonly~2\ntime points, which is insufficient to reconstruct a rapid trajectory or estimate reliable velocity\nprofiles. Therefore, the authors should increase the sampling frequency (e.g., ≥5-10 samples\npersaccade)forreliablerecordings.Otherwise,theauthorsshoulddroptheseclaims,andany\nconclusionsbasedon30fpsrestrictedtoregimeswhereitisadequate.\nReply: We sincerely thank the reviewer for pointing out the inaccuracies in our original\nmanuscript. In human eye tracking experiment and reading application of the revised\nmanuscript, we have removed all discussions related to saccade velocity and saccade\nidentification. These have been replaced with the terms \"continuous gaze coordinate\npositioning\" and \"frame-by-frame eye movement velocity calculation.\" In future studies, we\nplan to upgrade the eye tracking camera system to capture eye movement data at a higher\nsampling rate. This will enable us to properly analyze various eye movements such as\nsaccades, microsaccades, fixations, and smooth pursuit. The above explanations have been\nadded to the revised \"Discussion\" section to provide a more objective and comprehensive\nassessment of the current limitations of the eye-tracking technology based on EMFE contact\nlenses.\nSecondly, the manuscript provides limited evaluation and insufficient explanation of the key\ncharacteristicsoftheEMFEcontactlenses.\n1. The authors claim that specific patterns with vivid colors enable accurate and robust eye\ntracking. However, the manuscript lacks an explanation of how key design parameters—such\nas the number, size, shape, and color of the green solid circles or red dots—were optimized.\nTosupportthisclaim,theauthorsareencouragedtodescribethedesignrationaleandprovide\nexperimental evidence comparing different pattern configurations. For example, it would be\nhelpful to show whether increasing the number of dots enhances tracking accuracy, or to\nincludecomparativeresultsfordifferentcolors,shapes,andarrangements.\nReply: We appreciate the opportunity to provide further explanation of the key design\nparameters of the EMFE contact lenses and their influence on eye-tracking performance.\nDuring the research process, we experimented with various pattern designs for the EMFE\ncontact lenses, such as the four evenly distributed green solid circles and the twelve evenly\ndistributedgreensolidcircleswithreddots,asrespectivelyillustratedinFigure2.\nSince cosmetic contact lenses require a sufficiently large transparent optical zone to\nensure visual clarity, we tended to design the feature patterns within the peripheral annular\nregionofthelens.First,theeffectofthenumberofgreensolidcirclesongaze-angleaccuracy\nwasinvestigated.WedesignedandfabricatedtwotypesofEMFEcontactlenseswithdifferent\nnumbers of green solid circles: one with 4 circles and the other with 12 circles, and the eye\nmovementmodelwasemployedtocharacterizetheiraccuracyofgazeangle.Wemountedthe\n4-circleEMFEcontactlens(asshowninFigure2a)onamodeleyeandrotatedthemodeleye\nin steps of 10° within a range of ±40° in yaw and ±30° in pitch, capturing images at each\norientation.Byidentifyingthegreensolidcirclepatternsandextractingthecoordinatesoftheir\ncentroids, we constructed the mapping function between the centroid positions and the eye\nmovementanglesusing polynomialfittingtocharacterize theeye-trackingaccuracyof 4-circle\nEMFE contact lens. Figure 2b and c show the calculated distribution of gaze angles and the\nangular error distributions in the yaw and pitch directions, respectively. Statistically, the\neye-tracking angular error for 4-circle EMFE contact lens was 1.20° ± 0.72°. Figure 2d-f\npresent the eye-tracking accuracy of 12-circle EMFE contact lens, which achieved anangular\nerrorof0.74°±0.40°.The12-circlelensexhibitssuperioreye-trackingaccuracy,whichcanbe\nattributed to the camera’s ability to identify at least three green solid circles across various\ngaze angles. By applying their respective mapping functions and averaging the computed\ngaze angles, the system mitigates the effects of centroid deviations caused by environmental\nlight interference and pattern distortion due to eyelid occlusion. The results indicate that a\ngreater number of green solid circle features can improve the eye-tracking accuracy of EMFE\ncontactlens-basedsystems.\nFigure2.aPhotographsoftheEMFEcontactlenswithfourgreensolidcircles.b-cGazepoint\ncoordinatesanderrorstatisticofthe4greensolidcirclesEMFEcontactlens.dPhotographsof\nthe EMFE contact lens with twelve green solid circles. e-f Gaze point coordinates and error\nstatisticofthe12greensolidcirclesEMFEcontactlens.Intheerrorstatistic,themiddlelineis\ndetermined by median, the box is determined by the 25th and 75th percentiles, and the\nwhiskers are determined by the 5th and 95th percentiles. n = 63 independent gazing point\ncoordinates.\nFurthermore, a higher number of green solid circles offers greater robustness against\neyelid occlusion in off-axis imaging. Figure 3a shows a representative ocular image captured\nwhile wearing the 4-circle lens, where eyelid coverage prevents a complete view of all four\ncircles. In comparison, the 12-circle lens can expose more detectable circles under the same\nconditions (in Figure 3b). This not only enhances the robustness of eye movement feature\nrecognition but also reduces the error in gaze angle calculation caused by local pattern\ndistortions,asthecalculationcanrelyonalargersetofreliablefeatures.\nFigure 3. The EMFE contact lenses with different feature designs such as the four evenly\ndistributedgreensolidcirclesaandthetwelveevenlydistributedgreensolidcirclesb.\nHowever, within the constrained annular region, increasing the number of green solid\ncircles inevitably reduces their individual area and narrows the inter-circle spacing. A small\nareamakesitdifficulttoensurehighaccuracyinthecoordinatecalculationofeachgreensolid\ncircle, yet their coordinate information plays a critical role in functions such as gaze direction\nestimation and camera slippage compensation. We evaluated the above trade-off through\ntheoretical modeling. To ensure sufficient spacing between circles, we assumed that the\ndiameter of each green solid circle equals the spacing between adjacent circles.As shown in\nFigure 4, as the number of circles increases from 8 to 16, their diameter decreases from 2.2\nmmto1 mm.Basedonthecameraparameters,ifthedetectedradiusofagreensolidcirclein\ntheimage deviates by one pixel, alikely occurrencedue toimaging noiseand blurryedges of\nthe printed pattern, the resulting distance error increases from 0.6 mm to 1.2 mm. Thus, an\nappropriate number of green solid circles must be chosen to balance the accuracy of both\ngaze angle and circle coordinate estimation. Accordingly, we ultimately selected a ring\nconfiguration comprising 12 green solid circles. The 12-circle EMFE contact lens has a high\naccuracyof<1° andasmalldistanceerrorof<1mmatthesametime.\nFigure4.Effectofthenumberofgreensolidcirclesonthecoordinatecalculation.\nRegarding the colors of the eye-tracking feature patterns, we selected red, green, and\nblue for designing dot, solid circle, and ring patterns, respectively. This is because in the hue\ndomain, red, green, and blue are located at 0°, 120°, and 240°, respectively, exhibiting\nsignificant chromatic differences that facilitate accurate pattern recognition. Furthermore, the\ngreen solid circles are standard shapes with known diameters. Combined with the camera's\nimaging parameters, they enable the estimation of the pose information of the green solid\ncirclesinthecameracoordinatesystem.Thiscapabilityaidsindeterminingthespatialposition\nof the cosmetic contact lens, thereby supporting more advanced eye-tracking functionalities\nsuchascalibration-freegazedirectionestimationandcameraslippagecompensation.\nThe aforementioned experimental results and design rationale have been incorporated\nintothe“DesignofEyeMovementFeatureEnhanced(EMFE)CosmeticContactLens”section\nand “Eye Tracking Characterization using Eye Movement Model” section in the revised\nmanuscriptandsupplementarymaterials.\n2. Since the contact lens remains in continuous contact with tears, it would be advisable to\nassessthepotentialleakageofcosmeticdyefromthelensundertear-mimickingconditions.In\nparticular, the authors are recommended to investigate whether prolonged exposure to\nartificial tears or phosphate-buffered saline (PBS) at physiological temperature leads to dye\nleakageorcolorchanges.\nReply: We sincerely thank the reviewer for this valuable suggestion. Potential dye leakage\nand color changes in the cosmetic contact lenses are of significant importance for long-term\nbiocompatibility and the stability of eye tracking. The EMFE contact lens is fabricated by a\nmanufacturerofcosmeticcontactlenseswitharegistrationcertificateformedicaldeviceusing\nasandwich-like preparation process, in which theencoding patternis encapsulated within the\nhydrogel material. This design prevents direct contact between the cosmetic dye and the\neyelids/cornea, eliminates the risk of dye leakage, and forms the foundation for the long-term\npattern stability of the EMFE contact lens. To verify the stability, we immersed two EMFE\ncontact lenses in PBS and incubated them in a water bath maintained at 35 °C, the typical\ntemperature of the ocular surface, for 6 hours to simulate long time wear conditions.\nPhotographs of the EMFE contact lenses before and after the 6-hour immersion in PBS at\n35 °C are shown in Figure 5. As can be observed, the PBS solution remained clear and\ncolorlessafterimmersion,andnoobservablechangesincolororpatternweredetectedonthe\nEMFE contact lenses. Therefore, it can be concluded that no dye leakage occurred from the\nEMFE contact lenses. These experimental results have been included in the “Design of Eye\nMovement Feature Enhanced (EMFE) Cosmetic Contact Lens” section of the revised\nmanuscriptandthesupplementarymaterials.\nFigure5.PhotographsoftheEMFEcontactlensesbeforeandafterimmersioninPBSat\n35°Cfor6hours\nThirdly,additional experiments and descriptions are required to enhance the completeness of\nthemanuscript.\n1. The authors report that the system achieves an accuracy of <1° based on tracking\nexperiments. However, this value reflects tracking error from relatively coarse target spacing\nratherthanthesystem’sactualresolvingcapacity.Therefore,theauthorsarerecommendedto\nrigorouslyevaluate thesystem’sangular resolution bytestingpoint arrays of 1°or sub-degree\nspacingtomorepreciselyquantifytheminimumresolvableangularseparation.\nReply: We thank the reviewer for the comment, which has prompted a more rigorous\nevaluation of the accuracy of the EMFE contact lens-based eye-tracking technique. Following\nthesuggestion, wemountedthelensonamodeleye androtatedthemodeleye instepsof 1°\nwithin a range of ±40° in yaw and ±30° in pitch, enabling a finer quantitative assessment of\ngazeangleaccuracy.Figure6ashowstheresultingdistributionofthecomputedgaze angles,\ndemonstrating that the vast majority of gaze coordinates accurately align with the intended\ntargets. Figure 6b summarizes the yaw and pitch angular errors across all 4,941 gaze\ncoordinate points. The overall angular error was 0.29° ± 0.21° (mean ± S.D.). We observed\nthat the characterization data collected at 1° intervals yielded higher accuracy compared to\nthat obtained at 10° intervals. This improvement can be attributed to the non-uniform\ndistribution of angular errors across the eye movement range when using the EMFE contact\nlens. Specifically,thecomputed gaze angles exhibit minimalerrors in the central regionof the\neye movement range, while larger errors occur mainly at the four corners-corresponding to\nmoreextremegazeangles.Theseresidualerrorsstemfromthereducednumberofdetectable\nfeature patterns at extreme angles and the inherent limitations of polynomial-based fitting\nunder large-angle rotations. We have supplemented these experimental results in the “Eye\nTracking Characterization using Eye Movement Model” section of the revised manuscript and\nthesupplementarymaterials.\nFigure 6. a Gaze point coordinates when eyeball model rotated to different gaze directions in\nstepsof1° withinarangeof ±40° inyaw and ±30° inpitch.Thegray squaresrepresent the\nset gaze coordinates, and the red dots represent the calculated gaze coordinates. b Error\nstatistic of gaze point coordinates. The middle line is determined by median, the box is\ndetermined by the25th and 75th percentiles, and the whiskersare determined by the5th and\n95thpercentiles.n=4941independentgazingpointcoordinates.\n2.The authors demonstrated that the system recognizes targets under various environmental\nconditions, such as outdoors, indoors, and near windows, suggesting robust recognition\nperformance. However, these results are largely qualitative.Amore quantitative evaluation of\naccuracy would better substantiate the reliability of the system. For example, analyzing how\naccuracy varies with light intensity or light color would provide more rigorous validation. The\nauthorsarethereforeencouragedtoincludesuchadditionalanalysestoenhancethereliability\nofthesystem.\nReply:Wesincerelythankthereviewerforprovidinguswiththeopportunitytoconductamore\nrigorous evaluation of the accuracy of the EMFE contact lens-based eye-tracking technique\nunder different illumination scenarios. The characterization results of the model eye in an\nindoor environment has beenpresented inFigure3b-cin theoriginal manuscript. Building on\nthis, we have now supplemented the eye-tracking characterization with two additional\nrepresentative scenarios: beside a window and outdoors. The corresponding gaze angle\ndistributionsareshowninFigures7bandc,respectively.Figure7dsummarizestheyaw and\npitchangularerrorsunderthesethreelightingconditions.Overall,thetrackingaccuracy(mean\n±S.D.)was0.74°±0.40°indoors,0.95°±0.61°besideawindow,and0.96°±0.67°outdoors.\nThe slightly higher angular errors observed in the window-side and outdoor scenarios can be\nattributed to more complex lighting conditions in those environments, which introduced\ninterferenceinidentifyingthecentroidcoordinatesofthegreensolidcircles.Nevertheless,the\naccuracy remained better than 1° in all three scenarios, demonstrating the practical\napplicabilityand potentialof theEMFEcontact lens-based eye-trackingtechnique. InTable1,\nwe have also summarized the environmental illuminance, color temperature parameters, and\ncorresponding tracking accuracy for each scenario. The above experimental data and\nconclusions have been incorporated into the “Eye Tracking Characterization using Eye\nMovementModel”sectionoftherevisedmanuscriptandsupplementarymaterials.\nFigure 7. a-c Gaze point coordinates when eyeball model rotated to different gaze directions\nunder various environmental conditions, such as indoor, near window, and outdoor. d Error\nstatistic of gaze point coordinates under various environmental conditions. The middle line is\ndetermined by median, the box is determined by the 25th and 75th percentiles, and the\nwhiskers are determined by the 5th and 95th percentiles. n = 63 independent gazing point\ncoordinates.\nTable 1. The statistics of various environmental illumination parameters and\neye-trackingaccuracy\nCase Indoor Window Outdoor\nIntensity(lux) 27 322 25100\nColorTemperature(K) 5516 5207 5808\nMeanAbsoluteError(°) 0.74 0.95 0.96\nStandardDeviation(°) 0.40 0.61 0.67\n3. Although the authors claim to have addressed common challenges of vision-based eye\ntracking under individual variation, these aspects are not sufficiently demonstrated in the\ncurrent manuscript. In particular, the robustness of the system should be validated under\nconditions that reflect inter-individual differences such as pupil size, eyelid coverage, and\nblinking.Theauthorsareencouragedtoprovideexperimentaldatafrommultiplesubjectswith\ndiverseocularcharacteristicstosubstantiatetheclaimedadvantagesoftheproposedmethod.\nReply: We thank the reviewer for the valuable suggestion, which is crucial for enhancing the\ncompleteness of this work. The proposed EMFE contact lens-based eye-tracking technique\nachievesrobustnessagainstindividualvariationsbydetectingcustomizedeye-trackingfeature\npatterns printed on the lenses. This approach does not rely on the recognition of the pupil or\niris regions, that are often subject to significant individual differences, thereby improving the\ngeneral applicability of the method. Therefore, in principle, this eye-tracking technology is\ninherently immune to individual variations such as iris color and corneal curvature, as well as\nto the refractive effects of the cornea and aqueous humor. In parallel, four volunteers were\ninvited to participate in an eye-tracking test using sterilized EMFE contact lenses, and the\nocular characteristics of each volunteer were recorded. The group included two male and two\nfemale participants, all free of ocular diseases. Key ocular characteristics, such as pupil\ndiameter and the extent of eyelid coverage, are summarized in Table 2. Here, the degree of\neyelidcoverageis defined asthe ratioof thelensarea covered bytheeyelids tothetotal lens\narea.\nTable2.Inter-individualdifferencesinocularcharacteristics\nSex Age Pupildiameter Eyelidcoverage\nVolunteerA Male 23 3mm 23.2%\nVolunteerB Female 25 5mm 20.7%\nVolunteerC Male 22 4mm 24.0%\nVolunteerD Female 29 3mm 25.0%\nDuring the eye movement characterization experiment, the volunteers were instructed to\nobserve a whiteboard positioned 60 cm away. A two-dimensional array of gaze targets was\narranged on the whiteboard. While the human eye is capable of a wide range of rotational\nmovement, it generally prefers head turning for horizontal angles beyond approximately 16°.\nTherefore, the target points were confined within a range of ±16° in yaw and ±16° in pitch,\nspaced at 4° intervals, forming a 9×9 grid comprising 81 gaze targets. The volunteers were\nguided to fixate on each of these points sequentially, and six frames of eye images were\ncaptured per gaze point. The distributions of gaze angles, along with the calculated accuracy\nand precision for all four volunteers, are shown in Figure 8. The specific accuracy and\nprecisionvaluesforeachvolunteer(A,B,C,D)aresummarizedinTable3.Allfourvolunteers\nachieved eye-tracking accuracy and precision better than 1°, demonstrating that the\nEMFE-based eye-tracking technique can reliably determine the gaze direction. This\nperformance supports its potential application in cognitive, psychological, and\nhuman-computer interaction studies, and confirms the consistency and reliability of the\ntrackingresultsacrossdifferentindividuals.\nFigure 8. Gaze point map, accuracy, and precision of the EMFE contact lens-based\neye-trackingtechniqueinfourvolunteers.\nTable3.Eye-trackingaccuracyandprecisioninthefourvolunteers.\nAccuracy Precision\nVolunteerA 0.70°±0.38° 0.22°±0.13°\nVolunteerB 0.90°±0.50° 0.33°±0.25°\nVolunteerC 0.78°±0.67° 0.33°±0.28°\nVolunteerD 0.95°±0.61° 0.54°±0.42°\nEyelid coverage during blinking significantly reduces the success rate of ocular feature\nidentification in eye-tracking technologies, representing a common challenge in the field. To\nquantitatively evaluate the impact of eyelid coverage during blinking ontracking performance,\nweconductedexperimentswithhumanparticipants.Blinkstypicallylastbetween100-400ms,\nwith varying degrees of eyelid occlusion throughout the process. Volunteers wore an EMFE\ncontact lens on the left eye and were instructed to perform fast and heavy blinks respectively,\nthatowndifferentduration.Weconductedaframe-by-frameanalysisofthedetectability ofthe\neye-tracking enhancement patterns and the extent of eyelid coverage to assess the effect of\nblinking on tracking performance. Simultaneously, an infrared-equipped camera captured\nimages of the right eye to track eye movements via pupil recognition during blinking, allowing\nforcomparisonwiththeEMFEcontactlens-basedmethod.AsshowninFigure9a,thenumber\nofdetectablegreensolidcirclesdecreasedasthedegreeofeyelidcoverageincreased.When\ncoverage reached 80% or more, no green solid circles could be identified, resulting in\napproximately 66 ms of eye-tracking data loss. In comparison, the pupil was occluded more\neasilyduringblinks,leadingtoalonger failureperiodinpupil-basedtracking(about231 msof\ndata loss). Similar results were observed during heavy blinks, which involved moreprolonged\neyelid coverage. In these cases, data loss was approximately 198 ms for the EMFE contact\nlens-based method and 330 ms for the pupil-based method. In summary, when eyelid\nocclusion exceeds 80% during a blink, the identification of feature patterns becomes\nunfeasible, leading to temporary tracking failure. However, the failure duration is substantially\nshorter than that of pupil-based eye tracking, and tracking resumes immediately upon eye\nreopening.\nThe above experimental data and conclusions have been incorporated into the “Eye\nTracking Characterization in Human Eyes Wearing EMFE Cosmetic Contact Lenses” section\noftherevisedmanuscriptandsupplementarymaterials.\nFigure 9. Comparison of EMFE contact lens-based and pupil-based eye tracking\nperformanceduringfastandheavyblinks.\nLastly,thefollowingstatementsrequireappropriatereferencestosupporttheclaims.\n1. “Additionally, due to the human eye's attention mechanism, the brain primarily analyzes\nvisualinformationwithina1-2°fieldofviewcorrespondingtothefovea.”\n2. “Similarly,aneye movement angleerror of less than1°is sufficient toaccurately determine\nthegazepoint andanalyzetheregionsofvisualattention.”\nReply: We thank the reviewer for this suggestion. In the revised manuscript, we have\nincorporatedappropriatereferencestosupportthesestatements,asindicatedbelow:\n1. “Additionally, due to the human eye's attention mechanism, the brain primarily analyzes\nvisualinformationwithina1-2°fieldofviewcorrespondingtothefovea.50”\n2. “Similarly,aneye movement angleerror of less than1°is sufficient toaccurately determine\nthegazepoint andanalyzetheregionsofvisualattention.52”\nReferences:\n50. Poletti, M., Rucci, M., & Carrasco, M. Selective attention within the foveola. Nature\nNeuroscience,20, 1413-1417(2017).\n52. Martina P. An eye for detail: Eye movements and attention at the foveal scale, Vision\nResearch,211,108277(2023).\nResponse to Reviewer 2 Comments\nComments:\nThemanuscript,“Spatial-ChromaticEncodingCosmeticContactLensesforEnhancedNatural\nEye Tracking” introduces an innovative and practical approach to enhance eye tracking in\nnatural scenes by designing spatially and chromatically encoded cosmetic contact lenses\n(EMFE contact lenses). It cleverly utilizes widely available and highly acceptable cosmetic\ncontact products, avoiding the challenges associated with integrating complex electronic\ncomponents into contact lenses. The experimental validation is rigorous and comprehensive,\ndemonstrating high accuracy (<1°) and excellent recognition rates (93%) across a range of\ntests, from model eye verification to human trials. Furthermore, demonstrations in diverse\napplication scenarios underscore the method's significant advantages in enhancing the\nrobustness of eye movement feature recognition, tracking accuracy, and overall system\napplicability.However,severalspecificaspectsrequirefurtherscrutiny,asdetailedbelow.\nReply:Wesincerelythankthereviewerfortherecognitionofthenoveltyandpracticalvalueof\nour research work. Furthermore, we are grateful for their insightful comments, which have\nbeeninstrumentalinenhancingthescientificrigorandcompletenessofthispaper.Inresponse\nto the questions and suggestions raised, we have diligently performedadditional experiments\nandcollectedrelevantdataoverthepastperiod.Belowareourpoint-by-pointresponses.\n1. The manuscript establishes a crucial foundation by demonstrating the biosafety of the\nEMFE contact lens materials through cytotoxicity tests. However, for a device intended for\nprolonged ocular surface wear, biocompatibility is a multifaceted characteristic. Currently, the\nstudy lacks the characterization of two key physicochemical properties that are indispensable\nfor evaluating any contact lens material: surface wettability and oxygen permeability. These\nproperties are directly correlated with wearing comfort and ocular health and should be\ncomprehensivelyassessed.\nReply: We thank the reviewer for their suggestion. The surface wettability and oxygen\npermeability of contact lenses are crucial for wearing comfort and safety. The EMFE contact\nlenses presented in this work are made of hydrogel material, with a measured oxygen\npermeability (Dk) of and an oxygen transmissibility\n(Dk/t)of .ThewatercontentoftheEMFEcontactlensis\n18.2 × 10⁻¹¹(cm²/s)[mL·O₂/(mL·hPa)]\n56%,classifyingitasamedium-water-contenthydrogelcontactlens.\n19.8 × 10⁻⁹(cm/s)[mL·O₂/(mL·hPa)]\nTo evaluate surface wettability, we first removed excess water from the lens surface and\nthen applied a 5 μLwater droplet. The spreading process was recorded at 1 second intervals\nusing a camera. As shown in Figure 1, the droplet rapidly spread across the lens surface\nwithout maintaining a spherical shape. This behavior indicates that the interaction energy\nbetweenthewaterandthelenssurfacesignificantlyexceedsthecohesiveenergyofthewater\nitself,demonstratingexcellentsurfacewettabilityoftheEMFEcontactlens.\nAll the above physicochemical parameters and experimental data have been included in\nthe “Design of Eye Movement Feature Enhanced (EMFE) Cosmetic Contact Lens” section of\ntherevisedmanuscriptandsupplementarymaterials.\nFigure1.SurfacewettabilitycharacterizationoftheEMFEcontactlens.\n2. The manuscript currently assumes the stability of the encoding pattern during wear.\nHowever, contact lenses are subject to constant movement on the ocular surface during\nblinking and are exposed to the complex tear film environment. A critical concern is whether\nthe pattern could experience wear, deformation, or blurring due to mechanical friction against\nthe eyelid, tear permeation, or protein deposition. Such degradation could significantly impact\nthepattern'sopticalperformanceandthestabilityofeyetrackingrecognition.\nReply: We thank the reviewer for the opportunity to elaborate on the stability of eye tracking\nwith EMFE contact lenses during extended wear, which is crucial for demonstrating the\napplication potential of this technology. The EMFE contact lens is fabricated using a\nsandwich-like preparation process by a manufacturer of cosmetic contact lenses with a\nregistrationcertificateformedicaldevice, inwhichtheencodingpatternisencapsulatedwithin\nthe hydrogel material. This design prevents direct contact between the pattern and the\neyelids/cornea, eliminates the risk of dye leakage, and forms the foundation for the long-term\nstabilityoftheEMFEcontactlens.\nTo evaluate the long-term stability, a volunteer was instructed to wear an EMFE contact\nlens continuously for 6 hours. Eye-tracking performance was characterized both before and\nafter this period under the same experimental setup. During the eye movement\ncharacterization experiment, the volunteer was instructed to observe a whiteboard positioned\n60 cm away.Atwo-dimensional array of gaze targets was arranged on the whiteboard. While\nthe human eye is capable of a wide range of rotational movement, it generally prefers head\nturning for horizontal angles beyond approximately 16°. Therefore, the target points were\nconfinedwithinarangeof±16°inyaw and±16°inpitch,spacedat4°intervals,forminga9×9\ngrid comprising 81 gaze targets. The volunteer was guided to fixate on each of these points\nsequentially, and six frames of eye images were captured per gaze point. The distributions of\ngaze angles, along with the calculated accuracy and precision before and after the 6-hour\nwearing period, are shown in Figure 2. Statistically, the eye-tracking accuracy and precision\nwith the EMFE contact lens were 0.70° ± 0.38° and 0.22° ± 0.13°, respectively, before\nlong-time wearing, and 0.61° ± 0.34° and 0.28° ± 0.18° afterwards.After removal of the lens,\nno blurring or deformation of the feature patterns was observed (in Figure 3), confirming the\nstabilityoftheEMFEcontactlensforlong-termeye-trackingapplications.\nAlltheaboveexperimentaldatahavebeenincludedinthe“EyeTrackingCharacterization\nin Human Eyes Wearing EMFE Cosmetic Contact Lenses” section of the revised manuscript\nandsupplementarymaterials.\nFigure 2. Gaze point map, accuracy, and precision of the EMFE contact lens-based\neye-trackingtechniquebeforeandafter6-hourswearing.\nFigure3.PhotographoftheEMFEcontactlensafter6-hourswearing.\n3. While this study introduces a novel eye-tracking method leveraging encoded-pattern\ncosmetic lenses and reports key performance metrics, it lacks a systematic comparison\nagainst state-of-the-art academic solutions and commercially available devices. To more\neffectively articulate the unique contributions and overarching value of this research, it is\nrecommended to supplement a comparative analysis. This comparison should specifically\naddress critical system parameters such as accuracy, robustness, and sampling rate,\npositioningtheproposedmethodwithintheexistinglandscapeofeye-trackingtechnologies.\nReply: We thank the reviewer for this suggestion. We have surveyed representative\ncommercially available eye trackers and state-of-the-art eye-tracking technologies, and a\ncomparisonoftheirkeyparameters,advantages,andlimitationsisprovidedinthetablebelow.\nThistablehasbeenaddedtotherevisedsupplementarymaterials.\nReferences:\n1. Tobii Pro Glasses 3, https://www.tobii.com/products/eye-trackers/wearables/tobii-pro-gl\nasses-3, (2025).\n2. EyeLink3-EyeandHeadTracker,https://www.sr-research.com/eyelink-3/,(2025).\n3. Wang, J., Wang, T., Xu, B., Cossairt, O. & Willomitzer, F. Accurate eye tracking from\ndense 3D surface reconstructions using single-shot deflectometry. Nature\nCommunications16,2902(2025).\n4. Houben, M.M.J., Goumans, J. & van der Steen, J. Recording three-dimensional eye\nmovements: scleral searchcoils versus videooculography.InvestigativeOpthalmology &\nVisualScience47,179(2006).\n5. Nezvadovitz, J. & Rao, H. Using natural head movements to continually calibrate EOG\nsignals.JournalofEyeMovement Research15(5),1(2022).\n6. Frey, M., Nau, M. & Doeller, C.F. Magnetic resonance-based eye tracking using deep\nneuralnetworks.NatureNeuroscience24,1772-1779(2021).\n7. Shi,Y.etal.Eyetrackingandeyeexpressiondecodingbasedontransparent,flexibleand\nultra-persistentelectrostaticinterface.NatureCommunications14,3315(2023).\n8. Zhu, H. et al. Frequency-encoded eye tracking smart contact lens for human–machine\ninteraction.NatureCommunications15,3588(2024).\n9. Gan, X. et al. Closed-eye intraocular pressure and eye movement monitoring via a\nstretchablebimodalcontact lens.Microsystems&Nanoengineering11,83(2025).\n10. Khaldi,A.etal.Alaseremittingcontactlensforeyetracking.ScientificReports10,14804\n(2020).\n11. Othéguy, M., Nourrit, V. & de Bougrenet de la Tocnaye, J.-L. Instrumented Contact Lens\nto Detect Gaze Movements Independently of Eye Blinks. Translational Vision Science &\nTechnology13,12(2024).\n4.Thenaturalblinkingreflex,occurring10-20timesperminutewithdurationsofapproximately\n100-400 milliseconds each, leads to the complete or partial occlusion of the cornea by the\neyelid. This transient obscuration of the EMFE contact lens pattern presents a significant\nchallenge. The manuscript should clarify how the proposed algorithm effectively handles the\nsuddenabsenceoftrackingfeaturesduringblinks.Specifically,itiscrucialtoaddresswhether\nthis phenomenon can result in tracking signal interruption or lead to anomalous output\ngeneration.\nReply: We thank the reviewer for the comment. Eyelid coverage during blinking significantly\nreduces the success rate of ocular feature identification in eye-tracking technologies,\nrepresenting a common challenge in the field. To quantitatively evaluate the impact of eyelid\nocclusion during blinking on tracking performance, we conducted experiments with human\nvolunteers. Volunteers wore an EMFE contact lens on the left eye and were instructed to\nperform fast and heavy blinks, respectively. We conducted a frame-by-frame analysis of the\ndetectability of the eye-tracking enhancement patterns and the extent of eyelid occlusion to\nassess the effect of blinking on tracking performance. Simultaneously, an infrared-equipped\ncamera captured images of the right eye to track eye movements via pupil recognition during\nblinking, allowing for comparison with the EMFE contact lens-based method. As shown in\nFigure 4a, the number of detectable green solid circles decreased as the degree of eyelid\nocclusion increased. When coverage reached 80% or more, no green solid circles could be\nidentified, resulting in approximately 66 msof eye-tracking data loss. In comparison, the pupil\nwas occluded more easily during blinks, leading to a longer failure period in pupil-based\ntracking (about 231 ms of data loss). Similar results were observed during heavy blinks in\nFigure 4b, which involved more prolonged eyelid occlusion. In these cases, data loss was\napproximately 198 ms for the EMFE contact lens-based method and 330 ms for the\npupil-based method. In summary, when eyelid occlusion exceeds 80% during a blink, the\nidentification of feature patterns becomes unfeasible, leading to temporary tracking failure.\nHowever,thefailuredurationissubstantiallyshorterthanthatofpupil-basedeyetracking, and\ntrackingresumesimmediatelyuponeyereopening.\nThe above experimental data and conclusions have been incorporated into the “Eye\nTracking Characterization in Human Eyes Wearing EMFE Cosmetic Contact Lenses” section\noftherevisedmanuscriptandsupplementarymaterials.\nFigure 4. Comparison of EMFE contact lens-based and pupil-based eye tracking\nperformanceduringfastandheavyblinks.\n5. The scope of eye movement tested during human trials should be detailed, specifically the\nmaximum tested eye movement angle. Large-angle eye movements can potentially induce\ncontact lens displacement, leading to measurement errors. Moreover, the dynamic interaction\nbetweentheeyelidandthelensduringblinking,involvingrotationalandtranslationalforces,\ncan cause instantaneous, albeit minor, displacements, even with good lens-cornea adhesion.\nIt is critical to investigate the impact of such displacements on absolute pattern position, and\nonthegeometry-based3Dposeestimation.Furthermore,thetimerequiredforthealgorithmto\nregainstabletrackingafterablinkneedstobequantified.\nReply: We thank the reviewer for the valuable suggestion. Regarding the range of eye\nmovement testing, we have supplemented the revised manuscript with new in-vivo eye\nmovement characterization data. Under natural human eye movement behavior, although the\neye itself has a wide rotational range, individuals tend to prefer head movements over pure\neye rotations for gaze shifts exceeding approximately 16°. Therefore, in the new in-vivo\ncharacterization data, we focused on evaluating eye-tracking performance within a range of\n±16° in yaw and ±16° in pitch. Gaze targets were spaced at 4° intervals, forming a 9×9 grid\ncomprising 81 gaze target points. This setup for eye movement characterization has been\naddedtotherevisedmanuscript.\nToinvestigate potential lens displacement during large-angle eye rotations, we instructed\na volunteer to wear the EMFE contact lens and rotate their eyes toward various extreme\ndirections.Nosignificantlensslippagewasobserved,attributedtoitsmatchedbasecurvewith\nthecornea,thehighlylubriciouslenssurfaceanditsminimalthickness(approximately80μm),\nasshowninFigure5.\nFigure 5. Ocular images of a volunteer wearing an EMFE contact lens while gazing at\nextremeangles.\nPotential lens slippage during blinking represents acritical challenge to the accuracy and\npractical utility of EMFE contact lens-based eye tracking. To evaluate the impact of possible\nlens movement during blinks, we instructed a volunteer wearing an EMFE contact lens to\nmaintainfixationonatarget whileperformingbothgentle,fastblinksandslower,heavyblinks.\nEye images were captured at 30 frames per second, with simultaneous frame-by-frame\nidentification of the green solid circle features and the pupil to compute the gaze angles\nseparately for each method. Using the pupil-based gaze angle as a reference, we compared\nthe resulting error of the EMFE contact lens-based method. As shown in Figure 6, the\norange-shaded areas indicate periods of complete eyelid closure during blinking. In the\nsubsequent eye-opening phase, tangential forces from the eyelids induced vertical lens\nslippage, leading to errors of approximately 2-4° in the pitch angle. No significant horizontal\nslippage was observed, and the yaw gaze data aligned well with the pupil-based\nmeasurements. Benefiting from the spherical topography of the cornea, this vertical lens\ndisplacement quickly self-corrected after the eye reopened, with the resulting gaze error\neliminated within 0.3-0.7 seconds. In the future, on the one hand, the pattern features on the\neyeball can assist in the recognition of the flippage of the EMFE contact lens during blinking\nand compensate for the eye movement deviations caused by the lens slipping. On the other\nhand,thestabilityoflens-corneaadhesioncouldbefurtherimprovedthroughstructuraldesign,\nsuchasadoptingasclerallensdesignforbetterfitorincorporatingbioinspiredmicrostructures\\onthelensinnersurfacetoenhancethewet-frictioncoefficient.\nFigure6.ComparisonofcomputedeyemovementanglesfromEMFEcontactlensand\npupil-basedmethodsduringfastandheavyblinks\nThe above experimental data and discussions have been incorporated into the “Eye\nTracking Characterization in Human Eyes Wearing EMFE Cosmetic Contact Lenses” section\noftherevisedmanuscriptandsupplementarymaterials.\n6. The manuscript validates the system's accuracy under an ideal fixed configuration. In\npractical scenarios, factors such as variations in head-mounted device tightness, positioning,\nandframepitchandrollanglesduringdonninganddoffingcanaltertherelativeposebetween\nthe camera and the eyeball. This variability can significantly affect the accuracy of the\ncalibrated mapping function or geometric model. The manuscript should address whether\nthese real-world deployment challenges could lead to degraded accuracy in practical\napplications.\nReply: Wethank thereviewer fortheir valuable suggestion, whichis crucialforevaluating the\npracticalutilityoftheEMFEcontactlens-basedeye-trackingtechnique.Duringextendedwear,\nhead-mounteddevices oftenundergogradual slippage relative tothe user’shead, resulting in\nrelative displacement between the camera and the eye. This displacement introduces\nsignificant errors in gaze angle estimation based on mapping functions, since the function\nconstructed during calibration assumes a fixed eye-camera relative position. Tomitigate gaze\nangle errors induced by camera slippage, we developed a compensation algorithm. The\noverallworkflowisasfollows:\nCalibration Phase:The poseinformation of each green solid circleis computed todetermine\nthe spatial position of the eye. The polynomial mapping function is then fitted based on this\ninformation.\nTracking Phase:The pose of each green solid circle is again computed to derive the current\nspatial position of the eye. If this position matches that from the calibration phase, no camera\ndisplacement has occurred, and the mapping function is applied directly to estimate gaze\ndirection.Ifdisplacementisdetected,spatialcompensationisappliedtothegreensolidcircles\n(i.e.,subtractingthedisplacementvector),asshowninFigure7.Thecompensatedcirclesare\nprojectedbacktotheimageplanetoupdatetheircentroidcoordinates,whicharetheninputto\nthemappingfunctiontoobtainthecorrectedgazeangle.\nFigure7.Schematicdiagramofthecameraslippagecompensationalgorithm.\nWe validated the effect of this compensation algorithm on EMFE contact lens-based\ntracking performance under camera slippage using a model eye. Figure 8a shows the gaze\nangle distribution when the camera is in the calibration position, indicating strong agreement\nbetween the estimated and target gaze coordinates. Figure 8b shows the distribution of yaw\nand pitchangular errors at the calibration position, with an overall gaze error of 0.35° ± 0.27°.\nWe then shifted the camera upward by 2.5 mm relative to the eye. This caused noticeable\npixel-level shifts in the green solid circle centroids on the EMFE contact lens. Since these\nshifts did not originate from actual eye rotation, directly inputting the shifted centroid\ncoordinates into the mapping function led to large gaze errors with a trapezoidal distortion\npattern, as shown by the yellow points in Figure 8c. The overall gaze error reached 11.54° ±\n0.99%.Afterapplyingthecompensationalgorithm,whichestimatescameradisplacementfrom\nthe 3D pose of the green solid circles, compensates their spatial coordinates, and reprojects\nthem onto the image plane, the pixel shifts were largely corrected. The resulting gaze angles,\nshown as red points in Figure 8c, were significantly closer to the ground truth. As shown in\nFigure8d,theoverallgazeerrorwasreducedto0.80°±0.43°.Wefurthertestedthealgorithm\\whenthecamerawasshiftedoutwardbyanadditional2.5mm.Figure8eandfshowthegaze\nangle distributions and error distributions before and after compensation, respectively. With\ngreater camera displacement, the uncompensated gaze error increased to 17.14° ± 1.88°,\nwhile the compensated error was reduced to 2.03° ± 0.65°. The residual error after\ncompensationmainlystemsfrominaccuraciesinestimatingthe3Dpositionsofthegreensolid\ncirclesandtheeye.\nThe above experimental data and discussions have been incorporated into the “Eye\nTracking Characterization using Eye Movement Model” section of the revised manuscript and\nsupplementarymaterials.\nFigure 8. Characterization of EMFE contact lens-based eye tracking under camera\nslippage. a Gaze angle distribution at the calibration position. b Distribution of yaw and pitch\nangularerrors at thecalibration position. cComparison of gaze angle distributions beforeand\naftercompensationforanupwardcameraslippageof2.5mm.dDistributionsofyawandpitch\nangularerrors beforeand aftercompensationunder anupwardcameraslippageof 2.5 mm.e\nComparison of gaze angle distributions before and after correction for an additional outward\ncamera slippage of 2.5 mm. f Distributions of yaw and pitch angular errors before and after\ncorrection under an additional outward camera slippage of 2.5 mm. In the error plots, the\nmiddle line represents the median, the box corresponds to the 25th and 75th percentiles, and\nthe whiskers extend to the 5th and 95th percentiles. n = 63 independent gaze point\ncoordinates.\n7.Themanuscriptutilizes12uniformlydistributedgreensolidcirclesasthecorestatictracking\nfeatures. However, the rationale for selecting this specific number of feature points is not\nsufficiently elaborated.It isunclear whetheradifferent numberof featurepointscouldachieve\ncomparable or superior performance. The authors should clarify whether this choice was\nempirically determined or derived through systematic optimization. Providing the relevant\ndesign rationale or experimental validation for the feature point selection would significantly\nstrengthenthemanuscript.\nReply: We appreciate the opportunity to provide further explanation of the key design\nparameters of the EMFE contact lenses and their influence on eye-tracking performance.\nDuring the research process, except for the twelve evenly distributed green solid circles with\nred dots in the manuscript, we experimented with various pattern designs for the EMFE\ncontactlenses,suchasthefourevenlydistributedgreensolidcircles(inFigure9a).\nFigure9.aPhotographsoftheEMFEcontactlenswithfourgreensolidcircles.b-cGazepoint\ncoordinatesanderrorstatisticofthe4-green-solid-circleEMFEcontactlens.dPhotographsof\nthe EMFE contact lens with twelve green solid circles. e-f Gaze point coordinates and error\nstatistic of the 12-green-solid-circle EMFE contact lens. Inthe error statistic, the middle line is\ndetermined by median, the box is determined by the 25th and 75th percentiles, and the\nwhiskers are determined by the 5th and 95th percentiles. n = 63 independent gazing point\ncoordinates.\nThenumberofgreensolidcirclessignificantlyinfluencestheaccuracyofeyetracking.We\nmounted the second design of EMFE contact lens on a model eye and rotated the model eye\nin steps of 10° within a range of ±40° in yaw and ±30° in pitch, capturing images at each\norientation.Byidentifyingthegreensolidcirclepatternsandextractingthecoordinatesoftheir\ncentroids, we constructed the mapping function between the centroid positions and the eye\nmovement angles using polynomial fitting to characterize the eye-tracking accuracy of the\n4-circlescontactlens.Figure9bandcshowthecalculateddistributionofgazeanglesandthe\nangular error distributions in the yaw and pitch directions, respectively. Statistically, the\neye-trackingangularerrorfor4-circlescontactlenswas1.20°±0.72°.Figure9d-fpresentthe\neye-trackingaccuracyofthe12-circlesEMFEcontactlens,whichachievedanangularerrorof\n0.74°±0.40°.Thelens exhibits superior eye-trackingaccuracy,whichcanbeattributedto the\ncamera’s ability to identify at least three green solid circles across various gaze angles. By\napplying their respective mapping functions and averaging the computed gaze directions, the\nsystem mitigates the effects of centroid deviations caused by environmental light interference\nand pattern distortion due to eyelid occlusion. The results indicate that a greater number of\ngreensolidcirclefeaturescanimprovetheeye-trackingaccuracyofEMFEcontactlens-based\nsystems.\nHowever, within the constrained annular region, increasing the number of green solid\ncircles inevitably reduces their individual area and narrows the inter-circle spacing. A small\nareamakesitdifficulttoensurehighaccuracyinthecoordinatecalculationofeachgreensolid\ncircle, yet their coordinate information plays a critical role in functions such as gaze direction\nestimation and camera slippage compensation. We evaluated the above trade-off through\ntheoretical modeling. To ensure sufficient spacing between circles, we assumed that the\ndiameter of each green solid circle equals the spacing between adjacent circles.As shown in\nFigure10,asthenumberofcirclesincreasesfrom8to16,theirdiameterdecreasesfrom2.2\nmmto1 mm.Basedonthecameraparameters,ifthedetectedradiusofagreensolidcirclein\ntheimage deviates by one pixel, alikely occurrencedue toimaging noiseand blurryedges of\nthe printed pattern, the resulting distance error increases from 0.6 mm to 1.2 mm. Thus, an\nappropriate number of green solid circles must be chosen to balance the accuracy of both\ngaze angle and circle coordinate estimation. Accordingly, we ultimately selected a ring\nconfigurationcomprising12greensolidcircles.\nFigure10. Effectofthenumberofgreensolidcirclesonthecoordinatecalculation.\nThe aforementioned experimental results have been incorporated into the “Eye Tracking\nCharacterization using Eye Movement Model” section in the revised manuscript and\nsupplementarymaterials.\n8.Inthisarticle, theauthorsspendconsiderablespaceintroducingbioelectronicseye tracking\ntechnology. We suggest that the authors add some important research in the field of\nbioelectronics (see the following references: DOI: 10.1038/s41467-023-39315-6;\n10.1038/s41528-025-00458-9;10.1126/sciadv.abl8379).\nReply: We thank the reviewer for suggesting these important research works, which have\nenabledustopresent thebackgroundof ourstudy morecomprehensivelyandrigorously.The\ncorrespondingreferenceshavebeenincorporatedintothe“Introduction”sectionoftherevised\nmanuscript.\nReviewer#2(Remarksoncodeavailability):\nCompleteandreasonable.\nResponse to Reviewer 3 Comments\nComments:\nThe paper describes a new method for implementing camera-based eye trackers using\ncontact lenses. The system consists of two parts. First a contact lens with a blue peripheral\nring dotted with green and red dots spaced at regular intervals. The second part is the\nspectacleframeequippedwithRGBcameras.\nTheworking principleconsistsintakingimages of thelens, usethehighcolour contrastof the\nlarge green dots on the blue ring to compute the centroid of the detected green dots (called\ncircle in the article, I do not think it is the correct word), thereby yielding the gaze direction.\nLikewise, the red dots (much smaller than the green ones) generate streaks than are used to\nextracteyemovements.\nThe proposed new eye tracker implementation is interesting since it is using “classic” contact\nlens,thecontactlensremainspassive(nopower),doesnotrequirehighqualitycameraandis\nnotpronetoparasitelightinterference.\nOverall,Ifindthepaperwellwrittenwithveryinterestingresultsinthefieldofeyetracking.Still,\ntherearesomeissuesthatneedstobeaddressed.I’mlistingsomebelow.\nReply:Wesincerelythankthereviewer fortheirrecognitionof thenoveltyofourwork,aswell\nas for their valuable suggestions, which have been instrumental in enhancing the quality,\nscientific rigor, and completeness of this paper. Regarding the terminology for the feature\npattern, we have revised the term \"green circle\" to \"green solid circle\" in both the revised\nmanuscriptandsupplementarymaterials.\nThis adjustment was made for two main reasons. Onone hand, we utilize the centroid of\nthe solid green solid circle to calculate the gaze direction, which relies on its property as a\npoint. On the other hand, we leverage the elliptical projection of the circle in the image to\nestimate its 3D pose, enabling the computation of the relative position between the eye and\nthecamera.Therefore,referringtothepatternasa\"greensolidcircle\"moreaccuratelyreflects\nitsdualroleinourmethodology.\n1. The state-of-the art analysis is missing a recently published method which is similar to the\nonepresented inthe sensethat it usespassivecontact lens with specific featuresthat canbe\ndetectedusingacameratodeterminethegaze(FI.M.Fradkin,etal.,\"Contactlenswithmoiré\nlabels for precise eye tracking,\" Proc. SPIE 13414, Optical Architectures for Displays and\nSensing in Augmented, Virtual, and Mixed Reality (AR, VR, MR) VI, 134141W (21 March\n2025);https://doi.org/10.1117/12.3058057).\nI don’t think that embedding optolectronic devices on lens compromise transparency and\nraises biosafety as claimed in the introduction if proper precautions are taken as describes in\nthe references. I agree that it is easier to meet these requirements using the proposed\nmethods.\nReply: We sincerely thank the reviewer for bringing this important and cutting-edge literature\ntoourattention.Thereferencedworkintegratesapassiveopticalmodulewithinacontactlens,\ncomprisingtwooverlappinggratinglayersthatformamoirépatternsensitivetoeyemovement\nangles, achieving remarkably high angular resolution and strong resistance to ambient light\ninterference. We have incorporated this reference into the introduction of the revised\nmanuscripttoprovideamorecomprehensivebackground.\nRegarding biocompatibility, this study, along with other smart contact lenses for eye\ntracking,oftenemploys siliconeelastomers(e.g., PDMS,MED6015)toencapsulatefunctional\ncomponents. Silicone elastomers offer high transparency, high oxygen permeability, and\nexcellent biocompatibility. However, the cornea relies on the tear film for nutrient supply and\nrequiresacontinuoustearlayertoprevent dryeyesyndrome,makinggoodsurfacewettability\nof the lens essential for prolonged comfortable wear. In contrast, the inherently hydrophobic\nnatureof silicone makesit challengingtomaintainadequatesurfacewettabilityoverextended\nperiods.Inourwork,theEMFEcontactlensisfabricatedusingclassicalcontactlensmaterials\nand manufacturing processes, which inherently exhibit excellent surface wettability, as\ndemonstrated in Figure 1. The droplet rapidly spread across the lens surface without\nmaintainingasphericalshape.Thisbehaviorindicatesthattheinteractionenergybetweenthe\nwater and the lens surface significantly exceeds the cohesive energy of the water itself,\ndemonstratingexcellentsurfacewettabilityoftheEMFEcontactlens.\nFigure1.SurfacewettabilitycharacterizationoftheEMFEcontactlens.\nWe also agree that, with future advances in flexible optoelectronics technique and\ninterfacial engineering, smart contact lenses will eventually meet all fundamental\nphysicochemical requirements. Accordingly, we have revised the description of existing\neye-trackingsmartcontactlensesintheIntroductionsectionoftherevisedmanuscript.\n2. One thing that should be better explained. Based on the description, if the camera is\nsignificantly off centred with the eye, e.g. positioned below the eye as in Fig. 2., the camera\nsees moregreen dots at the bottom of the eye, even though the person looks straight ahead.\nSo computing the centroid, would indicated the person is looking down rather than straight\nahead.Thatdoesnotseemcorrect.\nReply: We thank the reviewer for their suggestion and apologize for any lack of clarity in our\noriginal description of the gaze angle calculation method. The procedure for using the EMFE\ncontactlensforeyetrackingisasfollows:\nAfter wearing the EMFE contact lens and the head-mounted eye tracker, the user first\nperformsacalibrationprocedure.Duringthisphase,theuserisguidedtofixatesequentiallyon\na set of visual targets at known positions (e.g., specified gaze angles or screen coordinates).\nThe eye tracker captures an image of the eye at each target. The regions of the green solid\ncircles are identified in each image, and their respective centroid pixel coordinates are\ncomputed.Apolynomial mapping function is then fitted for each green solid circle, relating its\ncentroid coordinates to the corresponding known gaze directions, thereby concluding the\ncalibration phase. Subsequently, during the eye-tracking phase, the eye tracker continuously\ncaptures eye images. The centroids of the detectable green solid circles are computed, and\ntheir corresponding mapping functions are applied to estimate the gaze angle. When multiple\ngreensolidcirclesaredetectedinbothcalibrationandtracking,multiplemappingfunctionsare\nconstructed and applied. The final gaze direction is obtained by averaging the individual\nestimatesfromallavailablecircles.\nThus,thespatialdistributionofthegreensolidcirclecentroidswithintheeyeisnotdirectly\nused to compute gaze direction; rather, it supports the establishment and application of\nindividualizedmappingfunctions.Thedetaileddescriptionofthiscalculationmethodhasbeen\naddedtothe“Methods”sectionoftherevisedmanuscript.\n3. I do not understand why it would not possible to use the green discs to obtain trajectories?\nWhytheneedtousetiny(comparedtothegreendots)reddots?\nReply: We thank the reviewer for raising this point, which touches upon the key working\nmechanism of the EMFE contact lens-based eye-tracking technique. Under static or\nlow-speed eye movement conditions, the cameracan reliably and accurately identify both the\ngreensolidcirclesandthereddots.Theircentroidcoordinatesarethencalculatedandusedin\namappingfunctiontoobtainprecisegaze angles.Bycomputingtheseanglesframe-by-frame\ninavideoandconnectingtheangularcoordinatesovertime,theeyemovementtrajectorycan\nbeconstructed.Duringdynamiceyemovements,boththegreensolidcirclesandreddotscan,\nin principle, contribute totrajectory extraction. However,due totheir smaller size, the reddots\nform more elongated and continuous smearing patterns under motion blur. This allows their\ntrajectory to be extracted more straightforwardly using a skeletonization algorithm on the\nconnected region. Figure 2 shows a representative image of an EMFE contact lens under\nmotion blur. The overlaid white markings represent the skeletons of the smeared green solid\ncircle and red dot regions, both obtained with the same skeletonization algorithm. As can be\nobserved, the skeleton of the red-dot region exhibits more consistent directionality, which\ndirectly indicates the actual movement direction of the eyeball. The rationale for including the\nred dots in the design has been added to the “Design of Eye Movement Feature Enhanced\n(EMFE)CosmeticContactLens”sectionoftherevisedmanuscript.\nFigure 2. Image of EMFE contact lens under the dynamic frame. The white markings are\ntheskeletonofthegreensolidcircleandthereddotundermotionblur.\n4. You have not explained how the various algorithms are implemented. What\nhardware/software platform is used? Is it embedded in the spectacle frame shown in Fig .1?\nYoushowoutdoorexperimentations,arecomputationdoneinrealordifferedtime?\nReply: We thank the reviewer for this suggestion, which has been instrumental in enhancing\nthe scientific clarity of the manuscript. To clarify, the proposed head-mounted eye tracker\nintegrates two front-facing cameras and one scene camera. The video streams from these\nthreecamerasaretransmittedtoalaptopviaaUSBhub.Therefore,thehead-mounteddevice\nfunctions primarily as an image/video data acquisition unit, while all image/video processing\nand storage are performed on the computer.The experiments reported in this work, including\neye-tracking feature recognition tests, model eye performance evaluation, in-vivo human\neye-tracking tests, and indoor/outdoor application demonstrations, were all conducted by\ncapturingeye or scene images usingthe head-mounted system,saving thedata locally tothe\ncomputer, and subsequently processing the images using MATLAB R2020b to obtain the\nreportedresults.\nSince the eye-tracking algorithm based on the EMFE contact lens involves only simple\nprocessing in the HSV color space and morphological analysis, it can be implemented for\nreal-time eye tracking using Python’s OpenCV, pandas, Matplotlib, SciPy, math libraries to\ncompletethecalibrationprocedure,acquirereal-timevideostreams,recognizeeyemovement\nfeaturepatterns,andcomputegazeangles.\nWe are grateful to the reviewer for highlighting the need for this clarification. A detailed\ndescriptionofthehardwareandsoftwaresetuphasbeenaddedtotherevisedmanuscript.\n5. It would also be interesting to better described your experiments, how many lens were\ntested,howmanypersonsinvolved,etcweredonetomeasureaccuracy.\nReply: We thank the reviewer for this suggestion, which is important for enhancing the\nscientific rigor of our work. Regarding the number of contact lenses tested in the eye tracking\naccuracy characterization, our EMFE contact lenses are of the daily disposable type.\nTherefore, for each volunteer, a brand-new EMFE contact lens was used. Owing to the\ntransfer printing process employed in the fabrication, the produced EMFE contact lenses\nexhibithighconsistencyintermsofcolorandpatternshape,asshowninFigure3.Asaresult,\nusing different individual lenses does not introduce significant variation in eye-tracking\nperformance.\nFigure 3. Photograph of the EMFE contact lenses, showing high consistency in the\ncolorandshapeofitsfeaturepatterns.\nConcerning the number of volunteers involved in the eye tracking accuracy\ncharacterization, we have now included eye movement characterization data from four\nparticipants in the revised manuscript and supplementary materials. The group included two\nmale and two female participants, all free of ocular diseases. During the eye movement\ncharacterization experiment, the volunteers were instructed to observe a whiteboard\npositioned 60 cm away. A two-dimensional array of gaze targets was arranged on the\nwhiteboard. Following the reviewer's suggestion regarding in-vivo eye movement\ncharacterization, the target points were confined to a range of ±16° in yaw and ±16° in pitch,\nspaced at 4° intervals, forming a 9×9 grid comprising 81 gaze targets. The volunteers were\nguided to fixate on each of these points sequentially, and six frames of eye images were\ncaptured per gaze point. The distributions of gaze angles, along with the calculated accuracy\nand precision for all four volunteers, are shown in Figure 4. The specific accuracy and\nprecisionvaluesforeachvolunteer(A,B,C,D)aresummarizedinTable1.Allfourvolunteers\nachieved eye-tracking accuracy and precision better than 1°, demonstrating that the\nEMFE-based eye-tracking technique can reliably determine the gaze direction. This\nperformance supports its potential application in cognitive, psychological, and\nhuman-computer interaction studies, and confirms the consistency and reliability of the\ntrackingresultsacrossdifferentindividuals.\nFigure 4. Gaze point map, accuracy, and precision of the EMFE contact lens-based\neye-trackingtechniqueinfourvolunteers.\nTable1.Eye-trackingaccuracyandprecisioninthefourvolunteers.\nAccuracy Precision\nVolunteerA 0.70°±0.38° 0.22°±0.13°\nVolunteerB 0.90°±0.50° 0.33°±0.25°\nVolunteerC 0.78°±0.67° 0.33°±0.28°\nVolunteerD 0.95°±0.61° 0.54°±0.42°\nThe above experimental data and setup have been incorporated into the “Eye Tracking\nCharacterization in Human Eyes Wearing EMFE Cosmetic Contact Lenses” section in the\nrevisedmanuscriptandsupplementarymaterials.\n6.Also, in Fig. 2 would be nice to have a short description of the experimental set up used to\nproducethe results. Yougive a recognition rate but you don’t say how many tests were done,\nonhowmanypersons.\nReply: We thank the reviewer for this suggestion. The eye-tracking feature recognition rate\ntest presentedin Figure2 of theoriginalmanuscript includesthree different scenarios: indoor\nartificial lighting, outdoor natural lighting, and window-side natural lighting. A total of 700\nimages with random gaze directions were collected from one volunteer and analyzed. This\ndetaileddescriptionoftheexperimentalsetuphasbeenaddedtotherevisedmanuscript.\n7.Fig.2andFig.2captionrefertoCCL,betteruseEMFEasdefinedinthemaintext.\nReply: We thank the reviewer for this suggestion. In the revised manuscript, we have\nstandardizedtheterminologyto\"EMFEcosmeticcontactlens\"throughout.\n8.Thehumaneyecanhaveawiderotationeyemovement,butusuallyabove16°horizontally,\none prefers turning the head. So steps of 10° seems a bit too large to assess accuracy,\nshouldn’tyouhavereducethestudybetween-16°and+16°usingsmallersteps?\nReply:Wesincerelythankthereviewerfortheirprofessionalcomments.Inresponse,wehave\nconducted a more comprehensive evaluation of the EMFE contact lens-based eye-tracking\naccuracythroughsystematicexperimentsusingboththemodeleyeandhumanvolunteers.\nWe mounted the lens on a model eye and rotated the model eye in steps of 1° within a\nrangeof±40°inyawand±30°inpitch,enablingafinerquantitativeassessmentofgazeangle\naccuracy. Figure 5a shows the resulting distribution of the computed gaze angles,\ndemonstrating that the vast majority of gaze coordinates accurately align with the intended\ntargets. Figure 5b summarizes the yaw and pitch angular errors across all 4,941 gaze\ncoordinate points. The overall angular error was 0.29° ± 0.21° (mean ± S.D.). We observed\nthat the characterization data collected at 1° intervals yielded higher accuracy compared to\nthat obtained at 10° intervals. This improvement can be attributed to the non-uniform\ndistribution of angular errors across the eye movement range when using the EMFE contact\nlens. Specifically,thecomputed gaze angles exhibit minimalerrors in the central regionof the\neye movement range, while larger errors occur mainly at the four corners, corresponding to\nmoreextremegazeangles.Theseresidualerrorsstemfromthereducednumberofdetectable\nfeature patterns at extreme angles and the inherent limitations of polynomial-based fitting\nunderlarge-anglerotations.\nFigure 5. a Gaze point coordinates when eyeball model rotated to different gaze directions in\nstepsof1° withinarangeof ±40° inyaw and ±30° inpitch.Thegray squaresrepresent the\nset gaze coordinates, and the red dots represent the calculated gaze coordinates. b Error\nstatistic of gaze point coordinates. The middle line is determined by median, the box is\ndetermined by the25th and 75th percentiles, and the whiskersare determined by the5th and\n95thpercentiles.n=4941independentgazingpointcoordinates.\nFor the in-vivo eye-tracking tests, we invited four volunteers and focused on evaluating\nthe gaze angle accuracy within a range of ±16° in yaw and ±16° in pitch. The detailed\nexperimentalsetup andcorresponding results havebeen presentedinresponseto Comment\n5. Overall, both the model eye and human participants exhibited eye-tracking accuracy better\nthan 1°. The model eye achieved superior accuracy compared to human subjects, which can\nbe primarily attributed to the inherent difficulty for humans to fixate on target points as\npreciselyandsteadilyasthemechanicalmodeleye.\nWe have supplemented these experimental results in the “Eye Tracking Characterization\nusing Eye Movement Model” section and the “Eye Tracking Characterization in Human Eyes\nWearing EMFE Cosmetic Contact Lenses” section of the revised manuscript and the\nsupplementarymaterials.\n9. The abstract claims that no calibration is required. Yet, in section Eye tracking\nCharacterization a 9-point calibration is used. This needs to be clarified, calibration or not\ncalibration?\nReply:Wesincerelythankthereviewerforthisvaluablesuggestion.Weapologizeforthelack\nof clarity regarding the working principle of the EMFE contact lens-based eye-tracking\ntechnique in the original manuscript. To achieve accurate gaze angle calculation, users are\nrequired to perform a 9-point calibration procedure after wearing the EMFE contact lens.This\nprocess establishes the mapping function between the pixel coordinates of the green solid\ncirclecentroids(theeye-trackingfeaturepatterns)and thecorresponding gazeangles. During\nthe eye-tracking phase, the system tracks the centroid pixel coordinates of the green solid\ncirclesandappliesthismappingfunctiontocomputetheprecisegazedirection.\nAdditionally, this manuscript presents an alternative approach for gaze direction\nestimation, mentioned in the original Figure 3d, which involves calculating the optical axis of\ntheeyebysolvingthe3Dposeofeachgreensolidcircle.Itshouldbenoted,however,thatthis\nmethod can only provide a coarse estimate of the gaze direction. This limitation arises\nbecausethe optical axis represents the geometric symmetry axis of the eye, whereas studies\nhave shown that there exists an angle, the Kappa angle, between the optical axis and the\nvisual axis (which passes through the fovea). Therefore, accurate gaze tracking cannot be\nachievedwithoutacalibrationproceduretoaccountforthisoffset.\nWe once again thank the reviewer for raising this critical point regarding calibration. The\nclaimof\"calibration-free\"operationhasbeencorrectedintherevisedmanuscript."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have proposed an interesting approach to enhance eye-tracking robustness by integrating spatial-chromatic\nencoding patterns into cosmetic contact lenses. The use of pad printing and the emphasis on spatial-chromatic features to\novercome environmental lighting challenges are noted as practical engineering efforts. However, after careful review of the\nrevised manuscript and the authors' responses, I remain concerned about several fundamental limitations that undermine\nthe scholarly impact and practical superiority of this work in its current form.\n1. The system’s sampling rate is limited to 30 fps, which is insufficient for capturing rapid ocular dynamics such as saccades.\nWhile the authors have refined their claims to focus on \"continuous gaze positioning,\" this low temporal resolution\nsignificantly narrows the application scope. For a device requiring the physical wearing of functional contact lenses, the\nperformance trade-off compared to non-invasive, high-speed (60–120 Hz) video-based trackers is not sufficiently justified.\n2. The initial appeal of this work relied heavily on its \"calibration-free\" potential. However, the authors’ acknowledgment of\nthe necessity of a calibration procedure to account for the Kappa angle diminishes the comparative advantage of the\nproposed method. Once calibration is required, the benefit of using artificial chromatic patterns over established iris/pupil-\nbased algorithms becomes marginal, especially considering the invasive nature of contact lenses.\n3. The optimization of the spatial patterns (e.g., the number and placement of circles) appears to be based on empirical trials\nrather than a rigorous theoretical or information-theoretic framework. Furthermore, although short-term biocompatibility was\naddressed, the potential for peripheral visual interference or long-term wearer discomfort from these specific chromatic\npatterns remains a critical concern for a wearable device.\nIn conclusion, while the manuscript presents an interesting engineering integration, the lack of high-speed tracking\ncapability and the retreat from the calibration-free claim suggest that the work does not yet represent a significant\nbreakthrough in the field of eye-tracking or wearable bioelectronics. Therefore, I recommend a rejection of the manuscript.\nHowever, the final decision remains entirely at the discretion of the Editor.", "reviewer_2": "The author has revised it as required, and I recommend accepting this manuscript.", "reviewer_3": "THe authors have ansewered my questions adequately.\nThe modified version of the paper along with the supplementary materail (if made available to the readers on the journal\nwebsite) is worth being published in my opinion."}, "author_response": "Response to Reviewer 1 Comments\nComments:\nThe authors have proposed an interesting approach to enhance eye-tracking robustness by\nintegrating spatial-chromatic encoding patterns into cosmetic contact lenses. The use of pad\nprinting and the emphasis on spatial-chromatic features to overcome environmental lighting\nchallenges are noted as practical engineering efforts. However, after careful review of the\nrevised manuscript and the authors' responses, I remain concerned about several\nfundamental limitations that undermine the scholarly impact and practical superiority of this\nwork in its current form.\nReply: We would like to extend our appreciation to the reviewer for acknowledging the\nenhanced robustness of our eye-tracking technique based on spatial-chromatic encoding\ncosmetic contact lenses against ambient light interference. We also thank the reviewer for their\nvaluable suggestions regarding further improving the practical superiority of our eye-tracking\ntechnique. Below are our point-by-point responses to the reviewer’s comments.\n1. The system’s sampling rate is limited to 30 fps, which is insufficient for capturing rapid\nocular dynamics such as saccades. While the authors have refined their claims to focus on\n\"continuous gaze positioning,\" this low temporal resolution significantly narrows the application\nscope. For a device requiring the physical wearing of functional contact lenses, the\nperformance trade-off compared to non-invasive, high-speed (60-120 Hz) video-based\ntrackers is not sufficiently justified.\nReply: Thank you for the professional comments. In both the initial and current rounds of\nreview, the reviewer pointed out that a 30 Hz eye-tracking sampling rate may be insufficient for\ncapturing rapid ocular dynamics such as saccades. The sampling rate of the proposed\neye-tracking system depends on the camera frame rate. To better capture fast eye movements,\nwe have increased the frame rate of the head-mounted eye tracker's eye-facing camera. We\nemployed a high-speed RGB camera (DH-FTGZL4222, Shenzhen Dehong Technology Co.,\nLtd.) capable of recording at 180 fps. A volunteer wearing EMFE cosmetic contact lenses was\ninstructed to read a passage of text while their eye movements were recorded. The resulting\neye movement trajectory is shown in Fig. 1a, where red dots represent the gaze position in\neach frame, and the color of the lines between frames indicates the instantaneous eye\nmovement speed. The trajectory clearly shows the volunteer’s eye movement pattern\nswitching between fixations and saccades, with regressions also observable. Fig. 1b plots the\ninstantaneous eye movement speed during this reading task, with the peak speed reaching\n1167 cm/s. In the future, further increasing the camera frame rate will help expand the\napplicability of this eye-tracking technique.\nThese experimental results have been added to the revised Supplementary Materials.\nFigure 1. a The eye movement trace of reading obtained by a high-speed (180 Hz) camera.\nThe red dots represent the coordinates of the gazing point per frame, and the lines present the\neye movement trace. Different colors represent varying eye movement velocity. b Velocity of\neye movement during reading.\n2. The initial appeal of this work relied heavily on its \"calibration-free\" potential. However, the\nauthors’ acknowledgment of the necessity of a calibration procedure to account for the Kappa\nangle diminishes the comparative advantage of the proposed method. Once calibration is\nrequired, the benefit of using artificial chromatic patterns over established iris/pupil-based\nalgorithms becomes marginal, especially considering the invasive nature of contact lenses.\nReply: Thank you for the suggestion. It is worth mentioning that, overall, the eye movement\nfeature enhancement design of the spatial-chromatic encoding cosmetic contact lenses\nimproves the performance of natural eye tracking in the following aspects:\n Superior Recognition Rate: A 93% overall recognition rate under complex lighting\nconditions, with the unrecognized rate reduced by one order of magnitude compared to\nbare-eye tracking.\n Excellent Accuracy: Achieves eye tracking accuracy of < 1° using only low-cost RGB\ncameras.\n Promising Human-Centric Evolution: highly off-axis camera setup, enabling\nuser-friendly and unobtrusive eye tracking.\nRegarding the calibration-free capability: In eye tracking technology, calibration serves not\nonly to obtain the user's Kappa angle (the angle between the visual axis and the optical axis,\nan individual anatomical parameter of the eye) but also to determine the relative spatial\nposition between the eye and the eye tracker1. Based on the known-size eye-feature patterns\non this contact lens, we can directly compute the 3D spatial pose information of each green\nsolid circle. Furthermore, by utilizing the known layout of the green solid circles (i.e., all circle\ncentroids are coplanar in 3D space, with the normal vector of this plane representing the\ndirection of the eye's optical axis), we can directly calculate the direction of the eye's optical\naxis and the spatial position of the eye in the camera coordinate system. Combined with\nimplicit calibration in the interactive software design in the future (e.g., prompting the user to\ngaze at a target with a known direction), rapid calibration can be achieved. This approach also\nallows for the compensation of tracking errors caused by slippage of the eye tracker, by\nleveraging the computed changes in the eye's position within the camera coordinate system.\n3. The optimization of the spatial patterns (e.g., the number and placement of circles) appears\nto be based on empirical trials rather than a rigorous theoretical or information-theoretic\nframework. Furthermore, although short-term biocompatibility was addressed, the potential for\nperipheral visual interference or long-term wearer discomfort from these specific chromatic\npatterns remains a critical concern for a wearable device.\nReply: Thank you for the suggestion. We fully agree that a rigorous theoretical or\ninformation-theoretic framework could provide a more solid and universal basis for design\nchoices and help explore the limits of performance. In our study, the optimization of the spatial\npatterns (e.g., the number and placement of circles) was primarily guided by several core\nconstraints:\n Visual Comfort: The patterns must be placed outside the optical zone of the contact lens\nto ensure a completely unobstructed central visual field.\n Tracking Accuracy: A larger number of circles helps mitigate the impact of centroid\nlocalization errors for individual circles through averaging, thereby significantly improving\ntracking accuracy. However, smaller area induced by a larger number of circles will\nreduce the accuracy of the circular pose calculation.\n 3D Pose Estimation: The coplanar design of the circles enables direct calculation of the\n3D pose of the eye, providing the foundational information necessary for rapid calibration\nand compensation for device slippage.\nOverall, the eye-tracking technology based on the EMFE cosmetic contact lenses has\nsuccessfully addressed core challenges such as ambient light interference and device\nslippage, demonstrating the substantial potential of this technical approach. We once again\nthank the reviewer for this valuable suggestion, which significantly enhances the depth of our\nresearch.\nThe issues of peripheral visual interference and long-term wearing comfort raised by the\nreviewer are also highly important. The proposed EMFE cosmetic contact lenses feature an\noptical zone with a diameter of 8 mm, which provides an unobstructed visual window and helps\nprevent visual blur caused by pattern occlusion. The EMFE lenses presented in this study are\nmanufactured by a certified cosmetic contact lens producer holding a medical device\nregistration certificate (No. 20253161083). These lenses are daily disposable type, with an\noxygen permeability (Dk) of 18.2×10 −11 (cm2/s) [mL∙O /(mL∙hPa)] , allowing for\n2\nsingle-wear of up to 6 hours. The global demand for contact lenses is evident, with over 140\nmillion wearers worldwide2, reflecting public acceptance of such devices.\nIn conclusion, while the manuscript presents an interesting engineering integration, the lack of\nhigh-speed tracking capability and the retreat from the calibration-free claim suggest that the\nwork does not yet represent a significant breakthrough in the field of eye-tracking or wearable\nbioelectronics. Therefore, I recommend a rejection of the manuscript. However, the final\ndecision remains entirely at the discretion of the Editor.\nReferences\n1. Lin, L. et al. Lightweight deep learning with multi-scale feature fusion for high-preci\nsion and low-latency eye tracking, Displays 91, 103260 (2026).\n2. Contact lenses Usage Statistics Worldwide, https://healthfulhelps.com/contact-lenses-\nusage-statistics-worldwide/#mcetoc_1i46q3k8n36e, August 1, (2024).\nResponse to Reviewer 2 Comments\nComments:\nThe author has revised it as required, and I recommend accepting this manuscript.\nReply: Thank you very much for your valuable suggestions. And we thank the reviewer for the\nrecommendation of accepting our manuscript in this journal.\nResponse to Reviewer 3 Comments\nComments:\nThe authors have answered my questions adequately.\nThe modified version of the paper along with the supplementary material (if made available to\nthe readers on the journal website) is worth being published in my opinion.\nReply: Thank you very much for your valuable suggestions. And we thank the reviewer for the\nrecommendation of publishing our manuscript in this journal."}]

Decision letter