Gaze-contingent display paradigms play an important role in vision research. The time delay due to data transmission from eye tracker to monitor may lead to a misalignment between the gaze direction and image manipulation during eye movements, and therefore compromise the contingency. We present a method to reduce this misalignment by using a compressed exponential function to model the trajectories of saccadic eye movements. Our algorithm was evaluated using experimental data from 1,212 saccades ranging from 3° to 30°, which were collected with an EyeLink 1000 and a Dual-Purkinje Image (DPI) eye tracker. The model fits eye displacement with a high agreement (R² > 0.96). When assuming a 10-millisecond time delay, prediction of 2D saccade trajectories using our model could reduce the misalignment by 30% to 60% with the EyeLink tracker and 20% to 40% with the DPI tracker for saccades larger than 8°. Because a certain number of samples are required for model fitting, the prediction did not offer improvement for most small saccades and the early stages of large saccades. Evaluation was also performed for a simulated 100-Hz gaze-contingent display using the prerecorded saccade data. With prediction, the percentage of misalignment larger than 2° dropped from 45% to 20% for EyeLink and 42% to 26% for DPI data. These results suggest that the saccade-prediction algorithm may help create more accurate gaze-contingent displays.

In recent years, visible light positioning (VLP) technology based on Complementary Metal Oxide Semiconductor (CMOS) sensors has been widely studied due to its high precision and high robustness. However, the existing VLP algorithm based on image sensors often fails to achieve a good positioning effect when the camera is tilted. In order to solve this problem, we propose a neural network algorithm to correct the error caused by the tilt angle of the camera. Because when the tilt angle is different, the LED image captured by the camera will be different and produce different characteristics. By extracting these features and using neural networks to establish the relationship between the characteristics of the LED image and the distance between the receiving and sending terminal, we finally achieve the positioning of the camera by the triangulation algorithm. Experiments demonstrate that our positioning algorithm can achieve high-precision positioning and can be applied to most indoor positioning systems.

Focusing is extensively researched in bioimaging, medicine, and quantum computation. However, single focal point and short focal length restrict imaging and optical manipulation at long distances. In this study, we propose what we believe to be a novel method, namely the coherent superposition of double-ring circular Airy Gaussian beams (DR-CAiGBs) to achieve multiple autofocusing over long distances. Without complex structures, theoretical simulations and experimental verifications demonstrate that the DR-CAiGBs can generate multiple autofocusing points along the optical axis, whose positions and quantities can be flexibly adjusted. Furthermore, we demonstrated the two-dimensional (2D) particle manipulation of the DR-CAiGBs by trapping multiple particles at different autofocusing points over 100 µm. Our research and findings establish new avenues for practical applications in biological cell analysis, particle transportation, and lithography.