# Eyelid Dynamics Characterization with 120 GHz mmW Radar
## 3 Simulations  
Electromagnetic simulations on a simplified dielectric model of a human eye were carried out to predict and interpret the radar backscattering experimental results. Figure 4 shows the model used in the evaluation of the radar backscattering. The eyeball was modeled as a dielectric sphere with a radius of 13 mm, a relative permittivity \(\varepsilon_{\text{r}}=10\), and a loss tangent \(\tan\delta=0.8\). A homogeneous permittivity sphere was assumed since the cornea, sclera, and iris have similar values of permittivity. The model values were obtained from the Foundation for Research on Information Technologies in Society (IT'IS), which provided the tissue properties of the eye components [18]. The lower and upper eyelids covering the eyeball were modeled with dielectric layers of a 2 and 3 mm thickness, respectively [19], with a relative permittivity of \(\varepsilon_{\text{r}}=8\) and \(\tan\delta=0.647\). The simulations were carried out using CST Microwave Studio. To capture the eyelid edge from different viewing angles, the upper eyelid used in the simulations has a thickness of 3 mm. In Figure 5a, a plane wave is illuminating the eye surface with the propagation vector directed horizontally towards it. The incidence angle  
Figure 3: Overview of the radar system. The DDS generates a frequency signal ranging from 47.65 to 48.05 MHz, which is frequency-multiplied through a phase-locked loop (PLL). A voltage-controlled oscillator (VCO) subsequently produces a 61 to 61.5 GHz signal for further frequency multiplication to reach a range of 122 to 123 GHz, which is used as the transmission frequency for observing the target. The echo signal, reflected from the eyelid, is captured by the receiving antenna \(R_{X}\), which is then down-converted in a mixer using the transmission signal as a reference. The resulting baseband signal is filtered and amplified, effectively removing high-frequency noise to enhance the signal quality. The received signal is digitized with a 12-bit ADC for further processing and calculation of the eyelid dynamics parameters. \(\theta_{\text{planewave}}\) is also visualized in Figure 4b. The upper eyelid has a 30\({}^{\circ}\) angle with respect to the vertical axis in this figure. In subsequent simulations, the eyelid closes until it reaches 180\({}^{\circ}\). The strong attenuation caused by the eye with a closed eyelid on the incoming field is shown in Figure 5b. Consequently, the penetration depth of the eye tissues is very small, and the eye components behind the cornea have a negligible influence on the radar measurement. Figure 6 displays the simulated phase and radar cross-section (RCS) during the eyelid closure progression, expressed as the eyelid angle. A noticeable oscillation in the RCS is attributed to the superposition of changing phase reflections from the eye and eyelid, dependent on the angle of the eyelid's closure. The phase rotates more than 360\({}^{\circ}\) with an eye closure angle of 55\({}^{\circ}\) to 85\({}^{\circ}\), with the transition of rotation from \(+\pi\) to \(-\pi\) shown by the vertical black lines. According to (9), a phase difference \(\Delta\phi_{\text{p}}=4\times 2\pi-2.2\) corresponds to a relative change in the distance of the object from the radar of \(\Delta R=4.5\) mm. When the closure angle is higher than 90\({}^{\circ}\), no significant backscattering changes are observed since the frontal area of the eye contributing to backscattering is stable. Figure 4: Approximated model of the anterior part of the eye. (**a**) Components of the eye model: (1) Upper eyelid, which will be closed in the simulation; (2) lower eyelid; (3) cornea; (4) anterior chamber; (5) sclera; (6) iris; and (7) pupils. (**b**) Front view of the eye model. Figure 5: Eye with lid model in Microwave Studio. (**a**) A horizontal plane wave is directed towards the eye. (**b**) Electric field amplitude in the eye model.