# Eyelid Dynamics Characterization with 120 GHz mmW Radar
## 5 Eyelid Results  
### Radar Pointing Horizontally  
Taking into account the ADC board's memory limitations, the radar was configured to acquire echo beating tone signals along 8000 consecutive chirps. With a chirp repetition period of 3 ms, the total acquisition time per observation was 24 s, which is enough to evaluate the performance of the proposed eye blink detection and eyelid dynamics characterization.  
The initial eyelid dynamics measurements were conducted with the radar beam aligned horizontally with the eye axis. Precise alignment of the radar was necessary due to the narrow beam of the antenna. A small corner reflector was used to confirm the correct pointing of the radar. Figure 8 shows the magnitude and phase of the resolution cell backscattering evolution corresponding to the observed eye. Several blink events can be identified as short and fast transient oscillations, which are present in both the magnitudes and the phase of the observed backscattering. The phase's slow negative slope trend reflects a small movement made by the subject head changing the target-radar range along the measurement window of 24 s. Phase unwrapping is needed to correctly recover the target motion to avoid the phase jumps observed close to the \(\pm\pi\) phase limits. After phase unwrapping, the value of the phase change peaks can be used to detect the blink events and determine the average blink period and the period dispersion or irregularity.  
Figure 9 shows the magnitude and phase of one of the blinks. The ripple in magnitude indicates an interference pattern between two or more scattering centers in the same resolution cell with different phase rotation paces. To reduce the impact of the face interference on the eyelid radar observations, we have used a two-scattering-center model. One of the scatterers is the fast-moving eyelid, with a fast phase rotation linked to blink closure and aperture. The second scatterer models the rest of the observed face, with slower magnitude and phase dynamics. Under this model, every transition between the local maxima and minima corresponds to a half-cycle relative phase turn (180 degrees) in the eyelid phase with  
Figure 7: Azimuth and elevation cuts of the antenna radiation pattern. **(a)** Azimuth cut. **(b)** Elevation cut.  
respect to the unwanted background of the face. The fact that the phase in the upper part in Figure 9a rotates only with fractions of a cycle indicates that the scattering of the face is dominant and the scattering of the eyelid has a smaller magnitude. Exploiting this model, the face contribution to the radar echo signal can be obtained from the evolution of maximum and minimum magnitude. For example, in both the maxima and minima samples, the phase of the observation corresponds to the phase of the dominant face background. The magnitude of the unwanted background can be obtained from the average value of consecutive maxima and minima magnitudes. This information was used to estimate the background face phasor and its evolution along each blink event. The lower part in Figure 9b shows the same blink event after subtracting the estimated contribution of the face background. This technique can be considered an adaptive extension of the classical Moving Target Indicator technique common in pulsed radars for rejecting unwanted static clutter by cancellation [20]. After background cancellation, the phase shows the expected multi-turn evolution, reproducing the eyelid motion in detail, in a similar way that was predicted by the numerical simulation. Note that the eye closes faster than it opens; in the closure step, the eyelid covers the cornea, implying a shorter radar range, which translates into a positive phase slope, and the opposite occurs for the aperture motion of a blink.