Beamforming Through Encapsulation Layers: Efficient Time-of-Flight Modeling for High-Resolution Ultrasound Imaging

Medical ultrasound probes commonly employ a polymer encapsulation over the transducer for electrical protection and acoustic impedance matching. However, the speed of sound mismatch between the encapsulant and biological tissue can introduce time of flight (TOF) errors that degrade beamforming coherence. This article presents a beamforming method that includes the encapsulating layer in the TOF calculation to improve image quality. Two TOF approximations, direct path (DP) and normal path (NP), are evaluated in terms of accuracy and computational cost. These are compared against the homogeneous direct path (HDP) model, which neglects the encapsulant, and the exact Snell's law path (SP), computed using ray-tracing. Simulations and experiments are performed on a silicone encapsulated row-column addressed (RCA) capacitive micromachined ultrasound transducer (CMUT) probe as a case study. DP and NP increased the processing time by only $1.2 \times$ compared to HDP, while SP increased it by $46 \times$ . The measured standard deviation of the TOF error was reduced from $0.10 \lambda$ (HDP) to $0.06 \lambda$ (DP) and $0.05 \lambda$ (SP), ensuring high interchannel coherence. Lateral resolution increased up to +47%, and contrast was enhanced by $\geq+2.1 \mathrm{~dB}$ using DP and SP models compared to HDP. The DP approximation achieved near-SP image quality, while maintaining HDP-level computational efficiency. The validity domain of NP and DP for any transducer was generalized using a critical F-number $\alpha$ . Overall, the proposed approximations provide a computationally efficient means to enhance resolution and contrast, establishing a practical solution for high-resolution real-time imaging.