This study aims to investigate the frequency-dependent characteristics of the focal length of an acoustic lens made of a material with a frequency-dependent acoustic refractive index (ARI). For this purpose, an exchangeable plano-spherical convex subsonic index lens (PSCSIL) was fabricated using a polydimethylsiloxane (PDMS) material. The ARI of the lens material was evaluated via the tone-burst through-transmission method over the frequency range of 1–10 MHz. The frequency dependence of the focal length of the fabricated PSCSIL was evaluated through graphical analysis of the acoustic field scanned by a hydrophone as well as of that simulated using the finite element method. The measured ARI and focal length were observed to be dependent on frequency. The simulated and measured focal lengths of the PSCSIL exhibited a great discrepancy with their respective values predicted using the conventional focal length equation. This discrepancy was further studied using the ray-tracing method and is described in the discussion section. In conclusion, the spherical curvature of PSCSIL does not induce the convergence of rays to meet in a point. The ray tracing method does not take into account the phase complexity of the near-field region inside the lens. This causes the actual focal length to be shorter than the predicted one.

这项研究旨在研究由具有频率依赖性声折射率（ARI）的材料制成的声透镜的焦距的频率依赖性特性。为此，使用聚二甲基硅氧烷（PDMS）材料制造了可更换的平面球面凸亚音速折射率透镜（PSCSIL）。在1–10 MHz的频率范围内，通过色调突发传输方法评估了镜片材料的ARI。通过对水听器扫描的声场以及使用有限元方法模拟的声场进行图形分析，可以评估所制造的PSCSIL焦距的频率依赖性。观察到的ARI和焦距取决于频率。PSCSIL的仿真和测量焦距与使用常规焦距方程预测的各自值存在很大差异。使用射线跟踪方法进一步研究了这种差异，并在讨论部分中进行了描述。总之，PSCSIL的球面曲率不会引起会聚光线的光线汇合在一个点上。光线跟踪方法没有考虑透镜内部近场区域的相位复杂性。这导致实际焦距短于预测的焦距。PSCSIL的球面曲率不会引起会聚光线的光线汇合在一个点上。光线追踪方法没有考虑透镜内部近场区域的相位复杂性。这导致实际焦距短于预测的焦距。PSCSIL的球面曲率不会引起会聚光线的光线汇合在一个点上。光线跟踪方法没有考虑透镜内部近场区域的相位复杂性。这导致实际焦距比预测的焦距短。