This article reports an investigation of an inverse-filter method to correct for experimental underestimation of pressure due to spatial averaging across a hydrophone sensitive element. The spatial averaging filter (SAF) depends on hydrophone type (membrane, needle, or fiber-optic), hydrophone geometrical sensitive element diameter, transducer driving frequency, and transducer ${F}$ number (ratio of focal length to diameter). The absolute difference between theoretical and experimental SAFs for 25 transducer/hydrophone pairs was 7% ± 3% (mean ± standard deviation). Empirical formulas based on SAFs are provided to enable researchers to easily correct for hydrophone spatial averaging errors in peak compressional pressure ( ${p}_{c}$ ), peak rarefactional pressure ( ${p}_{r}$ ), and pulse intensity integral. The empirical formulas show, for example, that if a 3-MHz, ${F}$ /2 transducer is driven to moderate nonlinear distortion and measured at the focal point with a 500- $\mu \text{m}$ membrane hydrophone, then spatial averaging errors are approximately 16% ( ${p}_{c}$ ), 12% ( ${p}_{r}$ ), and 24% (pulse intensity integral). The formulas are based on circular transducers but also provide plausible upper bounds for spatial averaging errors for transducers with rectangular-transmit apertures, such as linear and phased arrays.

中文翻译：

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修正水听器圆形声源的空间平均伪像

本文报告了一种反滤波方法的研究，以纠正由于水听器敏感元件上的空间平均导致的实验压力估计不足。空间平均滤波器（SAF）取决于水听器的类型（膜，针或光纤），水听器的几何敏感元件直径，换能器驱动频率和换能器 $ {F} $ 数字（焦距与直径之比）。25个换能器/水听器对的理论SAF与实验SAF之间的绝对差为7％±3％（均值±标准差）。提供了基于SAF的经验公式，以使研究人员能够轻松校正峰值压缩压力下水听器的空间平均误差（ $ {p} _ {c} $ ），峰值稀疏压力（ $ {p} _ {r} $ ）和脉冲强度积分。经验公式表明，例如，如果频率为3 MHz， $ {F} $ / 2换能器被驱动以消除非线性失真，并在焦点处用500- $ \ mu \ text {m} $ 膜水听器，则空间平均误差约为16％（ $ {p} _ {c} $ ），12％（ $ {p} _ {r} $ ）和24％（脉冲强度积分）。这些公式基于圆形换能器，但也为具有矩形传输孔径（例如线性和相控阵）的换能器的空间平均误差提供了合理的上限。