The letter provides alternatively a simple way of computing the Fresnel field integral, a further extension to the Gaussian-beam expansion. The zeroth-order Bessel function of the first kind is expanded into an approximate sum of Gaussian functions. The field integral is then expressible in terms of these simple functions. The approach is useful in treatment of the field radiation problem for a large and important group of piston sources in acoustics. As examples, the calculation results for the uniform and the simply-supported piston sources are presented, in a good agreement with those evaluated by numerical integration.

The volume of the lesions created by conventional single-frequency high-intensity focused ultrasound (HIFU) is small, which leads to long treatment duration in patients who are undergoing tumor ablation. In this study, the lesions induced by confocal dual-frequency HIFU in an optically transparent tissue-mimicking phantom were investigated and compared with the lesions created by conventional single-frequency HIFU. The results show that using different exposure times resulted in lesions of different sizes in both dual-frequency and single-frequency HIFU modes at the same spatially averaged intensity level (ISAL = 4900 W cm(-2)), but the lesion dimensions made in dual-frequency mode were significantly larger than those made in single-frequency mode. Difference frequency acoustic fields that exist in the confocal region of dual-frequency HIFU may be the reason for the enlargement of the lesions' dimensions. The dual-frequency HIFU mode may represent a new technique to improve the ablation efficiency of HIFU. The total time for the ablation of a tumor can be reduced, thus requiring less therapy time and reducing possible patient complications.

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