Phase shifts from scattering are used to analyze and engineer acoustic radiation forces. With the aid of phase shifts, analytical results for acoustic radiation forces can be simplified into compact and physically meaningful expressions, which can be used to develop a simplified procedure for the engineering of the radiation force. The desired radiation force can be fulfilled by a specific set of phase shifts up to a certain order, and then the required phase shifts can be fulfilled by engineering object and beam parameters. As an example, the phase shift approach is used to engineer the inner-to-outer radius ratio and the outer radius of a spherical shell to show how to use the phase shift method for the design of acoustic radiation forces. The example here is a force that is desired to pull particles against the propagation of a Bessel beam. A small paraxial parameter to pull a spherical shell is satisfied by in-phase scattering of monopole, dipole, quadrupole, octupole, and beyond. The example presented here is relatively simple yet reveals the advantages of the phase shift approach. The phase shift method can provide a simplified route for the design of acoustic tweezers using either traveling beams or standing waves.

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工程所需辐射力的相移方法：声学拉力示例

来自散射的相移用于分析和设计声辐射力。借助相移，声辐射力的分析结果可以简化为紧凑且具有物理意义的表达式，可用于开发辐射力工程的简化程序。所需的辐射力可以通过一组特定的相移达到某个阶来实现，然后所需的相移可以通过工程对象和梁参数来实现。例如，相移方法用于设计球壳的内外半径比和外半径，以展示如何使用相移方法设计声辐射力。这里的例子是一个力，需要拉动粒子以阻止贝塞尔光束的传播。通过单极子、偶极子、四极子、八极子等的同相散射来满足拉球壳的小旁轴参数。此处展示的示例相对简单，但揭示了相移方法的优势。相移方法可以为使用行波束或驻波的声学镊子的设计提供一种简化的途径。