Filtered Lebedev quadrature method for robust and efficient beam shape coefficient estimation in acoustic tweezers calibration

Abstract

Acoustic tweezers offer a contactless, three-dimensional, and selective approach to trapping objects by harnessing the acoustic radiation force. Precise control of this technique requires accurate calibration of the force, which depends on the object's properties and the spherical harmonics expansion of the incident field through the beam shape coefficients. Previous studies showed that these coefficients can be determined using either the Lebedev quadrature or the angular spectrum methods. However, the former is highly susceptible to noise, while the latter demands extensive implementation time due to the number of required measurement points. A filtered method with a reduced number of points is introduced to address these limitations. Initially, we emphasize the implicit filtering in the angular spectrum method, allowing relative noise insensitivity. Subsequently, we present its unfiltered version, enabling force estimation of a standing field. Finally, we develop a filtered method based on the Lebedev quadrature, requiring fewer points, and apply it to focused vortex beams. Numerical evaluation of the radiation force demonstrates the method's resilience to noise and a reduced need for points compared to previous methods. The filtered Lebedev method paves the way for characterizing high-frequency acoustic tweezers, where measurement constraints necessitate rapid and robust beam shape coefficient estimation techniques.