An Experimental Study of Focused Bessel Beams

The diffraction limit of the image resolution of a conventional optical microscope was found to be around 200 nm by Ernst Abbe in 1873. Since then many efforts have been made to overcome this limit to achieve a higher image resolution (super-resolution), including the 1994 stimulated emission depletion (STED) and 2006 photoactivated localization microscopy (PALM) that won the 2014 Nobel Prize in Chemistry. Recently, a general method called point-spread function (PSF) modulation super-resolution imaging was developed by the author (Lu, January 2024, IEEE TUFFC). This method uses modulator(s) (such as focused shear wave and nanoparticles) to modulate the amplitude, phase, or a combination of the amplitude and phase of the PSF of an imaging system to increase the spatial frequency of the PSF to achieve super-resolution.In this paper, an experiment was carried out using a focused Bessel beam to remotely produce a cylindrical ring of radiation force that can subsequently generate a shear wave focused at the center axis of the ring for a phase modulator of the imaging wave such as that in the pulse-echo B-mode imaging or photoacoustic imaging for super-resolution imaging. The results show that a cylindrical ring of radiation force of various diameters can be produced by a 2.5-MHz, 50-mm diameter, and 10-ring annular array transducer with piecewise aperture weightings using a Bessel function of scaling parameters such as 0.25b, 0.5b, and 1.0b, where b = 1202.45 m⁻¹, and a focal length of about 107 mm.This study paves a way to experimentally produce super-resolution images of mechanical properties (shear wave amplitude, speed, spectrum, and nonlinearity, etc.) of biological soft tissues that have a low shear-wave speed and small wavelength deep in the tissues with a focused Bessel beam, i.e., achieving a high image resolution that is normally possible with a higher frequency such as 5 MHz, 10 MHz, or higher using a low-frequency wave such as 2.5 MHz ultrasound. In addition to the experiment study in this paper, a comprehensive theoretical and computer-simulation study was conducted to remotely generate focused shear waves of low-sidelobes by a focused annular array, 2D array, or a 1D array transducer for super-resolution imaging (note that shear-waves may resonate to increase amplitude and thus the signal-to-noise ratio under certain boundary conditions), and the study was presented on the 188^th Acoustical Society of America (ASA) meeting in May 2025 and is to be submitted to the Proceedings of Meetings on Acoustics (POMA) of the ASA. The current experiment work is well supported by this study.