Super-resolution imaging of low-frequency sound sources using a corrected monopole time reversal method

A limitation of the monopole time reversal (MTR) method, which records and retransmits the monopole field only, is that the spatial resolution of the focus cannot be better than half a wavelength, and therefore it is not suitable for locating low-frequency sound sources. In this paper, the time-reversed pressure field obtained by the MTR method is first transformed into the wavenumber domain, and is then decomposed into a filter term that controls the spatial resolution of the focus and a source term that is related to the sound source and focusing plane. Subsequently, a correction is made to the time-reversed pressure field of the MTR method by replacing its filter with the filter for the time-reversed pressure gradient field of the dipole TR (DTR) method, a constant filter and an empirical filter, which makes it possible to include many more evanescent waves and obtain subwavelength focusing. Numerical simulation and experimental results show that compared to the original MTR method, the corrected one is able to dramatically improve the spatial resolution of the focus at low frequencies. It is also found that the constant filter is applicable when the signal-to-noise ratio (SNR) is high (generally above 30 dB), the filter for the time-reversed pressure gradient field of the DTR method works stably even in the situation of low SNR, and the empirical filter performs best when the SNR is above 10 dB.