Far-focused pixel-based imaging of defects in layered structures based on improved nonlinear beamforming

Layered structures have significant difficulties in ultrasonic far-focused pixel-based imaging (FPB) due to the large difference in interlayer acoustic impedance. To enhance the detection resolution and imaging quality of defects in the second layer of layered structures, an improved nonlinear beamforming method for FPB of layered structure defects —— Far-focused Pixel-Based imaging based on Nonlinear beamforming using Circular coherence factor and Baseband Delay-Multiply-and-Sum (CCB-NFPB) is proposed in this paper. Firstly, the spatial coherence of the received signal is introduced through Baseband Delay-Multiply-and-Sum (BB-DMAS) nonlinear beamforming to suppress background noise. By incorporating multiplicative operations between demodulated baseband signals, BB-DMAS introduces nonlinear characteristics that improve robustness to reverberation and signal interference. Then, the circular coherence factor (CCF) constructed using the phase information of the signal is adaptively weighted to further improve the image intensity of deep defect locations, in order to overcome the signal-to-noise ratio (SNR) degradation caused by sound wave propagation attenuation. The experiment is based on the k-wave acoustic field simulation platform to optimize the emission parameters (with 36 sub apertures and a focusing depth of 130 mm). Experimental results demonstrated that CCB-NFPB improved the SNR by 97.7 % compared to the conventional linear beamformed Delay-and-Sum (DAS) method, reduced lateral resolution error between adjacent defects by 55.1 %, and maintained over 93.8 % SNR improvement within the 15–25 mm depth range. The proposed method demonstrates a remarkable ability to suppress interface reflection noise and effectively resolves key challenges in second-layer defect imaging, including limited resolution and pronounced signal attenuation at greater depths. It offers robust performance in accurate defect characterization, effective noise mitigation, and resilience against amplitude degradation.