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Far-field wave imaging and inversion of objects with dimension and spacing much smaller than the wavelength are very difficult because of the well-known diffraction limit. The task becomes more challenging for quantitative shape reconstruction of closely spaced subwavelength impenetrable scatterers. Apart from the classic resolution limit, complex wave interaction including evanescent waves among impenetrable objects can be strong, but it is difficult to be fully utilized for correct shape inversion although it contains critical resolution information. Here we tackle this problem by proposing a level-set-based geometrical full-waveform inversion method. It makes full use of wave physics to directly reconstruct subwavelength objects of arbitrary shapes separated within half a wavelength. Shape reconstruction is controlled by the geometrical boundary gradient calculated from the finite-element formulation, and the important role of wave interaction among objects in the inversion is demonstrated. The boundaries of the objects are represented using the level-set method, allowing for reconstruction of multiple objects simultaneously. Numerical examples and experiments of ultrasonic waves in solid samples demonstrate that the method successfully reconstructs closely spaced subwavelength objects with far-field measurements, and the resolution is shown to be within a fraction of wavelength. This level of accuracy can be very useful in subsurface imaging applications such as ultrasonic nondestructive evaluation, medical diagnosis, and electromagnetic sensing.
Yin et al. (Wed,) studied this question.