Three-dimensional (3D) imaging revealing the structures hidden under the immediate object surface, whether it is an ultrasound baby scan or a 3D image of the living cell is undoubtedly a holy grail for any imaging technique, offering wealth of information on the studied object. While Atomic Force Microscopy (AFM) offers spatial resolution down to individual atoms, the contrast originating from the interaction of the nanoscale probe and the surface, restricts AFM to predominantly surface imaging. In order to overcome this, one can use ultrasonic wave that penetrates both transparent and opaque samples carrying 3D information to the sample surface where it is could be picked up by the scanning probe. Whereas such approach was experimentally realised in Ultrasonic Force Microscopy (UFM) , Heterodyne Force Microscopy and Ultrasonic Holography , and Atomic Force Acoustic Microscopy , the fundamental origin of the contrast is far from clear with some publications referring to the scattering of ultrasonic waves and some attributing it to the interaction of elastic field from AFM tip with the subsurface structures. Furtermore, some of the observed subsurface structures are empty voids, and some are stiff regions hidden under soft surface layers. Untangling this requires analysis of the near-field scattering of the ultrasonic waves, and the propagation of the stresses in a generally anisotropic media.
In this paper we show that given that in all cases of nanoscale ultrasonic imaging both the depth and size of subsurface features are orders of magnitude smaller than the ultrasonic wavelength, the ultrasonic wave interaction with the subsurface inclusion has to take into account the phase and amplitude of both the evanescent and radiated wave. We then show that the near-field corrugation of ultrasonic field on the sample surface is of negligible amplitude for the simple elastic discontinuity, but may be observable for the pure void. This strongly suggests that it is the oscillating stress field generated by the SPM tip-surface contact that provides a main source of the contrast in the subsurface ultrasonic imaging.
We further analyse stress propagation in the highly anisotropic material such as graphite, MoS2 or multilayer graphene - a transversely isotropic materials - and find that the stress field propagate as highly “focused” beam elongated according to the ratio of the out-of-plane Young modulus S33 and the in-plane shear modulus S44, explaining unusual experimental observations of “ultrasonic transparency” in  that allows to observe defects and structures deep under immediate surface of such materials.
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