A noise-tolerant approach to strain estimation in phase-sensitive optical coherence elastography, robust to decorrelation distortions, is discussed. The method is based on evaluation of interframe phase-variation gradient, but its main feature is that the phase is singled out at the very last step of the gradient estimation. All intermediate steps operate with complex-valued optical coherence tomography (OCT) signals represented as vectors in the complex plane (hence, we call this approach the ‘vector’ method). In comparison with such a popular method as least-square fitting of the phase-difference slope over a selected region (even in the improved variant with amplitude weighting for suppressing small-amplitude noisy pixels), the vector approach demonstrates superior tolerance to both additive noise in the receiving system and speckle-decorrelation caused by tissue straining. Another advantage of the vector approach is that it obviates the usual necessity of error-prone phase unwrapping. Here, special attention is paid to modifications of the vector method that make it especially suitable for processing deformations with significant lateral inhomogeneity, which often occur in real situations. The method’s advantages are demonstrated using both simulated and real OCT scans obtained during reshaping of a collagenous tissue sample irradiated by an IR laser beam producing complex spatially inhomogeneous deformations.

In compressional optical coherence elastography, phase-variation gradients are used for estimating quasistatic strains created in tissue. Using reference and deformed optical coherence tomography (OCT) scans, one typically compares phases from pixels with the same coordinates in both scans. Usually, this limits the allowable strains to fairly small values $<10−4$ to $10−3$, with the caveat that such weak phase gradients may become corrupted by stronger measurement noises. Here, we extend the OCT phase-resolved elastographic methodology by (1) showing that an order of magnitude greater strains can significantly increase the accuracy of derived phase-gradient differences, while also avoiding error-phone phase-unwrapping procedures and minimizing the influence of decorrelation noise caused by suprapixel displacements, (2) discussing the appearance of artifactual stiff inclusions in resultant OCT elastograms in the vicinity of bright scatterers due to the amplitude-phase interplay in phase-variation measurements, and (3) deriving/evaluating methods of phase-gradient estimation that can outperform conventionally used least-square gradient fitting. We present analytical arguments, numerical simulations, and experimental examples to demonstrate the advantages of the proposed optimized phase-variation methodology.

Logarithmic-in-time slow dynamics has been found for individual cracks in a solid. Furthermore, this phenomenon is observed during both the crack acoustic conditioning and the subsequent relaxation. A thermoelastic mechanism is suggested which relates the log-time behavior to the essentially 2D character of the heating and cooling of the crack perimeter and inner contacts. Nonlinear perturbation of the contacts by a stronger (pump) wave causes either softening or hardening of the sample, and induces either additional absorption or transparency for a weaker (probe) acoustic wave depending on frequency of the latter.

Rectification (demodulation) of high-frequency shear acoustic bursts is applied to probe the distribution of contact forces in 3D granular media. Symmetry principles allow for rectification of the shear waves only with their conversion into longitudinal mode. The rectification is due to nonlinear dynamic dilatancy, which is found to follow a quadratic or Hertzian power law in the shear wave amplitude. Evidence is given that a significant portion of weak contact forces is localized below ${10}^{-2}$ of the mean force—a range previously inaccessible by experiment. Strong anisotropy of nonlinearity for shear waves with different polarization is observed.