On the phase aberration estimation using common mid-angle correlations

Phase aberrations, despite degrading ultrasound images, also encode valuable information about the spatial distribution of the speed of sound in tissue. In pulse-echo ultrasound, we can quantify them by exploiting speckle correlations. Among existing strategies, correlations between steered acquisitions that share a common mid-angle have proven particularly effective for inferring the speed of sound. Their phases can be linearly related to the phase aberrations undergone by both the incident and reflected wavefronts. This relationship has so far been demonstrated only through geometric arguments based on point reflectors. Here, we develop a rigorous theoretical formalism that extends this relationship to the speckle regime, completing the previously established linear model and clarifying its underlying assumptions. More importantly, we build on this formalism to analyze correlation-phase fluctuations arising from aberration-induced speckle decorrelation. The analysis reveals that phase variance is governed by the relative loss of coherence, which increases approximately linearly with the square of the correlation phases. Local correlation-phase estimates therefore become increasingly uncertain as their magnitude grows. Experimental measurements in a uniform tissue-mimicking phantom show excellent agreement with the predicted variance. Beyond providing a theoretical basis for advancing speed-of-sound imaging, this formalism establishes the accuracy limit of common-mid-angle correlation phases, offering a benchmark for evaluating more advanced aberration-estimation techniques.