Self-Portrait of the Focusing Process in Speckle: II. Gouy Phase Shift for Defocus Correction and Pixel Depth Reassignment

Abstract

This is the second article in a series of three dealing with the exploitation of speckle for aberration correction and reverberation compensation in reflection imaging. When probing heterogeneous media with waves, we have to cope with multi-scale fluctuations of the wave velocity. On the one hand, short-scale heterogeneities induce back-scattered echoes whose random interference generate a speckle pattern on the beamformed image. On the other hand, large-scale fluctuations of the wave-velocity can distort the focused wave-fronts, resulting in aberrations on the same image. In this paper, we show how the self-portrait of the wave evolves as a function of the speed-of-sound model. Strikingly, a Gouy phase shift is observed when the speed-of-sound model is optimal. This particularly sensitive feature enables: (i) an optimization of the speed-of-sound model for each pixel of the image; (ii) a local and fine compensation of defocus across the field-of-view, thereby compensating for most aberrations in the image. Experiment in a tissue-mimicking phantom and numerical simulations are first presented to validate our method. It is then applied to in-vivo liver data of a difficult-to-image patient. The speed-of-sound optimization allows an axial compensation of aberrations and a depth-reassignment of each singly-scattered echo to the actual position of the associated scatterer. As distance measurement is often critical for diagnosis, such a wave speed optimization can be crucial for ultrasound but also for any other imaging methods based on the principle of echo-location.