Equivalence of time and aperture domain additive noise in ultrasound coherence

Ultrasonic echoes backscattered from diffuse media, recorded by an array transducer and appropriately focused, demonstrate coherence predicted by the van Cittert–Zernike theorem. Additive noise signals from off-axis scattering, reverberation, phase aberration, and electronic (thermal) noise can all superimpose incoherent or partially coherent signals onto the recorded echoes, altering the measured coherence. An expression is derived to describe the effect of uncorrelated random channel noise in terms of the noise-to-signal ratio. Equivalent descriptions are made in the aperture dimension to describe uncorrelated magnitude and phase apodizations of the array. Binary apodization is specifically described as an example of magnitude apodization and adjustments are presented to minimize the artifacts caused by finite signal length. The effects of additive noise are explored in short-lag spatial coherence imaging, an image formation technique that integrates the calculated coherence curve of acquired signals up to a small fraction of the array length for each lateral and axial location. A derivation of the expected contrast as a function of noise-to-signal ratio is provided and validation is performed in simulation.