Determine whether thickness discontinuities cause the secondary acoustic lobe

Determine whether diffraction induced by abrupt changes in acoustic-lens thickness is responsible for the appearance of a secondary lobe at the transducer’s center of curvature when phase unwrapping is not applied.

Background

The study compares conventional and phase-unwrapped bifocal acoustic lenses for transcranial holography. Increasing the lateral separation between targets increases the number of phase wraps and abrupt lens-thickness changes, which can refract and scatter the incident acoustic wave. The lens-design procedure models each pixel as an ideal phase shifter and therefore does not account for these refraction and scattering effects.

For larger target separations, especially 30 mm and 45 mm, the experiments reveal an unwanted secondary pressure lobe near the transducer’s center of curvature when phase unwrapping is omitted. Although phase unwrapping suppresses this lobe, the paper does not establish whether diffraction caused by abrupt thickness changes is the mechanism responsible for its formation.

References

A possible cause is a higher impact of refraction in unwrapped lenses. Indeed, when the number of phase wraps increases, the number of abrupt changes in lens thickness increases accordingly. Each abrupt change refracts and scatters the incoming acoustic wave. However, refraction and scattering are not taken into account in the design process because phase maps (unwrapped or not) are converted to local lens thickness by a formula that treats each lens pixel as an ideal phase shifter. Nevertheless, it remains to be demonstrated if diffraction induced by the abrupt changes are responsible for the appearance of a secondary lobe at the center of curvature of the transducer without unwrapping.

— Impact of Phase Unwrapping on Multitarget Acoustic Lenses for Transcranial Holography  (2609.18495 - Attali et al., 16 Sep 2026) in Section IV, Discussion