Bridging the numerical-physical gap in acoustic holography via end-to-end differentiable structural optimization

Acoustic holography provides a practical means of flexibly controlling acoustic wavefronts. However, high-fidelity shaping of acoustic fields remains constrained by the numerical-physical gap inherent in conventional phase-only designs. These approaches realize a two-dimensional phase-delay profile as a three-dimensional thickness-varying lens, while neglecting wave-matter interactions arising from the lens structure. Here, we introduce an end-to-end, physics-aware differentiable structural optimization framework that directly incorporates three-dimensional lens geometries into the acoustic simulation and optimization loop. Using a novel differentiable relaxation, termed Differentiable Hologram Lens Approximation (DHLA), the lens geometry is treated as a differentiable design variable, ensuring intrinsic consistency between numerical design and physical realization. The resulting Thickness-Only Acoustic Holograms (TOAHs) significantly outperform state-of-the-art phase-only acoustic holograms (POAHs) in field reconstruction fidelity and precision under complex conditions. We further demonstrate the application of the framework to spatially selective neuromodulation in a neuropathic pain mouse model, highlighting its potential for non-invasive transcranial neuromodulation. In summary, by reconciling numerical design with physical realization, this work establishes a robust strategy for high-fidelity acoustic wavefront shaping in complex environments.