Acoustic holograms shape sound wavefronts by encoding phase patterns in a physical lens. Design the lens computationally, fabricate it, and the sound field takes the desired shape. But there's a gap: the computation assumes idealized phase-only modulation, while the physical lens has three-dimensional geometry that introduces absorption, diffraction, and mode coupling absent from the phase-only model.
The authors (arXiv:2603.23475) close this gap by making the lens geometry differentiable. Instead of optimizing a phase pattern and then translating it to a physical structure, they optimize the three-dimensional lens directly within an acoustic simulation. The thickness profile is the optimization variable. Gradients flow through the simulation, and the optimization accounts for all the physical effects the phase-only model ignores.
The resulting Thickness-Only Acoustic Holograms outperform conventional designs under complex conditions — irregular skull geometries, heterogeneous tissue — because the optimization knows about the physics that the simplification discards.
The demonstration: non-invasive transcranial neuromodulation for neuropathic pain. The acoustic hologram focuses sound through the skull to stimulate specific brain regions. The differentiable framework handles the skull's irregular geometry and tissue heterogeneity without the phase-only approximation.
The through-claim: the numerical-physical gap in holography is a differentiability gap. Phase-only design can't be corrected after fabrication because it optimized the wrong quantity. Making the physical structure differentiable means the optimization and the physics share the same model. The gap closes because it was never a physics problem — it was an optimization problem.