Advances in additive manufacturing have enabled the realisation of inexpensive, scalable, diffractive acoustic lenses that can be used to generate complex acoustic fields via phase and/or amplitude modulation. However, the design of these holograms relies on a thin-element approximation adapted from optics which can severely limit the fidelity of the realised acoustic field. Here, we introduce physics-based acoustic holograms with a complex internal structure. The structures are designed using a differentiable acoustic model with manufacturing constraints via optimisation of the acoustic property distribution within the hologram. The holograms can be fabricated simply and inexpensively using contemporary 3D printers. Experimental measurements demonstrate a significant improvement compared to conventional thin-element holograms.

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