Fig. 1

The core principle of forming caustic patterns through acoustic modulation of a liquid surface. (a,b) illustrate how the liquid surface deforms into convex or concave shapes due to acoustic pressure, resulting in caustic pattern formation. When parallel light rays pass through the deformed refractive surface, they are either focused inward (convex) or dispersed outward (concave), creating distinct caustic patterns. This iterative optimization process adjusts the liquid surface shape to align the refracted light distribution with a desired target image. The results displayed in (c) are visualizations of a numerically simulated process. This process calculates the phase delay of each transducer in the acoustic phased array based on the distance to the focal point, thereby estimating the liquid surface shape and generating the caustic pattern. The leftmost image shows the acoustic pressure distribution used to deform the liquid surface, followed by the corresponding liquid surface deformation. Finally, the resulting caustic pattern is shown from the side and front views, revealing a bright ring with a darker center that closely matches the intended target image.