Design and validation of custom acoustic holograms for ultrasonic immersion testing of anisotropic silicon

Acoustic holograms offer powerful capabilities for manipulating ultrasonic fields, yet their application to immersed anisotropic materials remains challenging due to complex wave propagation behavior. This study advances acoustic holography by developing customized lenses that enhance ultrasonic beam focusing in anisotropic silicon wafers immersed in water. Using ray tracing combined with gradient descent optimization, novel lens geometries were designed to constrain wave propagation to a conical profile within [3 1 1] and [1 3 5] silicon orientations. The lenses were fabricated via stereolithographic 3-D printing and systematically compared against conventional spherical lenses through analytical modeling and experimental testing. Angular spectrum approach modeling demonstrated that the custom lenses produced improved focusing, with up to 41% higher amplitude and 49.8% better circularity compared to spherical lenses. Experimental validation using flat-bottom hole defects showed that the custom lenses achieved more refined defect signatures while requiring 10 dB less electrical gain than spherical lenses. The benefits were most pronounced in materials with lower crystal symmetry, where directionally varying focal patterns could be made more uniform through custom lens design. This work establishes a comprehensive framework for optimizing acoustic holograms that account for fluid–solid interfaces and anisotropic wave propagation, advancing capabilities for ultrasonic inspection of complex materials.