Differential angular spectrum method for acoustic hologram encryption

Ultrasonic holography offers substantial information capacity, yet its potential for information encryption remains largely unexplored with few experimental demonstrations. Here, we present acoustic holographic encryption using a compact single-element transducer. To simultaneously achieve high reconstruction fidelity and amplitude control under simplified hardware, we introduce a physics-informed, differentiation-enhanced computational framework—the Differential Angular Spectrum Algorithm (DASA). DASA augments band-limited angular-spectrum propagation with gradient-based phase optimization and a phase-plate correction, enabling faithful and uniform field synthesis. Reconstruction fidelity is validated by pressure-field measurements and microparticle manipulation, demonstrating practical field-based data encoding and decryption. DASA attains a mean-squared error of 1.5×10−4, peak signal-to-noise ratio of 38.323 dB, uniformity (U) of 0.995, and correlation of 0.995, all computed on 0, 1-normalized intensity maps within the target region of interest, outperforming the iterative angular spectrum algorithm across these metrics. The approach provides a robust and scalable route to secure, high-density information encoding with a single-transducer–single-lens architecture, with implications for acoustic communication, biomedical manipulation, and physical-layer security.