Dual-layer watermarking for secure Fourier ptychographic microscopy.

Fourier ptychographic microscopy (FPM) reconstructs a complex object from a multi-angle intensity stack, yet provenance and stack consistency can be lost when data are released across acquisition, reconstruction, cloud-analysis, and archival workflows. We present a synthetic-aperture-constrained dual-layer watermarking framework for post-acquisition FPM release. A robust layer carries a 256-bit authenticated provenance record through reliability-guided differential quantization index modulation of recoverable Fourier coefficient pairs, while a semi-fragile layer tests raw-stack consistency. Across six simulated acquisition conditions, the mean robust bit-error rate (BER) is 1.47%, whereas 1000 independent wrong keys yield 0.4998±0.0316 BER. A generic Fourier-QIM baseline exhibits a substantially larger BER, and representative raw-stack processing tests distinguish persistent provenance recovery from semi-fragile consistency rejection. A real blood-smear spectrum retains zero correct-key BER after model-consistent FPM release and sequential ePIE reconstruction, with amplitude SSIM 0.9971.