Lensless Kramers–Kronig holography with nonlocal flat optics

Holography enables quantitative access to complex-amplitude fields, supporting applications ranging from biological microscopy to industrial metrology. Although Kramers–Kronig (KK) holography offers an attractive route toward deterministic reconstruction, existing implementations rely on a lens-based 4 f system to construct the required half-plane-blocked spatial-frequency filter, limiting system miniaturization and reducing alignment tolerance. Here, we demonstrate lensless KK holography enabled by nonlocal flat optics, in which a 2 mm thick multilayer filter replaces the conventional 4 f system and directly provides the spatial-frequency filtering required for reconstruction. We recover amplitude and phase from artificial test targets and biological specimens over a 5.52 mm ×5.52 mm field of view with a 4.92 µm half-pitch resolution, while achieving a processing throughput of 1.94 megapixels per second on a laptop. Our approach combines the deterministic reconstruction capability of KK holography with a compact, large-FoV lensless architecture offering improved alignment tolerance, providing a route toward integrated and computationally efficient holographic imaging systems.