High‐Efficiency Label‐Free 3D Microscopy Using Kramers‐Kronig Relations‐Assisted Fourier Ptychographic Diffraction Tomography

Abstract A high‐efficiency 3D refractive index (RI) tomography method is presented, termed Kramers–Kronig relations‐assisted Fourier ptychographic diffraction tomography (KK‐FPDT). This approach integrates the spatial‐domain Kramers–Kronig (KK) relations with Fourier ptychographic diffraction tomography (FPDT), enabling high‐quality RI reconstruction from intensity images captured under both matched and non‐matched illuminations. By leveraging KK relations, the initial 3D scattering potential spectrum is generated deterministically, which significantly accelerates convergence in the subsequent iterative FPDT reconstruction process. KK‐FPDT overcomes the limitations of conventional KK‐ODT methods, which are constrained by matched illumination conditions, thereby improving spectral coverage and reconstruction quality significantly. Experiments on microspheres, resolution targets, and biological samples (including 3T3 cells and Pandorina morum ) validated KK‐FPDT's capability for high‐resolution 3D RI imaging with 340 nm lateral resolution. KK‐FPDT offers a robust and versatile solution for label‐free quantitative analysis of cellular and tissue morphology, paving the way for broader biomedical applications.