Analytic Fourier ptychotomography for aberration-free and high-resolution volumetric refractive index imaging

Three-dimensional (3D) refractive index tomography offers label-free quantitative volumetric imaging. However, existing tomography approaches are limited by optical aberrations, limited resolution, and computational complexity. To overcome these issues, we propose Analytic Fourier Ptychotomography (AFP), a computational microscopy technique that analytically reconstructs aberration-free, complex-valued 3D refractive index distributions without iterative optimization or axial scanning. AFP employs a unique prior based on the finite sample thickness to recast the inverse scattering problem into analytically solvable linear equations. Unlike iterative methods, AFP does not require parameter tuning and computationally intensive optimizations, and can achieve efficient, robust, and generalizable image reconstructions across diverse samples and systems. We experimentally demonstrated that AFP greatly enhanced image quality and resolution under various aberration conditions across a range of applications. AFP corrected aberrations associated with 25 Zernike modes (with maximal phase difference of 2.3π and maximal Zernike coefficient value of 4), extended the synthetic numerical aperture from 0.41 to 0.99, and provided a two-fold resolution enhancement in all directions. With its simplicity, robustness, and broad applicability, AFP offers a user-friendly imaging platform for quantitative 3D analysis in biology, microbial ecology, and clinical science.