Hessian intensity-only diffraction tomography for 3D refractive index reconstruction

Intensity-only optical diffraction tomography (IDT) is a recently developed label-free three-dimensional (3D) refractive index (RI) quantitative imaging technique for biomedical fields. However, its inherent missing cone problem and reliance solely on intensity measurement led to underestimation of RI in 3D space and elongation of RI distribution along the optical axis. In this paper, we propose Hessian Intensity-only diffraction tomography (Hessian-IDT) method to optimize the missing cone problem and the limitations associated with intensity-only measurements. Hessian-IDT iteratively reconstructs the scattering potential of the sample using the 3D extension of the Fourier Ptychographic Microscopy (FPM) algorithm, and Hessian regularization and non-negative constraints are added to the iterative process using the Split Bregman algorithm by incorporating prior knowledge about sample smoothness and positivity. Cell simulation and complex sample simulation demonstrate that Hessian-IDT yields higher-quality 3D RI reconstructions compared to existing IDT methods. Our experiments using microspheres, label-free cheek cells, and transverse sections of Hydra support this conclusion. Hessian-IDT shows potential for advancing applications in biomedical fields.