Frequency redistribution and weighting for discrete three-dimensional spectrum synthesis

Three-dimensional (3D) spectrum synthesis is critical for refractive-index (RI) reconstruction in optical diffraction tomography (ODT). However, discretization errors during spectrum mapping and non-uniform confidence among multi-angle measurements often lead to RI underestimation and axial artifacts. Here, we propose a non-iterative frequency redistribution and weighting (FRW) framework for discrete 3D spectrum synthesis. The method combines dual-neighbor spectral redistribution with power spectral density (PSD)-based weighting to improve Fourier-domain synthesis accuracy. Numerical simulations show PSNR improvements of 10.57% for the full field and 63.26% within the sample region. Experiments on polystyrene microspheres and HeLa cells demonstrate enhanced RI fidelity and reduced axial artifacts. Notably, FRW using only three illumination angles outperforms conventional nearest-neighbor reconstruction with 51 angles. The proposed framework provides a simple and efficient solution for high-fidelity ODT under sparse-angle acquisition.