  Solving the 3D refractive index (RI) from fluorescence images provides both
fluorescence and phase information about biological samples. However,
accurately retrieving the phase of partially coherent light to reconstruct the
unknown RI of label-free phase objects over a large volume, at high resolution,
and in reflection mode remains challenging. To tackle this challenge, we
developed fluorescence diffraction tomography (FDT) with explicit neural fields
that can reconstruct 3D RI from defocused fluorescence speckle images. The
successful reconstruction of 3D RI using FDT relies on four key components:
coarse-to-fine modeling, self-calibration, a differential multi-slice rendering
model, and partial coherent masks. Specifically, the explicit representation
efficiently integrates with the coarse-to-fine modeling to achieve high-speed,
high-resolution reconstruction. Moreover, we advance the multi-slice equation
to differential multi-slice rendering model, which enables the self-calibration
method for the extrinsic and intrinsic parameters of the system. The
self-calibration facilitates high accuracy forward image prediction and RI
reconstruction. Partial coherent masks are digital masks to resolve the
discrepancies between the coherent light model and the partial coherent light
data accurately and efficiently. FDT successfully reconstructed the RI of 3D
cultured label-free 3D MuSCs tube in a 530 $\times$ 530 $\times$ 300 $\mu m^3$
volume at 1024$\times$1024 pixels across 24 $z$-layers from fluorescence
images, demonstrating high fidelity 3D RI reconstruction of bulky and
heterogeneous biological samples in vitro.
