Holographic incoherent-light optical diffraction tomography: Theoretical equivalence to coherent optical diffraction tomography and simulation-based validation

Holographic Incoherent-light-source Quantitative Phase Imaging (hiQPI) provides coherence-gated optical sectioning under spatially incoherent illumination and thus offers a distinct route to volumetric quantitative phase imaging. Here, we establish the physical relationship between hiQPI-based Optical Diffraction Tomography (ODT), termed Holographic Incoherent-light-source Optical Diffraction Tomography (hiODT), and conventional angle-scanning coherent holographic tomography. Using the first Born approximation for weakly scattering specimens, we derive the three-dimensional coherent transfer function of hiODT and show that it is identical to that obtained by integrating holographic-tomography projections over the illumination angle. Consequently, in the weak-scattering regime, hiODT acquires three-dimensional information by axially stacking two-dimensional hiQPI optical sections, without synthesizing the volume from angular projections. The resulting stack carries the same spatial-frequency information as conventional coherent ODT. Direct deconvolution of this stack using the first Born-based transfer function provides a fast, approximate three-dimensional refractive-index reconstruction, analogous to deconvolution of intensity-based optical sections in confocal microscopy. Numerical simulations confirm close agreement between iterative refractive-index reconstructions from simulated hiQPI axial stacks and conventional ODT projections. Experiments on simple model specimens, measured in both modes with a single hybrid microscope, further show agreement between hiODT and coherent ODT reconstructions. However, the complexity of this pilot system increases its susceptibility to mechanical and optical instabilities, currently restricting comparisons to simple specimens. We therefore use a stable incubator-housed hiQPI microscope to obtain a full-field z-stack of live cells in collagen and reconstruct their refractive-index distribution by fast direct deconvolution, demonstrating the applicability of the confocal-like approach. This study establishes the physical foundation of hiODT as a tomographic modality. The experimental results provide initial proof of feasibility and identify instrumental developments required for validation on more complex specimens.