3D Computational Fluorescence Microscopy with Electrically Tunable Spatial Axial Shearing by Complex Coherence Function

We present a 3D fluorescence microscopy system based on spatial axial shearing interferometry, where the shear is electrically controlled by a liquid crystal lens and provide the analysis based on mutual coherence derivation. By integrating a four-step phase-shifting technique based on polarization dependency into incoherent digital holography (IDH), the system achieves twin-image- and DC-term-free reconstruction within a common-path architecture, enabling accurate retrieval of the complex spatial coherence function from fluorescence signals. The use of an electrically tuneable liquid crystal lens allows dynamic adjustment of axial shear, enhancing system flexibility and compactness. We validate the setup using fluorescent beads and demonstrate precise phase retrieval across varying axial distances, with reconstructed results showing strong agreement with expected depth-dependent structural features.