Incoherent 3D Holography Using a Spatial Axial Shearing Interferometer with Liquid Crystal Lens and Four-Step Phase Shifting

We report an incoherent three-dimensional fluorescence microscopy system that integrates spatial axial shearing interferometry with an electrically tunable liquid-crystal lens (LCL). The LCL enables precise electronic control of axial shear, eliminating mechanical adjustments and enhancing system compactness and stability. By combining this architecture with a four-step phase-shifting approach in incoherent digital holography (IDH), we achieve twin-image– and DC-term–free reconstructions within a common-path interferometer. This configuration allows robust retrieval of the complex spatial coherence function directly from fluorescence signals. Experimental validation with fluorescent microspheres confirms accurate phase reconstruction across varying axial positions, with results exhibiting strong agreement with expected depth-resolved structural features. The system provides a powerful platform for high-resolution, polarization-sensitive, and multidimensional fluorescence imaging, with strong potential for biomedical and life-science applications.