Experimental benchmarking of the incoherent transport of intensity equation using spatial axial shearing incoherent digital holography.

This paper presents an experimental benchmarking framework for evaluating phase retrieval consistency between the transport of intensity equation (TIE) and spatial axial shearing-based Incoherent Digital Holography (IDH) in fluorescence imaging. While TIE provides a non-interferometric, intensity-based approach for phase retrieval, its quantitative reliability under incoherent imaging conditions remains insufficiently validated against coherence-based techniques. Using a unified switchable experimental platform that ensures identical imaging conditions, we directly compare phase distributions retrieved by TIE and IDH from the same fluorescent objects. The IDH system employs spatial axial shearing and four-step phase shifting to reconstruct the complex spatial coherence function, providing a coherence-guided benchmark for comparison. Experimental results demonstrate strong agreement in the spatial extent and curvature of the retrieved phase profiles, while statistical analysis further confirms good consistency between the two methods across multiple fluorescent bead measurements. Under paraxial propagation conditions (Fresnel number (NF > 1), TIE reconstructions show close agreement with both IDH and the conventional fluorescence reference image, whereas coherence-guided IDH remains more robust at larger defocus distances. The proposed benchmarking framework provides an experimental basis for assessing the reliability and limitations of TIE-based phase retrieval in incoherent fluorescence imaging.