Persistent homology-based optical properties of microscopic turbid media for realistic light propagation analysis

The optical properties of microscopic turbid media are critical for understanding light-tissue interactions with applications in biomedical imaging and diagnostics. However, traditional scattering coefficient-based methods are limited in their ability to capture topological heterogeneities within tissue structures, which play a crucial role in describing the relationship between microscopic tissue characteristics and their corresponding light propagation behaviors. In this study, we propose using persistent homology-based persistent images (PIs) as a descriptor and optical property of microscopic tissues. As a proof of concept, we analyzed particle-distributed turbid media with uniform and clustered particle distributions by persistent homology analysis, demonstrating that PIs can capture topological characteristics that are not discernible using traditional scattering coefficient-based methods. Light propagation simulations using the beam propagation method (BPM) demonstrated that PIs correlate with optical behaviors, such as beam centroid displacement and distortion, providing a foundation for linking microscopic topological heterogeneities to light propagation behaviors. Our results validate PIs as a meaningful and predictive optical property, bridging microscopic turbid media topology with their light propagation behaviors. This work establishes PIs as a potential optical property of microscopic tissue, capturing its topological characteristics and offering predictive insights into light propagation behaviors.