Geometry-dependent reachability, homogenization, and redundancy in multi-view photoacoustic illumination

In deep scattering tissue, vascular geometry strongly modulates the optical fluence field, thereby complicating quantitative photoacoustic imaging and the assessment of multi-view illumination. This study establishes a geometry-consistent basis for comparing multi-view photoacoustic illumination across complex vascular geometries under a unified fluence-side criterion. Illumination directions are drawn from a fixed candidate view pool and accumulated as a stable prefix, while the unified reachability threshold is calibrated once from a baseline reference view and then applied to all geometries and all view counts. This protocol enables direct comparison of union-reachability coverage Ω _reach , fluence nonuniformity V _G , low-fluence-tail response, and view-response redundancy. Monte Carlo simulations on five aneurysm-like vascular geometries show that Ω _reach increases rapidly at small view numbers and then approaches geometry-dependent saturation levels of approximately 0.514 - 0.553, a behavior preserved under moderate optical-transport perturbations and controlled variations in thresholding, photon number, view ordering, and view selection. Matched-coverage analysis further shows that comparable reachability does not imply comparable homogenization, because V _G and the local response coefficient η_G * remain geometry dependent within the same coverage window. Spectral analysis of the view-response matrix reveals geometry-constrained effective low dimensionality, with terminal N_eff values of approximately 4.2 - 7.4, far below the nominal number of accumulated views. These results identify reachable-domain expansion, fluence homogenization, and response redundancy as coupled but non-equivalent aspects of multi-view photoacoustic illumination, providing physically interpretable criteria for assessing view accumulation in complex vascular geometries.