Thermal Heterogeneity Couples Hidden Modes in Photothermal Tomography

Limited-angle optical diffraction tomography incompletely samples refractive-index contrast. We examine whether spatially varying thermal conductivity transfers a spatial Fourier component from an unmeasured heat-source mode to a modeled sampled thermal mode, and whether the resulting contrast identifies its origin. A first-order Fourier perturbation analysis is tested against independent one-dimensional, two-dimensional, and three-dimensional solvers, directional negative controls, transient diffusion calculations, and local inverse-sensitivity tests. In the three-dimensional numerical phantom, a 10% conductivity modulation transfers 3.82% of the homogeneous source-mode amplitude to a selected neighboring mode under the adopted transmission-like sampling surrogate; the joint source–conductivity inverse remains ill-conditioned (condition number approximately 917). We further analyze a publicly deposited three-dimensional mid-infrared photothermal refractive-index contrast volume. On a 48 × 48 × 32-voxel region, spatially constant and deliberately heterogeneous conductivities, paired with different unconstrained effective sources, reproduce the identical contrast proxy to relative errors below 8 × 10⁻⁹. These results demonstrate spectral mode transfer in controlled models and a constructive nonuniqueness of single-volume source–conductivity inference. The deposited experiment does not independently establish conductivity-mediated mode coupling or recovery of hidden cellular structure.