Researchers at ExCELLS derive a coupled transport model that simultaneously reconstructs refractive-index fluctuations and attenuation coefficients without weak-absorption approximations, and experimentally verify optical reciprocity in HeLa cells.

Light traveling through living cells is shaped by two interlinked processes—refraction from inhomogeneous structure and attenuation from absorption and scattering. Conventional phase-imaging methods can describe only one at a time. A new study from the Exploratory Research Center on Life and Living Systems (ExCELLS) of the National Institutes of Natural Sciences introduces a unified transport model that captures both processes simultaneously, defines exactly where the model can be applied, and confirms that biological tissues preserve a fundamental symmetry of light propagation across three orders of magnitude in optical depth. The model’s outputs may further be translated into intracellular physical properties such as fluid viscosity, density, and local temperature, opening a route toward reading cellular environments quantitatively through light.

The authors further introduced an attenuation asymmetry parameter Aκ—quantifying the imbalance between forward and backward propagation—and measured it as a function of optical depth. Aκ was found to be statistically consistent with zero across three orders of magnitude in optical depth, with systematic errors from high-numerical-aperture optics remaining well below statistical uncertainties. This provides the first quantitative experimental confirmation that optical reciprocity is preserved in heterogeneous biological media at the wavelength scale.

Results for HeLa cells. (a) Optical path for the bright-field imaging system with a wide-field microscope. (b) Through-focus intensity distributions I(r⊥, z₀ − Δz), I(r⊥, z₀), and I(r⊥, z₀ + Δz). (c) Phase distributions reconstructed from the three intensity images. (d) Reconstructed spatial distribution of the refractive-index fluctuation Δn and (e) the attenuation coefficient μ. (f) Correlation pattern between Δn(r⊥, z₀) and μ(r⊥, z₀). The black solid line indicates the 3σ confidence level, and the green area shows the physical parameter boundaries (validity region) given by the validity-bound equation in the main text. In this sample, 65,055 events (24.82%) fall outside the green region. (g) Attenuation asymmetry Aκ as a function of optical depth log₁₀|μΔz|. The blue solid line and band denote the statistical mean and the root mean squared (RMS) value of Aκ, respectively, and the dashed line indicates Aκ = 0.