We present a goniometer designed for capturing spectral and angular-resolved data from scattering and absorbing media. The experimental apparatus is complemented by a comprehensive Monte Carlo simulation, meticulously replicating the radiative transport processes within the instrument’s optical components and simulating scattering and absorption across arbitrary volumes. Consequently, we were able to construct a precise digital replica, or “twin”, of the experimental setup. This digital counterpart enabled us to tackle the inverse problem of deducing optical parameters such as absorption and scattering coefficients, along with the scattering anisotropy factor from measurements. We achieved this by fitting Monte Carlo simulations to our goniometric measurements using a Levenberg–Marquardt algorithm. Validation of our approach was performed using polystyrene particles, characterized by Mie scattering, supplemented by a theoretical analysis of algorithmic convergence. Ultimately, we demonstrate strong agreement between optical parameters derived using our novel methodology and those obtained via established measurement protocols.

In this study, we conducted optical goniometric measurements of turbid media and utilized a Monte Carlo model to characterize their optical properties. Our methodology employs an inverse fitting approach that combines Monte Carlo simulations with a Levenberg-Marquardt optimization routine. To enhance the accuracy and robustness of the inverse fitting process, we incorporated second-order derivatives into the algorithm. We also investigated the critical role of the single-scattering phase function and assessed the limitations associated with the commonly used Henyey-Greenstein (HG) approximation. To address these limitations, we developed a fitting procedure that determines the single-scattering phase function via cubic splines. This allows for the simultaneous extraction of both the cubic spline phase function and the scattering and absorption coefficients from goniometric measurements. This approach provides a refined and novel model for analyzing turbid media.

In this study, we present measurements of the temperature-dependent optical scattering properties of 20% Intralipid across the spectral range of 400 nm to 900 nm and a temperature range of 11 ^∘ C to 57 ^∘ C. We provide a characterization of the scattering phase function using the two-parameter Reynolds-McCormick (RMC) model. Empirical expressions are derived to describe the wavelength dependence of the RMC phase function parameters g _s and α , as well as the combined wavelength and temperature dependence of the scattering coefficient μ _s . The measurements achieved a repeatability with standard deviations typically below 0.4% in determining scattering parameters. The results show good agreement with Mie-theory predictions—based on independently measured droplet size distributions—within 1.8%.

We present a goniometric method combining Monte Carlo simulations and inverse fitting to extract optical properties of turbid media. Our approach improves phase function modeling via cubic splines, enhancing accuracy beyond the Henyey-Greenstein approximation.

In the article “Characterization of temperature-dependent optical scattering of Intralipid fat emulsions from 400 nm to 900 nm” [ Opt. Lett. 51 , 1943 ( 2026 ) 10.1364/OL.592524 ], a typographical error was identified in the expression of the Reynolds–McCormick (RMC) phase function presented in Eq. (3). This erratum provides the corrected equation. The error is purely typographical and does not affect any calculations, results, discussion, or conclusions reported in the original paper.

Understanding light propagation in human dentin is critical for dental diagnostics, including optical coherence tomography (OCT) and early caries detection. Dentin’s heterogeneous microstructure—a dense network of cylindrical tubules (≈2μm diameter) embedded in an organic–inorganic matrix—induces both isotropic and anisotropic light propagation. Previous isotropic-only models cannot capture the pronounced angular dependence observed experimentally, leading to substantial errors in the estimation of optical parameters. We present a combined isotropic–anisotropic Monte Carlo model for light transport in dentin, incorporating directionally dependent propagation in tubules based on Maxwell’s equations for infinitely extended cylinders. Optical parameters were determined from angular-resolved goniometric measurements on three human teeth across wavelengths from 400 nm to 700 nm, with controlled tubule orientations. Using particle swarm optimization to fit the model to experimental data, we quantitatively characterized both propagation regimes: the intertubular matrix ( μ _a ≈0.5mm ⁻¹ , μ _s ≈1.8mm ⁻¹ , g ≈ 0.85) and tubule geometry (diameter 2.25 µm, areal density 19 000 mm ⁻² to 60 000 mm ⁻² ). Comparison with an isotropic-only model revealed that neglecting anisotropic propagation introduces absorption errors exceeding 40 %, emphasizing the importance of the combined approach. This framework enables robust inverse problem solving for dental optics and can be extended to study other tissues exhibiting anisotropic light propagation, such as brain white matter, tendon, and muscle.