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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. [ABSTRACT FROM AUTHOR]