Improved topographic reconstruction of turbid media in the spatial frequency domain including the determination of the reduced scattering and absorption coefficients.

The separation of scattering and absorption is of great importance for studying the radiative transfer in turbid media. Obtaining the corresponding coefficients for non-flat objects is difficult and needs special consideration. Building on our previous work [J. Opt. Soc. Am. A39, 1823 (2022)JOAOD60740-323210.1364/JOSAA.464007], we present an approach that takes the changing incident and detection angles relative to the surface normal of curved surfaces into account to improve the determination of the reduced scattering and absorption coefficients with measurements in the spatial frequency domain (SFD). The optical coefficients are reconstructed using a pre-calculated lookup table generated with Monte Carlo simulations on graphical processing units. With the obtained values, the error in the captured surface geometry of the object, which is due to the volume scattering, is compensated and reduced by 1 order of magnitude for measurements in the SFD. Considering the approximate surface geometry, the absorption and reduced scattering are accurately resolved for moderate object curvatures, with very low dependence on the tilt angle. In contrast to models that only correct the amplitudes of the SFD signal, our approach, in addition to the optical properties, predicts the phase values correctly, which is the reason why it can be used to correct the surface geometry.

Analytical solution of the radiative transfer theory for the coherent backscattering from two-dimensional semi-infinite media.

An analytical solution for coherent backscattering (CBS) in two dimensions was derived by solving the radiative transfer equation. Particularly, the single scattered radiance from a semi-infinite medium containing perpendicularly illuminated cylinders was obtained. At the boundary, a refractive index mismatch was taken into account. Furthermore, the link between the radiance and the CBS was shown in the small angle approximation. An excellent agreement was found between Monte Carlo simulations and the analytical solution. Additionally, it was shown that the often applied solution in the spatial frequency domain for quantifying the CBS delivered significantly different results compared to the derived exact analytical solution.

Improved topography reconstruction of volume scattering objects using structured light.

The use of structured light projection enables the reconstruction of three-dimensional topography of surface reflecting objects. However, if the investigated object exhibits volume scattering, the obtained topography is erroneously caused by light undergoing volume scattering inside the object. In this theoretical study, we investigate these errors using Monte Carlo simulations. Additionally, a method is proposed to correct the errors by quantifying the light propagation in the scattering object based on the radiative transfer equation. Reconstructed surfaces with a small spatial variation of topography can be quickly corrected using a local correction method that depends only on the directions of the incident and detected light relative to the surface. For surfaces that show a large spatial variation of the surface geometry, another approach is introduced by simulating the light propagation in the whole scanned three-dimensional object using graphics processing unit (GPU)-accelerated Monte Carlo simulations. A cylindrical object and an incisor tooth are, exemplarily, investigated. The results show a major improvement in the reconstructed topography due to the correction with the proposed methods.

Analytical solution of the vector radiative transfer equation for single scattered radiance.

In this paper, derivation of the analytical solution of the vector radiative transfer equation for the single scattered radiance of three-dimensional semi-infinite media with a refractive index mismatch at the boundary is presented. In particular, the solution is obtained in the spatial domain and spatial frequency domain. Besides the general derivation, determination of the amplitude scattering matrix, which is required for the analytical solution, is given in detail. Furthermore, the incorporation of Fresnel equations due to a refractive index mismatch at the boundary is presented. Finally, verification of the derived formulas is performed using a self-implemented electrical field Monte Carlo method based on Jones formalism. For this purpose, the solution based on Jones formalism is converted to Stokes-Mueller formalism. For the verification, spherical particles are assumed as scatterers, whereby arbitrary size distributions can be considered.

Analytical solution of the vector radiative transfer equation for single scattered radiance: erratum.

We have discovered a small error in our recently published work [J. Opt. Soc. Am. A39, 2045 (2022)JOSAAH0030-394110.1364/JOSAA.467890], which we correct in this erratum. The error is located in Section 2.D and affects the solution for polydisperse distributions.

Distance insensitive reflectance setup for the spectrally resolved determination of the optical properties of highly turbid media.

A measurement system for a distance insensitive acquisition of the reflectance from turbid media is presented. The geometric relationships of the detection unit are discussed theoretically and subsequently verified using Monte Carlo simulations. In addition, an experimental setup is presented to prove the theoretical considerations and simulations. The use of the presented measurement system allows measurements of the reflectance in a distance range of approximately 2.5cm with a deviation of less than ±0.5% for highly scattering media. This contrasts with the use of a fiber in a classical detection unit placed at a defined angle and position relative to the sample surface, which results in deviations of ±30% in the measured reflectance over the same distance range.