Philipp Krauter

Model-based analysis on the influence of spatial frequency selection in spatial frequency domain imaging

Frequency variation in spatial frequency domain imaging is a powerful tool for adjusting the penetration depth of the imaging signal and the parameter sensitivity toward absorption and diffusive and subdiffusive scattering. Through our computational analysis, using an analytical solution of the radiative transfer equation, we add quantitation to this tool by linking the different spatial frequency regimes to their relative information content and to their absolute depth sensitivity. Special focus is placed on high spatial frequencies by analysis of the phase function parameter γ and its significance and ambiguity in describing subdiffusive scattering.

Quantifying phase function influence in subdiffusively backscattered light

Abstract. Light backscattering at short source–detector separations is considerably influenced by the scattering phase function of a turbid medium. We seek to more precisely relate a medium’s subdiffusive backscattering to the angular scattering characteristics of its microstructure. First, we demonstrate the inability of the scattering asymmetry g1= to predict phase function influence on backscattering and reveal ambiguities related to the established phase function parameter γ. Through the use of high-order similarity relations, we introduce a new parameter that more accurately relates a scattering phase function to its subdiffusive backscattering intensity. Using extensive analytical forward calculations based on solutions to the radiative transfer equation in the spatial domain and spatial frequency domain, we demonstrate the superiority of our empirically derived quantifier σ over the established parameter γ.

Optical phantoms with adjustable subdiffusive scattering parameters

Abstract. A new epoxy-resin-based optical phantom system with adjustable subdiffusive scattering parameters is presented along with measurements of the intrinsic absorption, scattering, fluorescence, and refractive index of the matrix material. Both an aluminium oxide powder and a titanium dioxide dispersion were used as scattering agents and we present measurements of their scattering and reduced scattering coefficients. A method is theoretically described for a mixture of both scattering agents to obtain continuously adjustable anisotropy values g between 0.65 and 0.9 and values of the phase function parameter γ in the range of 1.4 to 2.2. Furthermore, we show absorption spectra for a set of pigments that can be added to achieve particular absorption characteristics. By additional analysis of the aging, a fully characterized phantom system is obtained with the novelty of g and γ parameter adjustment.

Surface layering properties of Intralipid phantoms

Intralipid has become an extensively studied and widely used reference and calibration phantom for diffuse optical imaging technologies. In this study we call attention to the layering properties of Intralipid emulsions, which are commonly assumed to have homogeneous optical properties. By measurement of spatial frequency domain reflectance in combination with an analytical solution of the radiative transfer equation for two-layered media, we make quantitative investigations on the formation of a surface layer on different dilutions of Intralipid. Our findings are verified by an independent spatially resolved reflectance setup giving evidence of a time dependent, thin and highly scattering surface layer on top of Intralipid-water emulsions. This layer should be considered when using Intralipid as an optical calibration or reference phantom.

Detecting structural information of scatterers using spatial frequency domain imaging

Abstract. We demonstrate optical phantom experiments on the phase function parameter γ using spatial frequency domain imaging. The incorporation of two different types of scattering particles allows for control of the optical phantoms’ microscopic scattering properties. By laterally structuring areas with either TiO2 or Al2O3 scattering particles, we were able to obtain almost pure subdiffusive scattering contrast in a single optical phantom. Optical parameter mapping was then achieved using an analytical radiative transfer model revealing the microscopic structural contrast on a macroscopic field of view. As part of our study, we explain several correction and referencing techniques for high spatial frequency analysis and experimentally study the sampling depth of the subdiffusive parameter γ.

Time-resolved measurements of the optical properties of fibrous media using the anisotropic diffusion equation.

Abstract. Transmittance and reflectance from spruce wood and bovine ligamentum nuchae as two different fibrous media are examined by time-of-flight spectroscopy for varying source detector separations and several orientations of the fibers in the sample. The anisotropic diffusion theory is used to obtain the absorption coefficient and the diffusion coefficients parallel and perpendicular to the fibers. The results are compared to those obtained with the isotropic diffusion theory. It is shown that for increasing source detector separations, the retrieved optical properties change as expected from Monte Carlo simulations performed in a previous study. This confirms that the anisotropic diffusion theory yields useful results for certain experimental conditions.

Resolving the depth of fluorescent light by structured illumination and shearing interferometry

A method for the depth-sensitive detection of fluorescent light is presented. It relies on a structured illumination restricting the excitation volume and on an interferometric detection of the wave front curvature. The illumination with two intersecting beams of a white-light laser separated in a Sagnac interferometer coupled to the microscope provides a coarse confinement in lateral and axial direction. The depth reconstruction is carried out by evaluating shearing interferograms produced with a Michelson interferometer. This setup can also be used with spatially and temporally incoherent light as emitted by fluorophores. A simulation workflow of the method was developed using a combination of a solution of Maxwells equations with the Monte Carlo method. These simulations showed the principal feasibility of the method. The method is validated by measurements at reference samples with characterized material properties, locations and sizes of fluorescent regions. It is demonstrated that sufficient signal quality can be obtained for materials with scattering properties comparable to dental enamel while maintaining moderate illumination powers in the milliwatt range. The depth reconstruction is demonstrated for a range of distances and penetration depths of several hundred micrometers.

Double anisotropic coherent backscattering of light

A double anisotropic coherent backscattering cone was found. In contrast to the (single) anisotropic coherent backscattering, which was observed in liquid crystals, here, the long axis of the elongated structures changes its orientation with angular distance. We compared our results with the two-dimensional Fourier transform of spatially resolved reflectance measurements and found good agreement, which is predicted by the reciprocity thesis. Furthermore, a Monte Carlo model was applied to reproduce successfully the results of the experiment, whereas the double anisotropy is not predicted by diffusion models.

Determination of three optical properties from subdiffusive spatially resolved reflectance calculations

Abstract. We report a theoretical study on the determination of three optical properties from spatially resolved reflectance calculations. In particular, the reduced scattering coefficient μs′, the absorption coefficient μa, and the recently defined phase function parameter σ are identified. The solution of the inverse problem is based on the principal component analysis of a large set of reflectance profiles that were calculated using an analytical solution of the radiative transfer equation. Different phase function types were studied to test the method in the range of 0.63  mm−1≤μs′≤4.2  mm−1 and 0.002  mm−1≤μa≤0.1  mm−1. For curves impaired with noise, we were able to reconstruct μs′ and μa with relative median errors of 2.5% and 12%, respectively, and σ with an absolute median error of 0.04.

Detecting Structural Information of Scatterers Using Spatial Frequency Domain Imaging

Spatial frequency domain imaging is frequently used to derive scattering and absorption maps of turbid media. Using high spatial frequencies, we demonstrate mapping of the phase function parameter gamma which provides microscopic information of scatterers.