Optical Goniometer Paired with Digital Monte Carlo Twin to Determine the Optical Properties of Turbid Media.

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.

Continuous Sizing and Identification of Microplastics in Water.

The pollution of the environment with microplastics in general, and in particular, the contamination of our drinking water and other food items, has increasingly become the focus of public attention in recent years. In order to better understand the entry pathways into the human food chain and thus prevent them if possible, a precise characterization of the particles concerning their size and material is indispensable. Particularly small plastic particles pose a special challenge since their material can only be determined by means of large experimental effort. In this work, we present a proof of principle experiment that allows the precise determination of the plastic type and the particle size in a single step. The experiment combines elastic light scattering (Mie scattering) with inelastic light scattering (Raman scattering), the latter being used to determine the plastic type. We conducted Monte Carlo simluations for the elastically scattered light for different kinds of plastics in a microfluidic cuvette which we could reproduce in the experiment. We were able to measure the Raman signals for different microplastics in the same measurement as the elastically scattered light and thereby determine their material. This information was used to select the appropriate Monte Carlo simulation data and to assign the correct particle size to different materials with only one calibration measurement.

Influence of Lambertian surface scattering on the spatially resolved reflectance from turbid media: a computational study.

The determination of the optical properties in turbid media plays an essential role in medical diagnostics and process control. The method of spatially resolved reflectance measurements is a frequently used tool to evaluate the reduced scattering coefficient as well as the absorption coefficient. In most cases a smooth interface is assumed between the medium under investigation and the surrounding medium. However, in reality, a rough surface is present at the interface, which alters the light interaction with the surface and volume of the turbid medium. Hence, the idea behind this paper was to investigate the influence of rough surfaces on the spatially resolved reflectance and thus on the determination of the optical properties of turbid media. Particularly, the influence of a Lambertian scattering surface on the result of Monte Carlo simulations of a spatially resolved reflectance setup is shown. In addition, we distinguish between the different interaction modes of surface scattering on the spatially resolved reflectance. There is a strong influence of roughness when the light enters and leaves the turbid medium. Furthermore, the simulations show that, especially for small reduced scattering coefficients and absorption coefficients, large errors in the determination of the optical properties are obtained.

Spatially resolved reflectance from turbid media having a rough surface. Part II: experiments.

Spatially resolved reflectance measurements are a standard tool for determining the absorption and scattering properties of turbid media such as biological tissue. However, in literature, it was shown that these measurements are subject to errors when a possible rough surface between the turbid medium and the surrounding is not accounted for. We evaluated these errors by comparing the spatially resolved reflectance measured on rough epoxy-based samples with Monte Carlo simulations using Lambertian surface scattering, the Cook-Torrance model, and the generalized Harvey-Shack model as surface scattering models. To this aim, goniometric measurements on the epoxy-based samples were compared to the angularly resolved reflectance of the three surface models to estimate the corresponding model parameters. Finally, the optical properties of the phantoms were determined using a Monte Carlo model with a smooth surface.

Spatially resolved reflectance from turbid media having a rough surface. Part I: simulations.

Determining the optical properties of turbid media with spatially resolved reflectance measurements is a well-known method in optical metrology. Typically, the surfaces of the investigated materials are assumed to be perfectly smooth. In most realistic cases, though, the surface has a rough topography and scatters light. In this study, we investigated the influence of the Cook-Torrance surface scattering model and the generalized Harvey-Shack surface scattering model on the spatially resolved reflectance based on Monte Carlo simulations. Besides analyzing the spatially resolved reflectance signal, we focused on the influence of surface scattering on the determination of the reduced scattering coefficients and absorption coefficients of turbid media. Both models led to significant errors in the determination of optical properties when roughness was not accounted for.

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.

Precise determination of the optical properties of turbid media using an optimized integrating sphere and advanced Monte Carlo simulations. Part 1: theory.

In this paper, we describe a method used to determine the optical properties, namely, the effective scattering and absorption coefficients, employing an optimized three-dimensional-printed single integrating sphere. The paper consists of two parts, and in Part 1, the theoretical investigation of an optimized measurement and the evaluation routine are presented. Using an analytical and a numerical model for the optical characterization of the integrating sphere, errors caused by the application of a non-ideal sphere (the one with ports or baffles) were investigated. Considering this research, a procedure for the precise determination of the optical properties, based on Monte Carlo simulations of the light distribution within the sample, was developed. In Part 2, we present the experimental validation of this procedure.

Precise determination of the optical properties of turbid media using an optimized integrating sphere and advanced Monte Carlo simulations. Part 2: experiments.

Based on theoretical investigations of the light propagation within an integrating sphere, we developed an accurate method to determine the optical properties of scattering media using an integrating sphere-based setup. The method takes into account the exact sphere geometry as well as the different angular distributions of the reflected and transmitted light from the sample and the calibration standard. We tested our novelties successfully in theory with Monte Carlo simulations and in practice using a 3D printed and professionally coated integrating sphere. As a result, we were able to determine precisely the effective scattering coefficient, µs', and the absorption coefficient, µa, between 400 nm and 1500 nm in a range of µa=1e-3mm-1 to 10mm-1 and µs'=0.2mm-1 to 100mm-1. Usually, the accuracy was around 1% for µs' and around 3% for µa for turbid phantom media with an optical thickness τ=µs'd>1 and a transmittance signal >0.1%.

Estimation of Photon Path Length and Penetration Depth in Articular Cartilage Zonal Architecture Over the Therapeutic Window.

OBJECTIVE: The key characteristics of light propagation are the average penetration depth, average maximum penetration depth, average maximum lateral spread, and average path length of photons. These parameters depend on tissue optical properties and, thus, on the pathological state of the tissue. Hence, they could provide diagnostic information on tissue integrity. This study investigates these parameters for articular cartilage which has a complex structure. METHODS: We utilize Monte Carlo simulation to simulate photon trajectories in articular cartilage and estimate the average values of the light propagation parameters (penetration depth, maximum penetration depth, maximum lateral spread, and path length) in the spectral band of 400-1400 nm based on the optical properties of articular cartilage zonal layers and bulk tissue. RESULTS: Our findings suggest that photons in the visible band probe a localized small volume of articular cartilage superficial and middle zones, while those in the NIR band penetrate deeper into the tissue and have larger lateral spread. In addition, we demonstrate that a simple model of articular cartilage tissue, based on the optical properties of the bulk tissue, is capable to provide an accurate description of the light-tissue interaction in articular cartilage. CONCLUSION: The results indicate that as the photons in the spectral band of 400-1400 nm can reach the full depth of articular cartilage matrix, they can provide viable information on its pathological state. Therefore, diffuse optical spectroscopy holds significant importance for objectively assessing articular cartilage health. SIGNIFICANCE: In this study, for the first time, we estimate the light propagation parameters in articular cartilage.

Impact of experimental setup parameters on the measurement of articular cartilage optical properties in the visible and short near-infrared spectral bands.

There is increasing research on the potential application of diffuse optical spectroscopy and hyperspectral imaging for characterizing the health of the connective tissues, such as articular cartilage, during joint surgery. These optical techniques facilitate the rapid and objective diagnostic assessment of the tissue, thus providing unprecedented information toward optimal treatment strategy. Adaption of optical techniques for diagnostic assessment of musculoskeletal disorders, including osteoarthritis, requires precise determination of the optical properties of connective tissues such as articular cartilage. As every indirect method of tissue optical properties estimation consists of a measurement step followed by a computational analysis step, there are parameters associated with these steps that could influence the estimated values of the optical properties. In this study, we report the absorption and reduced scattering coefficients of articular cartilage in the spectral band of 400-1400 nm. We assess the impact of the experimental setup parameters, including surrounding medium, sample volume, and scattering anisotropy factor on the reported optical properties. Our results suggest that the absorption coefficient of articular cartilage is sensitive to the variation in the surrounding medium, whereas its reduced scattering coefficient is invariant to the experimental setup parameters.

Broadband scattering properties of articular cartilage zones and their relationship with the heterogenous structure of articular cartilage extracellular matrix.

Significance: Articular cartilage exhibits a zonal architecture, comprising three distinct zones: superficial, middle, and deep. Collagen fibers, being the main solid constituent of articular cartilage, exhibit unique angular and size distribution in articular cartilage zones. There is a gap in knowledge on how the unique properties of collagen fibers across articular cartilage zones affect the scattering properties of the tissue. Aim: This study hypothesizes that the structural properties of articular cartilage zones affect its scattering parameters. We provide scattering coefficient and scattering anisotropy factor of articular cartilage zones in the spectral band of 400 to 1400 nm. We enumerate the differences and similarities of the scattering properties of articular cartilage zones and provide reasoning for these observations. Approach: We utilized collimated transmittance and integrating sphere measurements to estimate the scattering coefficients of bovine articular cartilage zones and bulk tissue. We used the relationship between the scattering coefficients to estimate the scattering anisotropy factor. Polarized light microscopy was applied to estimate the depth-wise angular distribution of collagen fibers in bovine articular cartilage. Results: We report that the Rayleigh scatterers contribution to the scattering coefficients, the intensity of the light scattered by the Rayleigh and Mie scatterers, and the angular distribution of collagen fibers across tissue depth are the key parameters that affect the scattering properties of articular cartilage zones and bulk tissue. Our results indicate that in the short visible region, the superficial and middle zones of articular cartilage affect the scattering properties of the tissue, whereas in the far visible and near-infrared regions, the articular cartilage deep zone determines articular cartilage scattering properties. Conclusion: This study provides scattering properties of articular cartilage zones. Such findings support future research to utilize optical simulation to estimate the penetration depth, depth-origin, and pathlength of light in articular cartilage for optical diagnosis of the tissue.

Determination of the spectrally resolved extinction coefficient of human dental enamel using collimated transmission spectroscopy.

OBJECTIVES: The determination of the extinction coefficient of human dental enamel to deliver further optical properties of enamel to improve the understanding of light propagation in teeth and to improve restoration materials. METHODS: The extinction coefficient was measured within a spectral range of 300-980 nm using a collimated transmission setup. 35 specimens from 16 donors were examined. The donors were categorized by age and the researched specimen were categorized by tooth type, tooth quality and lateral expansion of the enamel to clarify the influence of these parameters. RESULTS: The obtained spectrally resolved extinction coefficient was accurately described by a power law, which agrees with theoretical scattering models. The results were evaluated with regard to the influence of parameters such as subject age, tooth type, enamel sample quality and enamel width. For this purpose, both the average values of multiple measurements of a single sample in a defined spectral range as well as the curve slope of the averaged results versus wavelength were compared. SIGNIFICANCE: The results provide detailed information about the optical properties of human enamel. The wide spectrum investigated provides important information for the evaluation of the main scatterers and the optical impression under any light condition. However, the deviation of the extinction coefficient varies less between the mean values for the specimens grouped by several parameters than between the specimens themselves within a group. This indicates a unique optical behaviour for every specimen and this requires consideration in the development of artificial materials.

250 years Lambert surface: does it really exist?

The time-honored Lambert law is widely applied for describing the angle resolved reflectance from illuminated turbid media. We show that this law is only exactly fulfilled for a very special set of geometrical and optical properties. In contrast to what is believed so far, we demonstrate theoretically and experimentally that huge deviations from the Lambert law are ubiquitous. This finding is important for many applications such as those in biomedical optics.

Optical properties of fat emulsions.

We present measurements of the optical properties of six different fat emulsions from three different brands, Clinoleic, Lipovenoes and Intralipid, with fat concentrations from 10% to 30%. The scattering coefficient, the reduced scattering coefficient, and the phase function of each sample are measured for wavelengths between 350 nm and 900 nm. A method for the calculation of the particle size distribution of these fat emulsions is introduced. With the particle size distribution the optical properties of the fat emulsions are obtained with Mie theory. Simple equations for the calculation of the absorption coefficient, the scattering coefficient, the reduced scattering coefficient, the g factor, and the phase function of all measured samples are presented.

Light propagation in dry and wet softwood.

Light propagation in dry and wet softwood (silver fir) was investigated experimentally and theoretically. The spatially and time resolved reflectance from softwood was measured. Light propagation was modeled with Monte Carlo simulations considering the microstructure of softwood. By comparing the spatially resolved reflectance we found that all characteristics of the experimentally obtained iso-intensity contour lines were recovered by the theory. In addition, the reduced scattering and the absorption coefficients were determined in the time domain by fitting a solution of the diffusion equation to Monte Carlo simulations and to measurements. Good qualitative agreement was obtained between the experimentally and theoretically derived optical properties.

Spatially Resolved Lateral Transmission Measurements to Characterize Changes in the Scattering Coefficient and the Anisotropy Factor.

A new setup is described to characterize the scattering coefficient and the scattering phase function of liquid media. The setup utilizes the basic idea of a spatially resolved reflectance measurement combined with a sophisticated illumination geometry. The sample is illuminated parallel and close to the interface of the sample and a glass window to get information from single scattered and multiple scattered light. By illuminating the sample with a fiber orientated with the axis parallel to the glass surface, small distances to the source can be examined unimpeded by the illumination beam. The derived information is, for example, not only sensitive to the concentration of the scatterers but also to the size of the scattering particles. We present the setup including the theory to describe the light propagation in the whole configuration using Monte Carlo simulations. The validation has been done with polystyrene microsphere dispersions with different scattering coefficients. As application for the developed setup, we show measurements of different milk samples which vary in concentration of fat, protein, and in fat droplet size during homogenization process. By measuring milk, we show the ability of the sensor to determine information about the scattering phase function without diluting the sample. For sensors in the dairy industry, a measurement with no pre-processing and no diluting of the sample is worthwhile, because this can be used to determine the fat and protein concentration on-line.

Parallelized Monte Carlo software to efficiently simulate the light propagation in arbitrarily shaped objects and aligned scattering media.

A GPU-based Monte Carlo software (MCtet) was developed to calculate the light propagation in arbitrarily shaped objects, like a human tooth, represented by a tetrahedral mesh. A unique feature of MCtet is a concept to realize different kinds of light-sources illuminating the complex-shaped surface of an object, for which no preprocessing step is needed. With this concept, it is also possible to consider photons leaving a turbid media and reentering again in case of a concave object. The correct implementation was shown by comparison with five other Monte Carlo software packages. A hundredfold acceleration compared with central processing units-based programs was found. MCtet can simulate anisotropic light propagation, e.g., by accounting for scattering at cylindrical structures. The important influence of the anisotropic light propagation, caused, e.g., by the tubules in human dentin, is shown for the transmission spectrum through a tooth. It was found that the sensitivity to a change in the oxygen saturation inside the pulp for transmission spectra is much larger if the tubules are considered. Another "light guiding" effect based on a combination of a low scattering and a high refractive index in enamel is described.

Broadband Optical Properties of Milk.

Dairy products play an important role in our daily nutrition. As a turbid scattering medium with different kinds of particles and droplets, each alteration of these components changes the scattering properties of milk. The goal of this work is the determination of the amount of main scattering components, the fat droplets and the casein micelles, by understanding the light propagation in homogenized milk and in raw milk. To provide the absolute impact of these milk components, the geometrical and optical properties such as the size distribution and the refractive index (RI) of the components have to be examined. We determined the reduced scattering coefficient [Formula: see text] and the absorption coefficient [Formula: see text] from integrating sphere measurements. By use of a collimated transmission setup, the scattering coefficient [Formula: see text] was measured. Size measurements were performed to validate the influence of the fat droplet size on the results of the scattering properties; also, the RI of both components was determined by the said coefficients. These results were used to determine the absolute impact of the milk components on the scattering behavior. By fitting Mie theory calculations on scattering spectra [Formula: see text] and [Formula: see text] from different raw milk samples, it was possible to get reliable values for the concentrations of fat and casein and for the size of the fat droplets. By destroying the casein micelles, it was possible to separate the influence of the different scattering components on scattering behavior.

Detecting structural information of scatterers using spatial frequency domain imaging.

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.

Optical phantoms with adjustable subdiffusive scattering parameters.

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.