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

Reconstruction of Optical Properties in Turbid Media: Omitting the Need of the Collimated Transmission for an Integrating Sphere Setup

Currently, the most reliable approach to reconstruct optical properties, namely absorption coefficient, reduced scattering coefficient, scattering coefficient and asymmetry factor, of turbid media is through inverse Monte Carlo simulation. To determine these optical properties, three measurements are required: total transmission, total reflection and collimated transmission. However, the accurate determination of the collimated transmission is very difficult. To overcome the difficulty of measuring the collimated transmission, it is proposed to measure the total transmission and total reflection of the same sample with two different thicknesses instead. To prove this alternative solution, machine learning is used to prove that the repeated measurement for two different thicknesses carries all the necessary information. As a result, all four optical properties can be measured with high accuracy, particularly for interpolation problems where the test data fall within the range of the training data. For extrapolation problems, high accuracy can be achieved in the determination of at least the absorption coefficient, reduced scattering coefficient and scattering coefficient. Hence, these results allow that in the future, an easier and therefore more precise reconstruction of the optical properties is possible, potentially even with inverse Monte Carlo simulations as the current standard.

Digitizing translucent object appearance by validating computed optical properties

The optical properties available for an object are most often fragmented and insufficient for photorealistic rendering of the object. We propose a procedure for digitizing a translucent object with sufficient information for predictive rendering of its appearance. Based on object material descriptions, we compute optical properties and validate or adjust this object appearance model based on comparison of simulation with spectrophotometric measurements of the bidirectional scattering-surface reflectance distribution function (BSSRDF). To ease this type of comparison, we provide an efficient simulation tool that computes the BSSRDF for a particular light-view configuration. Even with just a few configurations, the localized lighting in BSSRDF measurements is useful for assessing the appropriateness of computed or otherwise acquired optical properties. To validate an object appearance model in a more common lighting environment, we render the appearance of the obtained digital twin and assess the photorealism of our renderings through pixel-by-pixel comparison with photographs of the physical object.

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.

Rapid inverse radiative transfer solver for multiparameter spectrophotometry without integrating sphere

Significance

Multiparameter spectrophotometry (MPS) provides a powerful tool for accurate characterization of turbid materials in applications such as analysis of material compositions, assay of biological tissues for clinical diagnosis and food safety monitoring.

Aim

This work is aimed at development and validation of a rapid inverse solver based on a particle swarm optimization (PSO) algorithm to retrieve the radiative transfer (RT) parameters of absorption coefficient, scattering coefficient and anisotropy factor of a turbid sample.

Approach

Monte Carlo (MC) simulations were performed to obtain calculated signals for comparison to the measured ones of diffuse reflectance, diffuse transmittance and forward transmittance. An objective function has been derived and combined with the PSO algorithm to iterate MC simulations for MPS.

Results

We have shown that the objective function can significantly reduce the variance in calculated signals by local averaging of an inverse squared error sum function between measured and calculated signals in RT parameter space. For validation of the new objective function for PSO based inverse solver, the RT parameters of 20% Intralipid solutions have been determined from 520 to 1000 nm which took about 2.7 minutes on average to complete signal measurement and inverse calculation per wavelength.

Conclusion

The rapid solver enables MPS to be translated into easy-to-use and cost-effective instruments without integrating sphere for material characterization by separating and revealing compositional profiles at the molecular and particulate scales.

Generic and Model-Based Calibration Method for Spatial Frequency Domain Imaging with Parameterized Frequency and Intensity Correction

Spatial frequency domain imaging (SFDI) is well established in biology and medicine for non-contact, wide-field imaging of optical properties and 3D topography. Especially for turbid media with displaced, tilted or irregularly shaped surfaces, the reliable quantitative measurement of diffuse reflectance requires efficient calibration and correction methods. In this work, we present the implementation of a generic and hardware independent calibration routine for SFDI setups based on the so-called pinhole camera model for both projection and detection. Using a two-step geometric and intensity calibration, we obtain an imaging model that efficiently and accurately determines 3D topography and diffuse reflectance for subsequently measured samples, taking into account their relative distance and orientation to the camera and projector, as well as the distortions of the optical system. Derived correction procedures for position- and orientation-dependent changes in spatial frequency and intensity allow the determination of the effective scattering coefficient μs' and the absorption coefficient μa when measuring a spherical optical phantom at three different measurement positions and at nine wavelengths with an average error of 5% and 12%, respectively. Model-based calibration allows the characterization of the imaging properties of the entire SFDI system without prior knowledge, enabling the future development of a digital twin for synthetic data generation or more robust evaluation methods.

Spotlight on Luminescence Thermometry: Basics, Challenges, and Cutting-Edge Applications

Luminescence (nano)thermometry is a remote sensing technique that relies on the temperature dependency of the luminescence features (e.g., bandshape, peak energy or intensity, and excited state lifetimes and risetimes) of a phosphor to measure temperature. This technique provides precise thermal readouts with superior spatial resolution in short acquisition times. Although luminescence thermometry is just starting to become a more mature subject, it exhibits enormous potential in several areas, e.g., optoelectronics, photonics, micro- and nanofluidics, and nanomedicine. This work reviews the latest trends in the field, including the establishment of a comprehensive theoretical background and standardized practices. The reliability, repeatability, and reproducibility of the technique are also discussed, along with the use of multiparametric analysis and artificial-intelligence algorithms to enhance thermal readouts. In addition, examples are provided to underscore the challenges that luminescence thermometry faces, alongside the need for a continuous search and design of new materials, experimental techniques, and analysis procedures to improve the competitiveness, accessibility, and popularity of the technology.

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.

Comparison of non-pulsating reflective PPG signals in skin phantom, wearable device prototype, and Monte Carlo simulations

We obtain and compare the non-pulsating part of reflective Photoplethysmogram (PPG) measurements in a porcine skin phantom and a wearable device prototype with Monte Carlo simulations and analyse the received signal. In particular, we investigate typical PPG wavelengths at 520, 637 and 940 nm and source-detector distances between 1.5 and 8.0 mm. We detail the phantom's optical parameters, the wearable device design, and the simulation setup. Monte Carlo simulations were using layer-based and voxel-based structures. Pattern of the detected photon weights showed comparable trends. PPG signal, differential pathlength factor (DPF), mean maximum penetration depth, and signal level showed dependencies on the source-detector distance d for all wavelengths. We demonstrate the signal dependence of emitter and detection angles, which is of interest for the development of wearables.

Radiative transfer equation-based color prediction and color adjustment strategies

This paper discusses different strategies for color prediction and matching. Although many groups use the two-flux model (i.e., the Kubelka-Munk theory or its extensions), we introduce a solution of the P _N approximation for the radiative transfer equation (RTE) with modified Mark boundaries for the prediction of the transmittance and reflectance of turbid slabs with or without a glass layer on top. To demonstrate the capabilities of our solution, we have presented a way to prepare samples with different scatterers and absorbers where we can control and predict the optical properties and discussed three color-matching strategies: the approximation of the scattering and absorption coefficient, the adjustment of the reflectance, and the direct matching of the color valueL ^∗ a ^∗ b ^∗.

Method for Measuring Absolute Optical Properties of Turbid Samples in a Standard Cuvette

Many applications seek to measure a sample's absorption coefficient spectrum to retrieve the chemical makeup. Many real-world samples are optically turbid, causing scattering confounds which many commercial spectrometers cannot address. Using diffusion theory and considering absorption and reduced scattering coefficients on the order of 0.01 mm-1 and 1 mm-1, respectively, we develop a method which utilizes frequency-domain to measure absolute optical properties of turbid samples in a standard cuvette (45 mm × 10 mm × 10 mm). Inspired by the self-calibrating method, which removes instrumental confounds, the method uses measurements of the diffuse complex transmittance at two sets of two different source-detector distances. We find: this works best for highly scattering samples (reduced scattering coefficient above 1 mm-1); higher relative error in the absorption coefficient compared to the reduced scattering coefficient; accuracy is tied to knowledge of the sample's index of refraction. Noise simulations with 0.1 % amplitude and 0.1° = 1.7 mrad phase uncertainty find errors in absorption and reduced scattering coefficients of 4 % and 1 %, respectively. We expect that higher error in the absorption coefficient can be alleviated with highly scattering samples and that boundary condition confounds may be suppressed by designing a cuvette with high index of refraction. Further work will investigate implementation and reproducibility.

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.

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.

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.

Chlorophyll- and anthocyanin-rich cell organelles affect light scattering in apple skin

Apple skin contains several groups of strongly absorbing cell organelles with pigments that change dynamically in type and concentration during fruit maturation. Chlorophylls and carotenoids, both primarily involved in photosynthesis, are found in the grana of chloroplasts, while anthocyanin vacuolar inclusions (AVIs) accumulate for light protection in red-skinned cultivars. A Mie model describing light scattering by absorbing spherical particles in a non-absorbing medium allowed to theoretically investigate the explicit influence of grana and AVIs on the effective scattering coefficient [Formula: see text] and the absorption coefficient [Formula: see text]. The reconstruction of the complex refractive indices of the organelles predicted anomalous dispersion, i.e., a local increase in the real part of the refractive index in the spectral regions with high chlorophyll and anthocyanin absorption, in agreement with the Kramers-Kronig relations. As a result, peaks in [Formula: see text] were predicted to be shifted to longer wavelengths compared to the corresponding [Formula: see text] bands. This selective scattering effect was confirmed experimentally with integrating sphere measurements for red- or green-skinned apple samples of the cultivars 'Elstar', 'Gala' or 'Jonagold'. Comparison between simulations and measurements indicated that the Soret bands of chlorophyll a and chlorophyll b are at 435 nm and 469 nm, respectively, and overlap with the absorption of carotenoids, whose red-most edge is at 488 nm. For anthocyanin absorption, a pronounced blue shift from 550 to 520 nm was observed, indicating structural or chemical changes of AVIs.

Simultaneous Determination of Droplet Size, pH Value and Concentration to Evaluate the Aging Behavior of Metalworking Fluids

Metalworking fluids (MWFs) are widely used to cool and lubricate metal workpieces during processing to reduce heat and friction. Extending a MWF’s service life is of importance from both economical and ecological points of view. Knowledge about the effects of processing conditions on the aging behavior and reliable analytical procedures are required to properly characterize the aging phenomena. While so far no quantitative estimations of ageing effects on MWFs have been described in the literature other than univariate ones based on single parameter measurements, in the present study we present a simple spectroscopy-based set-up for the simultaneous monitoring of three quality parameters of MWF and a mathematical model relating them to the most influential process factors relevant during use. For this purpose, the effects of MWF concentration, pH and nitrite concentration on the droplet size during aging were investigated by means of a response surface modelling approach. Systematically varied model MWF fluids were characterized using simultaneous measurements of absorption coefficients µ_a and effective scattering coefficients µ’_s. Droplet size was determined via dynamic light scattering (DLS) measurements. Droplet size showed non-linear dependence on MWF concentration and pH, but the nitrite concentration had no significant effect. pH and MWF concentration showed a strong synergistic effect, which indicates that MWF aging is a rather complex process. The observed effects were similar for the DLS and the µ’_s values, which shows the comparability of the methodologies. The correlations of the methods were R²_c = 0.928 and R²_P = 0.927, as calculated by a partial least squares regression (PLS-R) model. Furthermore, using µ_a, it was possible to generate a predictive PLS-R model for MWF concentration (R²_c = 0.890, R²_P = 0.924). Simultaneous determination of the pH based on the µ’_s is possible with good accuracy (R²_c = 0.803, R²_P = 0.732). With prior knowledge of the MWF concentration using the µ_a-PLS-R model, the predictive capability of the µ’_s-PLS-R model for pH was refined (10 wt%: R²_c = 0.998, R²_p = 0.997). This highlights the relevance of the combined measurement of µ_a and µ’_s. Recognizing the synergistic nature of the effects of MWF concentration and pH on the droplet size is an important prerequisite for extending the service life of an MWF in the metalworking industry. The presented method can be applied as an in-process analytical tool that allows one to compensate for ageing effects during use of the MWF by taking appropriate corrective measures, such as pH correction or adjustment of concentration.

Polydimethylsiloxane tissue-mimicking phantoms with tunable optical properties

SIGNIFICANCE

The polymer, polydimethylsiloxane (PDMS), has been increasingly used to make tissue simulating phantoms due to its excellent processability, durability, flexibility, and limited tunability of optical, mechanical, and thermal properties. We report on a robust technique to fabricate PDMS-based tissue-mimicking phantoms where the broad range of scattering and absorption properties are independently adjustable in the visible- to near-infrared wavelength range from 500 to 850 nm. We also report on an analysis method to concisely quantify the phantoms' broadband characteristics with four parameters.

AIM

We report on techniques to manufacture and characterize solid tissue-mimicking phantoms of PDMS polymers. Tunability of the absorption (μa  (  λ  )  ) and reduced scattering coefficient spectra (μs'(λ)) in the wavelength range of 500 to 850 nm is demonstrated by adjusting the concentrations of light absorbing carbon black powder (CBP) and light scattering titanium dioxide powder (TDP) added into the PDMS base material.

APPROACH

The μa  (  λ  )   and μs'(λ) of the phantoms were obtained through measurements with a broadband integrating sphere system and by applying an inverse adding doubling algorithm. Analyses of μa  (  λ  )   and μs'(λ) of the phantoms, by fitting them to linear and power law functions, respectively, demonstrate that independent control of μa  (  λ  )   and μs'(λ) is possible by systematically varying the concentrations of CBP and TDP.

RESULTS

Our technique quantifies the phantoms with four simple fitting parameters enabling a concise tabulation of their broadband optical properties as well as comparisons to the optical properties of biological tissues. We demonstrate that, to a limited extent, the scattering properties of our phantoms mimic those of human tissues of various types. A possible way to overcome this limitation is demonstrated with phantoms that incorporate polystyrene microbead scatterers.

CONCLUSIONS

Our manufacturing and analysis techniques may further promote the application of PDMS-based tissue-mimicking phantoms and may enable robust quality control and quality checks of the phantoms.

Compact setup to determine size and concentration of spherical particles in a turbid medium

We propose a compact setup to determine the size and concentration of spherical particles in a turbid medium. A pair of plane mirrors is used to multifold the undeviated laser beam, and measure it at a detector placed close to the sample, to determine the interaction coefficient. The size of particles is uniquely determined by comparison of the scattered light from the medium, measured at two separate detectors placed at two different angular positions, with that from Monte Carlo simulations. The methodology is verified using measurements with turbid samples comprising polystyrene spheres.

Random laser as a potential tool for the determination of the scattering coefficient

The determination of the optical properties of a turbid medium is a major topic in the field of optics. Generally, they comprise the parameters µ _a , µ _s , g and n. There is, however, a lack of techniques for the direct determination of the scattering coefficient µ _s . This study, therefore, proposes the random laser (RL) as a tool to directly measure µ _s - and not μ s ' . Evidence is found that it is possible to determine µ _s in the diffusive regime by means of the RL. Based on these findings, a local model of the RL is developed and presented in this study.

Ex Vivo Determination of Broadband Absorption and Effective Scattering Coefficients of Porcine Tissue

A novel approach for precise determination of the optical scattering and absorption properties of porcine tissue using an optimized integrating sphere setup was applied. Measurements on several sample types (skin, muscle, adipose tissue, bone, cartilage, brain) in the spectral range between 400 nm and 1400 nm were performed. Due to the heterogeneity of biological samples, measurements on different individual animals as well as on different sections for each sample type were carried out. For all samples, we used an index matching method to reduce surface roughness effects and to prevent dehydration. The derived absorption spectra were used to estimate the concentration of important tissue chromophores such as water, oxy- and deoxyhemoglobin, collagen and fat.

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.