Optical Properties Of Turbid Media Research Articles

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.

Estimation of optical properties of turbid media using spatially resolved diffuse reflectance combined with LSTM-attention network.

The accurate estimation of the optical properties of turbid media by using a spatially resolved (SR) technique remains a challenging task due to measurement errors in the acquired spatially resolved diffuse reflectance (SRDR) and challenges in inversion model implementation. In this study, what we believe to be a novel data-driven model based on a long short-term memory network and attention mechanism (LSTM-attention network) combined with SRDR is proposed for the accurate estimation of the optical properties of turbid media. The proposed LSTM-attention network divides the SRDR profile into multiple consecutive and partially overlaps sub-intervals by using the sliding window technique, and uses the divided sub-intervals as the input of the LSTM modules. It then introduces an attention mechanism to evaluate the output of each module automatically and form a score coefficient, finally obtaining an accurate estimation of the optical properties. The proposed LSTM-attention network is trained with Monte Carlo (MC) simulation data to overcome the difficulty in preparing training (reference) samples with known optical properties. Experimental results of the MC simulation data showed that the mean relative error (MRE) with 5.59% for the absorption coefficient [with the mean absolute error (MAE) of 0.04 cm-1, coefficient of determination (R2) of 0.9982, and root mean square error (RMSE) of 0.058 cm-1] and 1.18% for the reduced scattering coefficient (with an MAE of 0.208 cm-1, R2 of 0.9996, and RMSE of 0.237 cm-1), which were significantly better than those of the three comparative models. The SRDR profiles of 36 liquid phantoms, collected using a hyperspectral imaging system that covered a wavelength range of 530-900 nm, were used to test the performance of the proposed model further. The results showed that the LSTM-attention model achieved the best performance (with the MRE of 14.89%, MAE of 0.022 cm-1, R2 of 0.9603, and RMSE of 0.026 cm-1 for the absorption coefficient; and the MRE of 9.76%, MAE of 0.732 cm-1, R2 of 0.9701, and RMSE of 1.470 cm-1for the reduced scattering coefficient). Therefore, SRDR combined with the LSTM-attention model provides an effective method for improving the estimation accuracy of the optical properties of turbid media.

Two-photon polymerization for random rough surface preparation

A typical tool to characterize diffuse materials is the determination of the scattering and absorption coefficients. Most of these evaluation methods consider optically smooth surfaces between the investigated and the surrounding medium. However, realistic surfaces generally show a distinct roughness, which influences the reflected and transmitted light of the investigated material. Hence, it is necessary to understand the optical behavior of these rough surfaces. We present a method for the preparation of such optically rough surfaces using two-photon polymerization. The properties of these rough surfaces can be precisely adjusted within a range of a few hundred nanometers. Additionally, an easy-to-use preparation method is shown to compensate for reflections from the backside of the used substrate. Hence, these surfaces can be used for measuring the reflectance leading to a better understanding of the scattering behavior of rough surfaces and their influence on the determination of the optical properties of turbid media.

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.

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.

Optical Characterization of Homogeneous and Heterogeneous Intralipid-Based Samples

Different scattering processes take place when photons propagate inside turbid media. Many powerful experimental techniques exploiting these processes have been developed and applied over the years in a large variety of situations from fundamental and applied research to industrial applications. In the present paper, we intend to take advantage of Static Light Scattering (SLS), Dynamic Light Scattering (DLS), and Time-Resolved Transmittance (TRT) for investigating all the different scattering regimes by using scattering suspensions in a very large range of scatterer concentrations. The suspensions were prepared using Intralipid 20%, a material largely employed in studies of the optical properties of turbid media, with concentrations from 10−5% to 50%. By the analysis of the angular and temporal dependence of the scattered light, a more reliable description of the scattering process occurring in these samples can be obtained. TRT measurements allowed us to obtain information on the reduced scattering coefficient, an important parameter largely used in the description of the optical properties of turbid media. TRT was also employed for the detection of inclusions embedded in Intralipid suspensions, by using a properly designed data analysis. The present study allowed us to better elucidate the dependence of scattering properties of Intralipid suspensions in a very large concentration range and the occurrence of the different scattering processes involved in the propagation of light in turbid media for the first time to our knowledge. In so doing, the complementary contribution of SLS, DLS, and TRT in the characterization of turbid media from an optical and structural point of view is strongly evidenced.

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%.

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.

Combining light polarization and speckle measurements with multivariate analysis to predict bulk optical properties of turbid media.

This study aims to investigate the combination of speckle pattern analysis, polarization parameters, and chemometric tools to predict the optical absorption and scattering properties of materials. For this purpose, an optical setup based on light polarization and speckle measurements was developed, and turbid samples were measured at 405 and 660 nm. First, a backscattered polarized speckle acquisition was performed on a set of 41 samples with various scattering (${\mu}_s$μs) and absorbing (${{\mu}_a}$μa) coefficients. Then, several parameters were computed from the polarized speckle images, and prediction models were built using stepwise multiple linear regression. For scattering media, ${{\mu}_s}$μs was predicted with ${R^{2} = 0.9}$R2=0.9 using two parameters. In the case of scattering and absorbing media, prediction results using two parameters were ${R^{2} = 0.62}$R2=0.62 for ${{\mu}_s}$μs and ${R^{2} = 0.8}$R2=0.8 for ${{\mu}_a}$μa. The overall results obtained in this research showed that the combination of speckle pattern analysis, polarization parameters, and chemometric tools to predict the optical bulk properties of materials show interesting promise.

Imaging the optical properties of turbid media with single-pixel detection based on the Kubelka-Munk model.

We present a diffuse optical imaging system with structured illumination and integrated detection based on the Kubelka-Munk light propagation model for the spatial characterization of scattering and absorption properties of turbid media. The proposed system is based on the application of single-pixel imaging techniques. Our strategy allows us to retrieve images of the absorption and scattering properties of a turbid media slab by using integrating spheres with photodiodes as bucket detectors. We validate our idea by imaging the absorption and scattering coefficients of a spatially heterogeneous phantom.

Application of single integrating sphere system to obtain the optical properties of turbid media

In this study, a simple method to determine the reflectance and transmittance of turbid media is proposed. The method is based on a single integrating sphere system. The integrating sphere theory is used to calculate the reflectance and transmittance under diffuse and directional illumination, and an experimental setup is proposed to measure these quantities. This method was used to determine the reflectance and transmittance of poly(vinyl alcohol) (PVA) hydrogels. Monte Carlo calculations were also implemented to validate our results. The comparison shows that the optical properties obtained through this method propagate low values of uncertainty, and a setup simpler than that of the double integrating sphere system can be realized. However, our system is limited to the diffuse–diffuse transmittance. The results suggest that the single sphere system and Monte Carlo method can be a strong combination to calculate the inherent optical properties of PVA samples.

Simultaneous recovery of a full set of optical properties in turbid media using incomplete P5 approximation to CW radiance.

Traditional methods for determining the optical properties of turbid media are implemented in diffusive regimes, where the scattering coefficient μs and anisotropy factor g are inseparable due to the similarity relation for anisotropy scattering. Determining μs and g in addition to the absorption coefficient μa normally requires measurements using thin samples or media of low scattering, which are inappropriate for in vivo applications. In this work, we propose an analytical method to simultaneously recover μa, μs, and g based on the incomplete P5 approximation (P5in) to the continuous wave (CW) radiative transport equation. The proposed method was verified using both simulated and experimental data with the relative errors less than 6.6%, 11.6%, and 8.2% for μa ranging 0.0071-0.0168 mm-1, μs ranging 2.35-8.47 mm-1, and g ranging 0.61-0.81, respectively. Since the P5in-based radiance method can be easily implemented with several measurements, it is expected to be used for recovering a full set of the optical properties in vivo.

Characterization of the Optical Properties of Turbid Media by Supervised Learning of Scattering Patterns

Fabricated tissue phantoms are instrumental in optical in-vitro investigations concerning cancer diagnosis, therapeutic applications, and drug efficacy tests. We present a simple non-invasive computational technique that, when coupled with experiments, has the potential for characterization of a wide range of biological tissues. The fundamental idea of our approach is to find a supervised learner that links the scattering pattern of a turbid sample to its thickness and scattering parameters. Once found, this supervised learner is employed in an inverse optimization problem for estimating the scattering parameters of a sample given its thickness and scattering pattern. Multi-response Gaussian processes are used for the supervised learning task and a simple setup is introduced to obtain the scattering pattern of a tissue sample. To increase the predictive power of the supervised learner, the scattering patterns are filtered, enriched by a regressor, and finally characterized with two parameters, namely, transmitted power and scaled Gaussian width. We computationally illustrate that our approach achieves errors of roughly 5% in predicting the scattering properties of many biological tissues. Our method has the potential to facilitate the characterization of tissues and fabrication of phantoms used for diagnostic and therapeutic purposes over a wide range of optical spectrum.

Vertical-cavity surface-emitting laser sources for gigahertz-bandwidth, multiwavelength frequency-domain photon migration.

.Frequency-domain photon migration (FDPM) uses modulated laser light to measure the bulk optical properties of turbid media and is increasingly applied for noninvasive functional medical imaging in the near-infrared. Although semiconductor edge-emitting laser diodes have been traditionally used as miniature light sources for this application, we show that vertical-cavity surface-emitting lasers (VCSELs) exhibit output power and modulation performance characteristics suitable for FDPM measurements of tissue optical properties at modulation frequencies exceeding 1 GHz. We also show that an array of multiple VCSEL devices can be coherently modulated at frequencies suitable for FDPM and can improve optical power. In addition, their small size and simple packaging make them an attractive choice as components in wearable sensors and clinical FDPM-based optical spectroscopy systems. We demonstrate the benefits of VCSEL technology by fabricating and testing a unique, compact VCSEL-based optical probe with an integrated avalanche photodiode. We demonstrate sensitivity of the VCSEL-based probe to subcutaneous tissue hemodynamics that was induced during an arterial cuff occlusion of the upper arm in a human subject.

Determination of optical properties of turbid medium from relative interstitial CW radiance measurements using the incomplete P3 approximation.

Interstitial determination of the tissue optical properties is important in biomedicine, especially for interstitial laser therapies. Continuous wave (CW) radiance techniques which examine light from multiple directions have been proposed as minimally invasive methods for determining the optical properties under an interstitial probe arrangement. However, both the fitting algorithm based on the P3 approximation and the analytical method based on the diffusion approximation (DA), which are currently used recovery algorithms, cannot extract the optical properties of tissue with low transport albedos accurately from radiance measurements. In this paper, we proposed an incomplete P3 approximation for the radiance, the P3in for short, which is the asymptotic part of the solution for the P3 approximation. The relative differences between the P3in and the P3 were within 0.48% over a wide range of clinically relevant optical properties for measurements at source detector separations (SDS) from 5 mm to 10 mm and angles from 0° to 160°. Based on the P3in, we developed an analytical method for extracting the optical properties directly using simple expressions constructed from the radiance measurements at only two SDSs and four angles. The developed recovery algorithm was verified by simulated and experimental radiance data. The results show that both the absorption and reduced scattering coefficients were recovered accurately with relative errors within 5.28% and 3.86%, respectively, from the simulated data and with relative errors within 10.82% and 10.67%, respectively, from the experimental data over a wide range of albedos from 0.5 to 0.99. Since the developed P3in-based radiance technique can obtain the optical properties rapidly from the measurements at only two SDSs and four angles, it is expected to be used for in vivo and in situ determination of the optical properties in online treatment planning during laser therapies.

Single snapshot multiple frequency modulated imaging of subsurface optical properties of turbid media with structured light

We report a novel demodulation method that enables single snapshot wide field imaging of optical properties of turbid media in the Spatial Frequency Domain (SFD). This Single Snapshot Multiple frequency Demodulation (SSMD) method makes use of the orthogonality of harmonic functions to extract the modulation transfer function (MTF) at multiple modulation frequencies simultaneously from a single structured-illuminated image at once. The orientation, frequency, and amplitude of each modulation can be set arbitrarily subject to the limitation of the implementation device. We first validate and compare SSMD to the existing demodulation methods by numerical simulations. The performance of SSMD is then demonstrated with experiments on both tissue mimicking phantoms and in vivo for recovering optical properties by comparing to the standard three-phase demodulation approach. The results show that SSMD increases significantly the data acquisition speed and reduces motion artefacts. SSMD exhibits excellent noise suppression in imaging as well at the rate proportional to the square root of the number of pixels contained in its kernel. SSMD is ideal in the implementation of a real-time spatial frequency domain imaging platform and will open up SFDI for vast applications in imaging and monitoring dynamic turbid medium and processes.

Time-resolved subtraction method for measuring optical properties of turbid media.

Near-infrared spectroscopy is a noninvasive optical method used primarily to monitor tissue oxygenation due to the absorption properties of hemoglobin. Accurate estimation of hemoglobin concentrations and other light absorbers requires techniques that can separate the effect of absorption from the much greater effect of light scattering. One of the most advanced methods is time-resolved near-infrared spectroscopy (TR-NIRS), which measures the absorption and scattering coefficients of a turbid medium by modeling the recorded distribution time of flight of photons. A challenge with TR-NIRS is that it requires accurate characterization of the dispersion caused by the system. In this study, we present a method for circumventing this problem by applying statistical moment analysis to two time-of-flight distributions measured at separated source-detector distances. Simulations based on analytical models and Monte Carlo code, and tissue-mimicking phantoms, were used to demonstrate its accuracy for source-detector distances typically used in neuroimaging applications. The simplicity of the approach is well suited to real-time applications requiring accurate quantification of the optical properties of a turbid medium.

Implementation of the swept source optical coherence tomography (SSOCT) system with a statistical method to analyze optical properties of turbid media

We present a spectroscopic OCT (sOCT) system to extract spectroscopic properties of turbid liquid media using principle component analysis (PCA) and swept source optical coherence tomography (SSOCT). Extracted results are well comparable with the standard photo spectrometer technique. This system has potential for real time measurement of blood oxygen saturation and monitoring of relative concentration for other metabolic compounds inside human body. Liquid media was prepared with ethanol (10% v/v), citric acid (5% v/v) and water. A linear mathematical model for depth resolved diffuse reflectance was build from sOCT signal. Then PCA was applied on resultant model to extract absorption coefficients of different constituents of the media. Extracted information is well comparable with the standard photo spectrometer technique. This system has potential to monitor relative concentration change of metabolic compounds inside any system.

Robust metamodel-based inverse estimation of bulk optical properties of turbid media from spatially resolved diffuse reflectance measurements.

Estimation of the bulk optical properties of turbid samples from spatially resolved reflectance measurements remains challenging, as the relation between the bulk optical properties and the acquired spatially resolved reflectance profiles is influenced by wavelength-dependent properties of the measurement system. The resulting measurement noise is apparent in the estimation of the bulk optical properties. In this study, a constrained inverse metamodeling approach is proposed to overcome these problems. First, a metamodel has been trained on a set of intralipid phantoms covering a wide range of optical properties to link the acquired spatially resolved reflectance profiles to the respective combinations of bulk optical properties (absorption coefficient and reduced scattering coefficient). In this metamodel, the wavelength (500 - 1700 nm) is considered as a third input parameter for the model to account for the wavelength dependent effects introduced by the measurement system. Secondly, a smoothness constraint on the reduced scattering coefficient spectra was implemented in the iterative inverse estimation procedure to robustify it against measurement noise and increase the reliability of the obtained bulk absorption and reduced scattering coefficient spectra. As the estimated values in some regions may be more reliable than others, the difference between simulated and measured values as a function of the evaluated absorption and scattering coefficients was combined in a 2D cost function. This cost function was used as a weight in the fitting procedure to find the parameters of the µ(s)' function giving the lowest cost over all the wavelengths together. In accordance with previous research, an exponential function was considered to represent the µ(s)' spectra of intralipid phantoms. The fitting procedure also provides an absorption coefficient spectrum which is in accordance with the measurements and the estimated parameters of the exponential function. This robust inverse estimation algorithm was validated on an independent set of intralipid® phantoms and its performance was also compared to that of a classical single-wavelength inverse estimation algorithm. While its performance in estimating µ(a) was comparable (R2 of 0.844 vs. 0.862), it resulted in a large improvement in the estimation of µ(s)' (R2 of 0.987 vs. 0.681). The change in performance is more apparent in the improvement of RMSE of µ(s)', which decreases from 10.36 cm(-1) to 2.10 cm(-1). The SRS profiles change more sensitively as a function of µ(a). As a result, there is a large range of µ(s)' and a small range of µa resulting in a good fit between measurement and simulation. The robust inverse estimator incorporates information over the different wavelengths, to increase the accuracy of µ(s)'estimations and robustify the estimation process.

Estimation of bulk optical properties of turbid media from hyperspectral scatter imaging measurements: metamodeling approach.

In many research areas and application domains, the bulk optical properties of biological materials are of great interest. Unfortunately, these properties cannot be obtained easily for complex turbid media. In this study, a metamodeling approach has been proposed and applied for the fast and accurate estimation of the bulk optical properties from contactless and non-destructive hyperspectral scatter imaging (HSI) measurements. A set of liquid optical phantoms, based on intralipid, methylene blue and water, were prepared and the Vis/NIR bulk optical properties were characterized with a double integrating sphere and unscattered transmittance setup. Accordingly, the phantoms were measured with the HSI technique and metamodels were constructed, relating the Vis/NIR reflectance images to the reference bulk optical properties of the samples. The independent inverse validation showed good prediction performance for the absorption coefficient and the reduced scattering coefficient, with R(2)(p) values of 0.980 and 0.998, and RMSE(P) values of 0.032 cm(-1) and 0.197 cm(-1) respectively. The results clearly support the potential of this approach for fast and accurate estimation of the bulk optical properties of turbid media from contactless HSI measurements.