Structurally anisotropic materials are ubiquitous in several application fields, yet their accurate optical characterization remains challenging due to the lack of general models linking their scattering coefficients to the macroscopic transport observables and the need to combine multiple measurements to retrieve their direction-dependent values. Here, we present an improved method for the experimental determination of light-transport tensor coefficients from the diffusive rates measured along all three directions, based on transient transmittance measurements and a generalized Monte Carlo model. We apply our method to the characterization of light-transport properties in two common anisotropic materials—polytetrafluoroethylene tape and paper—highlighting the magnitude of systematic deviations that are typically incurred when neglecting anisotropy.
In this study, we investigate the use of microlasers as light sources for digital holographic microscopy embedded in the sample. Microlasers are 50-μm sized dye-doped self-assembled cholesteric liquid-crystal microdroplets that isotropically emit single-mode laser light. By employing an epi-illumination configuration of a standard optical microscope, we excited a single microlaser beneath the sample plane and subsequently acquired in-line holograms of various samples placed between the microlaser and microscope objective. Embedding the light source enabled us to uniquely acquire in-line digital holograms in transmission even though the sample is observed in an epi-illumination configuration and could in principle be infinitely thick on one side.
In many biological tissues such as muscles, dental enamel and mucosa that exhibit macroscopic and/or microscopic spatially anisotropic structures the nature of light scattering becomes anisotropic. This well-known property of tissues is usually neglected, which is rooted in the fact that the available open-source numerical solutions to the radiative transfer equation based on the stochastic Monte Carlo (MC) method do not allow simulations with anisotropic optical properties. In this contribution, we present an extension to our massively parallel PyXOpto (https://github.com/xopto/pyxopto) simulation engine that enables highly efficient and user-friendly MC simulations for layered or voxelated sample geometries with anisotropic scattering properties, both in the steady state and time-resolved domain.
Turbid phantoms play a crucial role in evaluating optical systems and estimating optical properties. Liquid phantoms offer precise tuning of optical properties, but accurately determining their scattering properties is challenging. By using aqueous suspensions of standardized polystyrene microspheres, their optical properties can be theoretically derived using Mie theory. The parameters involved in calculating the scattering coefficient and phase function of microspheres in a liquid medium include the refractive index, density, size probability distribution and solid content of the microspheres and refractive index of the medium. The accuracy of these parameters directly affects the accuracy of calculated optical properties. A lack of clear protocols for phantom preparation and conflicting data in the literature may lead to easily avoidable inaccuracies. We introduce an open-source software that offers a detailed mixing protocol and subsequent optical property calculations for turbid phantoms. The software allows users to input details of the microsphere suspension, target optical property values, and choose between individual or sequentially diluted phantom mixing. It also accommodates the introduction of non-scattering molecular dyes to achieve specific absorption coefficients. The software facilitates recalculations of optical properties based on the actual quantities used during phantom preparation, offering flexibility and increased accuracy. Error estimates are provided using Monte Carlo sampling and error propagation. The open-source software is established as a comprehensive tool for preparing liquid turbid phantoms using microsphere suspensions, accessible to non-experts with basic familiarity of pipetting and use of analytical scales.
Structurally anisotropic materials are ubiquitous in several application fields, yet their accurate optical characterization remains challenging due our incomplete understanding of how anisotropic light transport properties arise from the microscopic scattering coefficients. In fact, even when the dynamics of light transport is directly measured, coarse simplifications are often introduced due to a lack of established theoretical models or numerical methods. Here, we apply a general Monte Carlo implementation capable of handling direction-dependent scattering to the analysis of light transport in a sample of polytetrafluoroethylene (PTFE) tape. Using only a set of transient transmittance intensity profiles, the analysis retrieves the tensor components of the diffusive rates and the scattering coefficients along all three directions, in excellent agreement with Monte Carlo simulations.
Lensless on-chip microscopy comprises a simple and compact setup in which the sample is placed close to the imaging sensor and illuminated by a coherent light source. The acquired in-line hologram carries information about the amplitude and phase image of the sample, which can be numerically reconstructed. Contrary to conventional microscopy, the reconstructed images can be numerically refocused at desired focus planes effectively providing three-dimensional information. For reliable object reconstruction, a proper focus plane must be selected, which can be done automatically using an autofocusing algorithm. The autofocusing algorithms are commonly evaluated on synthetic or experimentally acquired in-line holograms. First are usually simulated with the same numerical propagation method as used for reconstruction and are not able to simulate holograms of truly three-dimensional objects, while experimentally acquired holograms can be affected by measurement noise and model mismatch artefacts. In this paper, we propose an objective evaluation of autofocusing algorithms on in-line holograms simulated by Mie theory and T-matrix method which can simulate holograms of truly three-dimensional spherical objects distributed in various spatial positions. We evaluate and compare different autofocusing algorithms in terms of the accuracy of the estimated focus plane and computational efficiency. Finally, we present a proof-of-concept real-time implementation of the autofocusing algorithm based on the open-source PyOpenCL framework. We found that the implemented autofocusing algorithms provided the best average accuracy of 1.75 μm and required 330 μs per evaluation cycle resulting in around 20 frames per second for autofocusing a 1024×1024 hologram.
KEYWORDS: Monte Carlo methods, Computer simulations, Reflectivity, Sensors, Tissues, Transmittance, Signal to noise ratio, Optical properties, Refractive index, Multilayers
Significance: Current open-source Monte Carlo (MC) method implementations for light propagation modeling are many times tedious to build and require third-party licensed software that can often discourage prospective researchers in the biomedical optics community from fully utilizing the light propagation tools. Furthermore, the same drawback also limits rigorous cross-validation of physical quantities estimated by various MC codes.
Aim: Proposal of an open-source tool for light propagation modeling and an easily accessible dataset to encourage fruitful communications amongst researchers and pave the way to a more consistent comparison between the available implementations of the MC method.
Approach: The PyXOpto implementation of the MC method for multilayered and voxelated tissues based on the Python programming language and PyOpenCL extension enables massively parallel computation on numerous OpenCL-enabled devices. The proposed implementation is used to compute a large dataset of reflectance, transmittance, energy deposition, and sampling volume for various source, detector, and tissue configurations.
Results: The proposed PyXOpto agrees well with the original MC implementation. However, further validation reveals a noticeable bias introduced by the random number generator used in the original MC implementation.
Conclusions: Establishing a common dataset is highly important for the validation of existing and development of MC codes for light propagation in turbid media.
KEYWORDS: Monte Carlo methods, Data modeling, Reflectivity, Optical properties, Computer simulations, Spatial frequencies, Signal to noise ratio, Sensors, Scattering, Imaging systems
We propose neural network-based regression model for efficient Monte Carlo simulations of subdiffusive reflectance for spatial frequency domain imaging with low NA and validate the methodology with inverse models for estimation of optical properties.
In this work, we use a statistical skin model to compare the measured distribution of optical path lengths to time-resolved Monte Carlo simulated reflectance and validate the simulations by the use of optical phantoms.
We present a multi-layered and voxel-based Monte Carlo methods with auxiliary utilities implemented in Python for user-friendly, open-source and multi-purpose modeling of light propagation in turbid media based on PyOpenCL computational platform.
We present a simple approach to determine the refractive index of polystyrene microspheres which are frequently utilized as scatterers in turbid phantoms. The approach is based on Mie theory and transmittance measurements of polystyrene microspheres suspended in media with different refractive indices allowing simultaneous optimization of the diameter and refractive index of the polystyrene microspheres. The refractive index of the medium is changed through the addition of sucrose. Based on our preliminary results, the estimated refractive index of polystyrene microspheres deviates from the literature values by 0.2% and the estimated diameter by 20 nm from the nominal value provided by the manufacturer.
Reflectance spectroscopy shows itself as a useful tool to characterize turbid media, such as biological tissues. The light backscattered from the medium is usually collected by imaging systems or optical fiber probes. In this work we used an optical fiber probe, with a linear arrangement of the source and detection fibers that allows spatially resolved reflectance (SRR) measurements. Through the use of inverse model, the collected SRR can be exploited to estimate the optical properties of the turbid medium. The estimation process involves matching of the measured and simulated SRR that accounts for all the details of the measurement setting. At small source-detector separations and/or non-negligible absorbance, the reflectance becomes highly dependent on the scattering phase function of the medium, which can be efficiently described by the higher order Legendre moments and related scattering phase function quantifiers (PFQ). In our previous studies, we utilized the Gegenbauer Kernel (GK) scattering phase function to describe the light propagation in turbid samples. However, the domain of GK-based PFQs is quite small and fails to fully encompass the scattering phase functions of microspherical suspensions, typically used for calibration and validation of SRR measurement settings. This limitation could be overcome by utilizing scattering phase function models with a large PFQ domain that may also lead to more accurate and robust inverse model predictions. To verify this hypothesis, we evaluate various scattering phase function models that maximize the PFQ domain and experimentally validate the inverse models by SRR collected from optical phantoms and various turbid samples.
KEYWORDS: Monte Carlo methods, Reflectivity, Computer simulations, Optical properties, Scattering, Signal to noise ratio, Photon transport, Error analysis, Optical fibers, Data modeling
Monte Carlo (MC) method is regarded as the gold standard for modeling the light transport in biological tissues. Due to the stochastic nature of the MC method, many photon packets need to be processed to obtain an adequate quality of the simulated reflectance. The number of required photon packets further increases if the numerical aperture of the detection scheme is low. Consequently, extensively long simulation times may be required to obtain adequate quality of the reflectance for such detection schemes. In this paper we propose an efficient regression model that maps reflectance simulated at the maximum acceptance angle of 90◦ to the reflectance corresponding to a much smaller realistic acceptance angle. The results of validation on spatially resolved reflectance and inverse models for estimation of optical properties show that the regression models are accurate and do not introduce additional errors into the spatially resolved reflectance or the optical properties estimated by appropriate inverse models from the regressed reflectance.
In this paper, we propose a novel calibration procedure based on modeling and measurement of the reflectance distance profiles from a metallic mirror. We observe a remarkable agreement of our reflectance distance profile model with the measurements yielding repeatable calibration factors within 2% when tested on silver and aluminum mirrors. Comparison to widely acceptable calibration using polystyrene microspheres suspensions yields errors of below 10%.
Experimental setup geometry in Monte Carlo (MC) simulations is often simplified to shorten computation times. We investigate the effect of these simplifications on the accuracy of the spatial frequency domain (SFD) reflectance. We also introduce a new detection scheme in the MC method that eliminates the often overlooked errors arising from the Hankel transform of the spatially discretized reflectance profiles to SFD reflectance. Finally, we propose and evaluate an artificial neural network-based framework capable of estimating high-definition maps of optical properties in real-time.
To overcome the drawbacks of the commonly used lookup table inverse models, we propose a novel custom OpenCL™- accelerated artificial neural network inverse model for spatial frequency domain imaging (https://bitbucket.org/xopto /rftroop). Utilizing a mid-range graphics processing unit, the proposed inverse model can estimate high-definition (1920 × 1080) maps of the absorption and reduced scattering coefficients and two scattering phase function related quantifiers at a rate of more than 50 frames per second. We show that the artificial neural network inverse model can be seamlessly extended to estimate multiple optical properties independently, thus providing a versatile framework that allows introduction of new quantifiers.
Biomedical optical systems and models can be easily validated by the use of tissue-simulating phantoms. They can consist of water-based turbid media which often include inks (India ink and molecular dyes) as absorbers. Optical stability of commonly exploited inks under the influence of light, pH changes and the addition of TiO2 and surfactant, was studied. We found that the exposure to ultraviolet and visible light can crucially affect the absorption properties of molecular dyes. On average, absorption peaks decreased by 47.3% in 150 exposure hours. Furthermore, dilution can affect ink’s pH and by that, its decay rate under light exposure. When TiO2 was added to the phantoms, all molecular dyes decayed rapidly. Photocatalytic nature of TiO2 can be partially avoided by selecting TiO2 with surface and crystal structure modification. Surfactant, normally present in the phantoms with polystyrene spheres, can cause absorption peak shifts up to 20 nm and amplitude changes of 29.6%. Therefore, it is crucial to test the optical stability of inks in the presented manner before their exploitation in water-based phantoms.
Stochastic Monte Carlo method (MC) is often used to model light propagation in biological tissues. Since many photon packets need to be process to attain good quality of the simulated data, the experimental geometry in MC simulations is usually substantially simplified to shorten the computation times. However, such simplifications have been shown to introduce large simulation errors when using optical fiber probes. In our previous study, we have shown that the frequently used laterally uniform probe-sample interface simplification can introduce significant errors into the MC simulations of spatially resolved reflectance (SRR) potentially exceeding 200 %. Unfortunately, using full details of the probe tip in the MC simulations breaks down the radial symmetry of the detection scheme. Consequently, the simulation time required to obtain a good quality SRR increases by about two orders of magnitude. In this study, we introduce a framework for efficient and accurate MC simulations of SRR acquired by optical fiber probes that accounts for all the details of the probe tip including reflectance from the stainless steel and the refractive indices of the epoxy fill and optical fibers. For this purpose, we introduce an efficient regression model that maps SRR obtained through fast MC simulations based on simplified geometry to the SRR simulated by full details of the probe-sample interface. We show that a small number of SRR samples is sufficient to determine the parameters of the regression model. Finally, we use the regression model to simulate SRR for a stainless steel optical probe with six linearly placed fibers and build inverse models for estimation of absorption and reduced scattering coefficients and subdiffusive scattering phase function related quantifiers.
A measurement system was developed to acquire and analyze subdiffusive spatially resolved reflectance using an optical fiber probe with short source-detector separations. Since subdiffusive reflectance significantly depends on the scattering phase function, the analysis of the acquired reflectance is based on a novel inverse Monte Carlo model that allows estimation of phase function related parameters in addition to the absorption and reduced scattering coefficients. In conjunction with our measurement system, the model allowed real-time estimation of optical properties, which we demonstrate for a case of dynamically induced changes in human skin by applying pressure with an optical fiber probe.
Timely estimation of optical properties from spatially resolved reflectance is a challenging task since the inverse light propagation model needs to be evaluated in real time. In this paper, we propose and extensively evaluate artificial neural network based regression model for estimation of optical and structural sample properties from spatially resolved reflectance acquired by optical fiber probes. We show that the proposed regression model can be prepared from datasets of Monte Carlo simulated spatially resolved reflectance and evaluated significantly faster than the frequently used dense lookup table inverse model. We observed computation time improvements exceeding 4 orders of magnitude. Moreover, the regression model can be easily extended to estimate more free parameters without reducing the estimation accuracy. Finally, we utilized the proposed regression model to estimate optical properties of human skin subjected to dynamically changing contact pressure applied by an optical fiber probe.
We significantly improve the estimation of the absorption and reduced scattering coefficients, and second-order similarity parameter γ from spatially resolved reflectance by extending the inverse model with the third-order similarity parameter δ.
For a given experimental setting, the measured spatially resolved reflectance rapidly drops with decreasing numerical aperture of the detection scheme. Consequently, for detection schemes with small numerical apertures, the computational time of MC simulations required to obtain adequate signal-to-noise ratio of the spatially resolved reflectance can become very long. We mitigate the issue by virtually increasing the numerical aperture of the detection scheme in MC simulations and devise a criterion for robust estimation of its maximum value. By using the proposed methodology, we show that the acceptance angle of a selected imaging system can be virtually increased from 3 to 11 while preserving a low relative error of the simulated spatially resolved reflectance over a wide range of tissue-like optical properties. As a result, a more than eightfold improvement in the computation time is attained.
We propose and objectively evaluate an inverse Monte Carlo model for estimation of absorption and reduced scattering coefficients and similarity parameter γ from spatially resolved reflectance (SRR) profiles in the subdiffusive regime. The similarity parameter γ carries additional information on the phase function that governs the angular properties of scattering in turbid media. The SRR profiles at five source-detector separations were acquired with an optical fiber probe. The inverse Monte Carlo model was based on a cost function that enabled robust estimation of optical properties from a few SRR measurements without a priori knowledge about spectral dependencies of the optical properties. Validation of the inverse Monte Carlo model was performed on synthetic datasets and measured SRR profiles of turbid phantoms comprising molecular dye and polystyrene microspheres. We observed that the additional similarity parameter γ substantially reduced the reflectance variability arising from the phase function properties and significantly improved the accuracy of the inverse Monte Carlo model. However, the observed improvement of the extended inverse Monte Carlo model was limited to reduced scattering coefficients exceeding ∼15 cm−1, where the relative root-mean-square errors of the estimated optical properties were well within 10%.
In this paper, the commonly used inverse Monte Carlo model based on absorption and reduced scattering coefficients is extended by a well-known similarity parameter γ (gamma), which carries additional information on the phase function. Sub-diffuse reflectance measurements at five source-detector separations were used to extract the absorption and reduced scattering coefficients and phase function information encapsulated in γ. The performance of the extended inverse Monte Carlo model was evaluated by simulated and experimental reflectance spectra of turbid phantoms. A three-fold increase in the accuracy of the extended inverse Monte Carlo model that incorporates γ was observed.
In this paper, diffuse reflectance hyperspectral images of a light beam propagating through a semi-infinite homogeneous layer were simulated by a modified version of the open source Monte Carlo (MC) for multi-layered tissues. Subsequently, the optical properties in terms of absorption and reduced scattering coefficients were extracted from the simulated hyperspectral images by an inverse MC model based on a criterion function that exploits the spatially resolved information of hyperspectral images. The method was validated on real hyperspectral images of turbid phantoms with exactly defined optical properties.
We assess the properties of contact pressure applied by manually operated fiber-optic probes as a function of the operator, probe contact area, and sample stiffness. First, the mechanical properties of human skin sites with different skin structures, thicknesses, and underlying tissues were studied by in vivo indentation tests. According to the obtained results, three different homogeneous silicone skin phantoms were created to encompass the observed range of mechanical properties. The silicon phantoms were subsequently used to characterize the properties of the contact pressure by 10 experienced probe operators employing fiber-optic probes with different contact areas. A custom measurement system was used to collect the time-lapse of diffuse reflectance and applied contact pressure. The measurements were characterized by a set of features describing the transient and steady-state properties of the contact pressure and diffuse reflectance in terms of rise time, optical coupling, average value, and variability. The average applied contact pressure and contact pressure variability were found to significantly depend on the probe operator, probe contact area, and surprisingly also on the sample stiffness. Based on the presented results, we propose a set of practical guidelines for operators of manual probes.
Diffuse reflectance spectroscopy utilizing optical fiber probes is a useful and simple method for non-invasive determination of biological tissue optical properties. In order to extract the optical properties from the acquired diffuse reflectance spectra, an accurate light propagation model, such as Monte Carlo, is required. The results obtained by the model can significantly depend on the description of the tissue and optical fiber probe geometry. Optical fiber probes commonly comprise fibers arranged into a desired source-detector layout enclosed in a stainless steel ferrule. By using Monte Carlo simulations, we investigate the impact of the stainless steel optical fiber probe-tissue interface on the diffuse reflectance spectra. For this purpose, a commonly used simple laterally uniform optical probe-tissue interface with mismatched refractive indices was compared to the improved optical probe-tissue interface taking into account the fiber layout and the specular reflections from the stainless steel probe tip. The results show that the error introduced into the simulated diffuse reflectance by the simplified probe-tissue interface can easily exceed 5%.
Diffuse reflectance spectroscopy is a popular approach for non-invasive assessment of optical properties in turbid media. The acquired spectra are analyzed by various light propagation models or by purely empirical methods. In this study, we quantitatively asses the experimental data and Monte Carlo lookup table-based inverse models by extracting the optical properties from the diffuse reflectance spectra of two carefully prepared turbid phantom sets with exactly defined optical properties. The first turbid phantom set was used for the creation of the experimental data-based lookup table model and calibration of the Monte Carlo lookup table-based inverse model. The second phantom set was used for the evaluation and comparative assessment of the two lookup table-based inverse models. In addition, we investigate the possible sources of errors introduced by the inverse models and show that the lookup table-based models disregard important information regarding the medium scattering phase function.
Cancer is the main cause of canine morbidity and mortality. The existing evaluation of tumors requires an experienced veterinarian and usually includes invasive procedures (e.g., fine-needle aspiration) that can be unpleasant for the dog and the owner. We investigate visible and near-infrared diffuse reflectance spectroscopy (DRS) as a noninvasive optical technique for evaluation and detection of canine skin and subcutaneous tumors ex vivo and in vivo. The optical properties of tumors and skin were calculated in a spectrally constrained manner, using a lookup table-based inverse model. The obtained optical properties were analyzed and compared among different tumor groups. The calculated parameters of the absorption and reduced scattering coefficients were subsequently used for detection of malignant skin and subcutaneous tumors. The detection sensitivity and specificity of malignant tumors ex vivo were 90.0% and 73.5%, respectively, while corresponding detection sensitivity and specificity of malignant tumors in vivo were 88.4% and 54.6%, respectively. The obtained results show that the DRS is a promising noninvasive optical technique for detection and classification of malignant and benign canine skin and subcutaneous tumors. The method should be further investigated on tumors with common origin.
Light propagation in highly scattering biological tissues is often treated in the so-called diffusion approximation (DA).
Although the analytical solutions derived within the DA are known to be inaccurate near tissue boundaries and absorbing
layers, their use in quantitative analysis of diffuse reflectance spectra (DRS) is quite common. We analyze the artifacts in
assessed tissue properties which occur in fitting of numerically simulated DRS with the DA solutions for a three-layer
skin model. In addition, we introduce an original procedure which significantly improves the accuracy of such an inverse
analysis of DRS. This procedure involves a single comparison run of a Monte Carlo (MC) numerical model, yet avoids
the need to implement and run an inverse MC. This approach is tested also in analysis of experimental DRS from human
skin.
Measurement of diffuse reflectance spectra (DRS) is a common experimental approach for non-invasive determination of tissue optical properties, as well as objective monitoring of various tissue malformations. Propagation of light in scattering media is often treated in diffusion approximation (DA). The major advantage of this approach is that it leads to enclosed analytical solutions for tissues with layered structure, which includes human skin. Despite the fact that DA solutions were shown to be inaccurate near tissue boundaries, the practicality of this approach makes it quite popular, especially when attempting extraction of specific chromophore concentrations from measured DRS. In this study we analyze the discrepancies between DRS spectra as obtained by using the DA solutions for three-layer skin model and more accurate predictions from Monte Carlo (MC) modeling. Next, we analyze the artifacts which result from the above discrepancies when extracting the parameters of skin structure and composition by fitting the DA solutions to the MC spectra. The reliability and usefulness of such a fit is then tested also on measurements of seasonal changes in otherwise healthy human skin.
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