Studying the depolarization rate of light emerging from a turbid medium holds promise for the non-invasive characterization of its single-scattering properties, with relevant application in the quality analysis of different specimens or for diagnostic purposes in the biomedical field, to name a few. However, irrespective of sample geometry, the dynamics of light depolarization takes place on a time scale of few ps, which is too fast for traditional detection methods. Here, we present experimental results on the time-domain evolution of the depolarization ratio of light that is diffusely reflected from a scattering medium, using linearly polarized fs pulses in an all-optical gating scheme. Time-resolved reflectance curves are recorded in the parallel and perpendicular polarization channels relative to the illumination beam, granting direct access to the depolarization rate. We demonstrate our experimental approach on a lipid emulsion, fitting the data with a polarized Monte Carlo simulation to retrieve the average particle size and scattering asymmetry factor using just two time-domain reflectance measurements in a semi-infinite geometry.
The invention of the random laser has opened a new frontier in optics, providing also the opportunity to explore new possibilities in the field of sensing. Random lasing have been proposed as promising opportunity to extend the potentiality given by optical sensing strategies, in particular in the field of the measurement of diffusive properties. Compared to the other used strategies, random laser-base systems has the advantage to show amplification of the signal by stimulated emission, as well as spectral modification. In particular, a non-invasive type of random laser sensor, that exploits a transparent physical separation between the gain material and the diffusive sample, has been reported. Here we present an improvement of the experimental setup used for such a kind of sensor. By the use of a optical fibers system and a couple of twin sensors, we report an enhancement of the accuracy, stability, reproducibility, as well an measurement method easy to perform, without resorting to complicated numerical or analytic inversion procedures. Since the possibility to perform local direct measurement on diffusive samples, such a “active” method can be a promising strategy in the field of biomedical optics and for non-invasive diagnostic purposes.
Usually, in biomedical optics, the average photon fluence rate, evaluated in a subvolume of a propagating medium, is obtained by Monte Carlo simulations by calculating the power deposited by photons absorbed in the subvolume. We propose an alternative method based on evaluating the average path length traveled by all photons injected within the subvolume. Application examples are given. This method also works for a zero absorption coefficient and for a nonconstant spatial distribution of the absorption coefficient within the subvolume. The proposed approach is a re-visitation of a well-known method applied to nuclear and radiation physics. The results obtained show that a potential advantage of the proposed method is that it can improve the convergence of Monte Carlo simulations. Indeed, when calculating the fluence in a region of interest with the proposed method, all photons passing through the region are considered. Whereas with the traditional approach, only absorbed" photons are considered. In the latter case, this can produce a poorer Monte Carlo statistic for the same number of photons launched.
The Monte Carlo (MC) method is a gold standard for "solving" the radiative transport equation even in complex geometries and distributions of optical properties. The exact analytical benchmark provided by the invariant total mean path length law spent by light injected with uniform Lambertian illumination within nonabsorbing scattering media is used to verify Monte Carlo codes developed for biomedical optics applications. The correctness of an MC code can be evaluated with a sample t-test. In addition, the invariance of the mean path length ensures that the expected value is known regardless of the complexity of the medium. The accuracy of the estimated mean path length can progressively increase as the number of simulated trajectories increases. The method can be used regardless of the scattering and geometric properties of the medium, as well as in the presence of refractive index mismatch between the medium and the outer region and between different regions of the medium. The proposed method is particularly reliable for detecting inaccuracies in the treatment of finite media boundaries. The results presented in this contribution, obtained with a standard computer, show a verification of our MC code to the sixth decimal place. This method can provide a fundamental tool for verification of Monte Carlo codes in the geometry of interest without resorting to simpler geometries and uniform distribution of the scattering properties.
We propose a novel analytical time-domain model for migration of Raman scattered photons in inhomogeneous two-layer diffusive media. Based on this model, the methods for reconstruction of the Raman spectra of the two layers are developed, tested in simulations and validated on phantom measurements data.
The Monte Carlo method is a gold standard for “solving” the radiative transport equation even in complex geometries and distributions of the optical properties. The exact analytical benchmark provided by the law of the invariant total mean pathlength spent by light injected with uniform Lambertian illumination inside non-absorbing scattering media is used to verify Monte Carlo codes developed for biomedical optics applications. The correctness of an MC code can be assessed with a one-sample t-test. Further, the invariance of the average path length guarantees that the expected value is known regardless of the complexity of the medium. The results obtained show that the accuracy of the estimated average pathlength can be progressively increase as the number of simulated trajectories increases. The method can be applied in total generality versus the scattering and geometrical properties of the medium, as well as in presence of refractive index mismatch between the medium and the external region and between different regions of the medium. The proposed verification method is especially reliable to detect inaccuracies in the treatment of boundaries of finite media. The results presented in this contribution, obtained by a standard computer machine, show a verification of our Monte Carlo code up to the sixth decimal digit. This method can provide a fundamental tool for the verification of Monte Carlo codes in the geometry of interest, without resorting to simpler geometries and uniform distribution of the scattering properties.
The invention of the random laser has opened a new frontier in optics, providing also the opportunity to explore new possibilities in the field of sensing. The research in optical sensors has indeed been largely encouraged by the demand for low-cost and non-invasive new detection strategies. The main advantage in exploiting the physical principle of the random laser in optical sensors is due to the presence of the stimulated emission mechanism, which allows amplification and spectral modification of the signal. We present here a step forward in the exploitation of this optical sensor device by an improved revisitation of a previous experimental setup, both in the instrumentation and in the measurement method, to mitigate the instability of the results due to shot-to-shot pump energy fluctuations. The novelties introduced, the use of optical fibers, a reference sensor, and a peristaltic pump have shown to eliminate optical beam alignment issues and the problems linked to variation in pump energy. The implemented sensor allows easy and rapid change of the sensed medium. These results pave the way for a portable device to directly measure the scattering of liquid samples, without resorting to complicated numerical or analytic inversion procedures of the measured data, provided that a suitable calibration of the system is performed.
Traditionally, in biomedical optics, the photons mean fluence rate assessed in a sub-volume of a propagating medium is obtained with Monte Carlo (MC) simulations by calculating the deposited power by the absorbed photons in the sub-volume. We propose an alternative method based on the assessment of the mean pathlength traveled by all the injected photons inside the sub-volume. Examples of its applications are given. This method also works for nil absorption coefficient and for a non-constant spatial distribution of the absorption coefficient inside the sub-volume. The proposed approach is a re-visitation of a well-known method applied in radiation and nuclear physics. The relation at the basis of the method descends from the ground definitions of quantities employed in radiative transfer. The results obtained show that a potential advantage of the proposed method is that it can improve the convergence of the MC simulations. Indeed, when calculating the fluence in a region of interest with the proposed method all the photons that cross the region are considered. While, with the traditional approach only the “absorbed”photons can contribute to the calculated fluence. In the latter case, this may produce a poorer MC statistic for the same number of launched photons.
This second edition is completely revised and improved and contains eight new chapters and six new appendixes. In addition to the theoretical background on light propagation through diffusive media, this update also provides new didactical material, including:
• A comprehensive statistical approach to the photon penetration depth in diffusive media
• An introduction to anomalous transport
• An anisotropic transport approach within the framework of diffusion theory
• An introduction to the invariance properties of radiative transfer in non-absorbing media
• A heuristic explanation of ballistic photon propagation
• An expanded description of core Monte Carlo simulation methods
• A series of new analytical solutions of the diffusion equation for new geometries
• Some original solutions in the time domain of the diffusion equation in the presence of Raman and fluorescence interactions
• New MATLAB® codes of the presented solutions
• A revised and enlarged set of numerical Monte Carlo results for verification of the presented solutions
• An augmented bibliography covering the field of tissue optics
Although the theoretical and computational tools provided in this book have their primary use in the field of biomedical optics, there are many other applications in which they can be used, including, for example, analysis of agricultural products, study of forest canopies or clouds, and quality control of industrial food, plastic materials, or pharmaceutical products, among many others.
Significance: Code verification is an unavoidable step prior to using a Monte Carlo (MC) code. Indeed, in biomedical optics, a widespread verification procedure for MC codes is still missing. Analytical benchmarks that can be easily used for the verification of different MC routines offer an important resource.
Aim: We aim to provide a two-step verification procedure for MC codes enabling the two main tasks of an MC simulator: (1) the generation of photons’ trajectories and (2) the intersections of trajectories with boundaries separating the regions with different optical properties. The proposed method is purely based on elementary analytical benchmarks, therefore, the correctness of an MC code can be assessed with a one-sample t-test.
Approach: The two-step verification is based on the following two analytical benchmarks: (1) the exact analytical formulas for the statistical moments of the spatial coordinates where the scattering events occur in an infinite medium and (2) the exact invariant solutions of the radiative transfer equation for radiance, fluence rate, and mean path length in media subjected to a Lambertian illumination.
Results: We carried out a wide set of comparisons between MC results and the two analytical benchmarks for a wide range of optical properties (from non-scattering to highly scattering media, with different types of scattering functions) in an infinite non-absorbing medium (step 1) and in a non-absorbing slab (step 2). The deviations between MC results and exact analytical values are usually within two standard errors (i.e., t-tests not rejected at a 5% level of significance). The comparisons show that the accuracy of the verification increases with the number of simulated trajectories so that, in principle, an arbitrary accuracy can be obtained.
Conclusions: Given the simplicity of the verification method proposed, we envision that it can be widely used in the field of biomedical optics.
Diffuse correlation spectroscopy (DCS) is an emerging diffuse optical technique that quantifies microvascular blood flow. In spite of the wide range of clinical/research applications, DCS instrumentation is not yet standardized. In this study, we have analyzed the effect of experimental parameters as the measurement duration time and the number of detectors, at different photon count-rates, on the precision of a DCS experiment. This provides a recipe for finding device and experimental settings that optimize the precision while balancing cost and temporal resolution.
Time Domain Diffuse Optical Tomography (TD-DOT) performed at multiple wavelengths can be used to non-invasively probe tissue composition. Then, tissue composition can be related to breast tissue and lesion type. Thus, TD-DOT could be used for therapy monitoring for breast cancer. We developed a software tool for multi-wavelength TD-DOT and performed a validation on meat phantoms to mimic tissue heterogeneity. An inclusion of different meat was exploited to mimic the presence of a lesion in the breast. Results show good localization of the inclusion, but poor quantification of the reconstructed breast composition. The use of a morphological prior constraint, providing information on inclusion geometry and position, significantly improves both localization and composition estimate.
A random laser is an optical system where the light is amplified by stimulated emission along random paths in a disordered medium. In recent years, a new kind of non-invasive sensor based on random lasing has been proposed. The striking point is that a sensor based on random lasing has an emission "fed" by the feedback due to the scattering properties of the medium, making such a system a natural candidate for studying materials with strong disorder. Here, we report the recent advances in the sensor structure and performances.
Time domain Diffuse Optical Tomography (TD-DOT) non-invasively probes the optical proprieties of biological tissue. These can be related to changes in tissue composition, thus making TD-DOT potentially valuable for cancer imaging. In particular, an application of interest is therapy monitoring for breast cancer. Thus, we developed a software tool for multiwavelength TD-DOT in reflectance geometry. While the use of multiple wavelengths probes the main components of the breast, the chosen geometry offers the advantage of linking the photon flight time to the investigated depth. We validated the tool on silicon phantoms embedding an absorbing inclusion to simulate a malignant lesion in breast tissue. Also, we exploited the a priori information on position and geometry of the inclusion by using a morphological prior constraint. The results show a good localization of the depth of inclusion but a reduced quantification. When the morphological constraint is used, though, the localization improves dramatically, also reducing surface artifacts and improving quantification as well. Still, there is room for improvement in the quantification of the “lesion” properties.
Light is a powerful non-invasive tool that can be exploited to probe highly scattering media like biological tissues for different purposes, from the detection of brain activity to the characterization of cancer lesions. In the last decade, timedomain diffuse optics (TDDO) systems demonstrated improved sensitivity when using time-gated acquisition chains and short source-detector separations (ρ), both theoretically and experimentally. However, the sensitivity to localized absorption changes buried inside a diffusive medium strongly depends on many parameters such as: SDS, laser power, delay and width of the gating window, absorption and scattering properties of the medium, instrument response function (IRF) shape, etc. In particular, relevant effects due to slow tails in the IRF were noticed, with detrimental effects on performances. We present simulated experimental results based on the diffusion approximation of the Radiative Transfer Equation and the perturbation theory subjected to the Born approximation. To quantify the system sensitivity to deep (few cm) and localized absorption perturbations, we exploited contrast and contrast-to-noise ratio (CNR), which are internationally agreed on standardized figures of merit. The purpose of this study is to determine which parameters have the greatest impact on these figures of merit, thus also providing a range of best operative conditions. The study is composed by two main stages: the former is a comparison between simulations and measurements on tissue-mimicking phantom, while the latter is a broad simulation study in which all relevant parameters are tuned to determine optimal measurement conditions. This study essentially demonstrates that under the influence of the slow tails in the IRF, the use of a small SDS no longer corresponds to optimal contrast and CNR. This work sets the ground for future studies with next-generation of TDDO components, presently under development, providing useful hints on relevant features to which one should take care when designing TDDO components.
In this work an analytical model for the time-resolved signal emitted by a
uniformly distributed Raman scatterer in a diffusive parallelepiped is derived and validated
with Monte Carlo (MC) simulations.
Optical sensing has been subject to a great interest for the moderate intrusiveness of its operation. The introduction of random lasers in ’90s has opened the door for developing a new kind of optical sensors. In such a source, disorder is introduced within an inverted medium, increasing the lifetime of the radiation without the presence of an optical cavity. The striking point is that the spectral characteristics of the output emission are strongly dependent on the scattering properties of the medium, suggesting new methods to investigate disordered materials. Recently, a novel concept for optical sensing based on the physics of random laser has been reported,1 overcoming the limits due to the alteration of the investigated sample by injecting an active material. Here we present a characterization of such a kind of sensor, suggesting non-invasive and also in-vivo applications.
The study of photon migration through highly scattering media opens the way to the non-invasive investigation of biological tissues well below the skin surface. When the medium is addressed in reflectance geometry, a key issue is to maximize the depth reached by migrating photons. By exploiting the Diffusion Approximation of the Radiative Transfer Equation, we calculated the time-resolved and continuous-wave probability density functions for the maximum depth reached by detected photons, for both a homogeneous and a layered laterally-infinite diffusive slab. From the probability density functions it is possible to calculate the mean value of the maximum depth at which detected photons have undergone scattering events.
In this work, we have tested the optimal estimation (OE) algorithm for the reconstruction of the optical properties of a two-layered liquid tissue phantom from time-resolved single-distance measurements. The OE allows a priori information, in particular on the range of variation of fit parameters, to be included. The purpose of the present investigations was to compare the performance of OE with the Levenberg–Marquardt method for a geometry and real experimental conditions typically used to reconstruct the optical properties of biological tissues such as muscle and brain. The absorption coefficient of the layers was varied in a range of values typical for biological tissues. The reconstructions performed demonstrate the substantial improvements achievable with the OE provided a priori information is available. We note the extreme reliability, robustness, and accuracy of the retrieved absorption coefficient of the second layer obtained with the OE that was found for up to six fit parameters, with an error in the retrieved values of less than 10%. A priori information on fit parameters and fixed forward model parameters clearly improves robustness and accuracy of the inversion procedure.
A mechanically switchable solid inhomogeneous phantom simulating localized absorption changes was developed and characterized. The homogeneous host phantom was made of epoxy resin with black toner and titanium dioxide particles added as absorbing and scattering components, respectively. A cylindrical rod, movable along a hole in the block and made of the same material, has a black polyvinyl chloride cylinder embedded in its center. By varying the volume and position of the black inclusion, absorption perturbations can be generated over a large range of magnitudes. The phantom has been characterized by various time-domain diffuse optics instruments in terms of absorption and scattering spectra, transmittance images, and reflectance contrast. Addressing a major application of the phantom for performance characterization for functional near-infrared spectroscopy of the brain, the contrast was measured in reflectance mode while black cylinders of volumes from ≈20 mm3 to ≈270 mm3 were moved in lateral and depth directions, respectively. The new type of solid inhomogeneous phantom is expected to become a useful tool for routine quality check of clinical instruments or implementation of industrial standards provided an experimental characterization of the phantom is performed in advance.
Diffuse optics is a powerful tool for clinical applications ranging from oncology to neurology, but also for molecular imaging, and quality assessment of food, wood and pharmaceuticals. We show that ideally time-domain diffuse optics can give higher contrast and a higher penetration depth with respect to standard technology. In order to completely exploit the advantages of a time-domain system a distribution of sources and detectors with fast gating capabilities covering all the sample surface is needed. Here, we present the building block to build up such system. This basic component is made of a miniaturised source-detector pair embedded into the probe based on pulsed Vertical-Cavity Surface-Emitting Lasers (VCSEL) as sources and Single-Photon Avalanche Diodes (SPAD) or Silicon Photomultipliers (SiPM) as detectors. The possibility to miniaturized and dramatically increase the number of source detectors pairs open the way to an advancement of diffuse optics in terms of improvement of performances and exploration of new applications. Furthermore, availability of compact devices with reduction in size and cost can boost the application of this technique.
We propose a simple and reliable solid phantom for mimicking realistic localized absorption changes within a diffusive medium. The phantom is based on a solid matrix holding a movable black inclusion embedded in a rod. Translating the rod parallel to the phantom surface, the inhomogeneity can be positioned beneath the source-detector pair (perturbed case) or far from it (unperturbed case). Examples of time-resolved transmittance measurements and time-resolved reflectance scans are shown to demonstrate the properties and the versatility of the phantom.
We propose a simple and reliable solid phantom for mimicking localized absorption changes within a diffusive medium. The phantom is based on the Equivalence Relation stating that any realistic absorption inhomogeneity can be mimicked by a totally absorbing sphere of adequate volume. Applying this concept, we constructed a solid phantom holding a movable black inclusion to be positioned beneath the source-detector pair (perturbed case) or far from it (unperturbed case). Different absorption perturbations can be mimicked by changing the volume and the position of the black object both in transmittance and reflectance configuration. Time-resolved measurements of transmittance images and a lateral reflectance scan are presented.
Diffuse Optics is growing in terms of applications ranging from e.g. oximetry, to mammography, molecular imaging, quality assessment of food and pharmaceuticals, wood optics, physics of random media. Time-domain (TD) approaches, although appealing in terms of quantitation and depth sensibility, are presently limited to large fiber-based systems, with limited number of source-detector pairs. We present a miniaturized TD source-detector probe embedding integrated laser sources and single-photon detectors. Some electronics are still external (e.g. power supply, pulse generators, timing electronics), yet full integration on-board using already proven technologies is feasible. The novel devices were successfully validated on heterogeneous phantoms showing performances comparable to large state-of-the-art TD rack-based systems. With an investigation based on simulations we provide numerical evidence that the possibility to stack many TD compact source-detector pairs in a dense, null source-detector distance arrangement could yield on the brain cortex about 1 decade higher contrast as compared to a continuous wave (CW) approach. Further, a 3-fold increase in the maximum depth (down to 6 cm) is estimated, opening accessibility to new organs such as the lung or the heart. Finally, these new technologies show the way towards compact and wearable TD probes with orders of magnitude reduction in size and cost, for a widespread use of TD devices in real life.
Application of light spectroscopy based techniques for the detection of cancers have emerged as a promising approach for tumor diagnostics. In-vivo or freshly excised samples are normally used for point spectroscopic studies. However, ethical issues related to in-vivo studies, rapid decay of surgically excised tissues and sample availability puts a limitation on in-vivo and in-vitro studies. There has been a few studies reported on the application of formalin fixed samples with good discrimination capability. Usually formalin fixation is performed to prevent degradation of tissues after surgical resection. Fixing tissues in formalin prevents cell death by forming cross-linkages with proteins. Previous investigations have revealed that washing tissues fixed in formalin using phosphate buffered saline is known to reduce the effects of formalin during spectroscopic measurements. But this could not be the case with reflectance measurements. Hemoglobin is a principal absorbing medium in biological tissues in the visible range. Formalin fixation causes hemoglobin to seep out from red blood cells. Also, there could be alterations in the refractive index of tissues when fixed in formalin. In this study, we propose to investigate the changes in tissue optical properties between freshly excised and formalin fixed brain tissues. The results indicate a complete change in the spectral profile in the visible range where hemoglobin has its maximum absorption peaks. The characteristic bands of oxy-hemoglobin at 540, 580 nm and deoxy-hemoglobin at 555 nm disappear in the case of samples fixed in formalin. In addition, an increased spectral intensity was observed for the wavelengths greater than 650 nm where scattering phenomena are presumed to dominate.
The nEUROPt protocol is one of two new protocols developed within the European project nEUROPt to characterize the performances of time-domain systems for optical imaging of the brain. It was applied in joint measurement campaigns to compare the various instruments and to assess the impact of technical improvements. This protocol addresses the characteristic of optical brain imaging to detect, localize, and quantify absorption changes in the brain. It was implemented with two types of inhomogeneous liquid phantoms based on Intralipid and India ink with well-defined optical properties. First, small black inclusions were used to mimic localized changes of the absorption coefficient. The position of the inclusions was varied in depth and lateral direction to investigate contrast and spatial resolution. Second, two-layered liquid phantoms with variable absorption coefficients were employed to study the quantification of layer-wide changes and, in particular, to determine depth selectivity, i.e., the ratio of sensitivities for deep and superficial absorption changes. We introduce the tests of the nEUROPt protocol and present examples of results obtained with different instruments and methods of data analysis. This protocol could be a useful step toward performance tests for future standards in diffuse optical imaging.
We present the experimental implementation and validation of a phantom for diffuse optical imaging based on totally absorbing objects for which, in the previous paper [J. Biomed. Opt.18(6), 066014, (2013)], we have provided the basic theory. Totally absorbing objects have been manufactured as black polyvinyl chloride (PVC) cylinders and the phantom is a water dilution of intralipid-20% as the diffusive medium and India ink as the absorber, filled into a black scattering cell made of PVC. By means of time-domain measurements and of Monte Carlo simulations, we have shown the reliability, the accuracy, and the robustness of such a phantom in mimicking typical absorbing perturbations of diffuse optical imaging. In particular, we show that such a phantom can be used to generate any absorption perturbation by changing the volume and position of the totally absorbing inclusion.
Using Monte Carlo simulations we demonstrate that a realistic absorption inhomogeneity embedded in a diffusive medium can be effectively mimicked by a small black object of a proper volume (Equivalence Relation). Applying this concept we propose the construction of simple and well reproducible inhomogeneous phantoms.
The optical properties of the human head in the range from 600 nm to 1100 nm have been non-invasively in-vivo investigated by various research groups using different diffuse optics techniques and data analysis methods.
The design of inhomogeneous phantoms for diffuse optical imaging purposes using totally absorbing objects embedded in a diffusive medium is proposed and validated. From time-resolved and continuous-wave Monte Carlo simulations, it is shown that a given or desired perturbation strength caused by a realistic absorbing inhomogeneity of a certain absorption and volume can be approximately mimicked by a small totally absorbing object of a so-called equivalent black volume (equivalence relation). This concept can be useful in two ways. First, it can be exploited to design realistic inhomogeneous phantoms with different perturbation strengths simply using a set of black objects with different volumes. Further, it permits one to grade physiological or pathological changes on a reproducible scale of perturbation strengths given as equivalent black volumes, thus facilitating the performance assessment of clinical instruments. A set of plots and interpolating functions to derive the equivalent black volume corresponding to a given absorption change is provided. The application of the equivalent black volume concept for grading different optical perturbations is demonstrated for some examples.
We consider four different Monte Carlo methods, widely used in tissue optics, based on four different ways to build photons’ trajectories. By means of numerical results we compare the temporal point spread functions calculated by the four methods for a wide range of the optical properties in the slab and semi-infinite medium geometry. Therefore, we show the statistical equivalence of the four methods and some of their convergence characteristics.
Different strategies for Monte Carlo simulations are currently used in tissue optics. In this work we analyze and compare four Monte Carlo methods based on different ways to extract the photons’ trajectories. By using theoretical arguments we show that the four methods are statistically equivalent. Afterwards we study the convergence of the four methods both in time and continuous wave domains. Our results show that those Monte Carlo methods based on photons’ annihilation or survival converge faster for continuous wave calculations and at shorter source-detector distances. On the contrary Monte Carlo methods based on weight assignment provide a better representation of the temporal point spread function in time domain.
Novel protocols were developed and applied in the European project “nEUROPt” to assess and compare the performance
of instruments for time-domain optical brain imaging and of related methods of data analysis. The objective of the first
protocol, “Basic Instrumental Performance”, was to record relevant basic instrumental characteristics in a direct way.
The present paper focuses on the second novel protocol (“nEUROPt” protocol) that was devoted to the assessment of
sensitivity, spatial resolution and quantification of absorption changes within inhomogeneous media. It was implemented
with liquid phantoms based on Intralipid and ink, with black inclusions and, alternatively, in two-layered geometry.
Small black cylinders of various sizes were used to mimic small localized changes of the absorption coefficient. Their
position was varied in depth and lateral direction to address contrast and spatial resolution. Two-layered liquid phantoms
were used, in particular, to determine depth selectivity, i.e. the ratio of contrasts due to a deep and a superficial
absorption change of the same magnitude. We introduce the tests of the “nEUROPt” protocol and present exemplary
results obtained with various instruments. The results are related to measurements with both types of phantoms and to
the analysis of measured time-resolved reflectance based on time windows and moments. Results are compared for the
different instruments or instrumental configurations as well as for the methods of data analysis. The nEUROPt protocol
is also applicable to cw or frequency-domain instruments and could be useful for designing performance tests in future
standards in diffuse optical imaging.
We propose and validate the design of inhomogeneous phantoms for diffuse optical imaging purposes using
totally absorbing objects embedded in a diffusive medium. From Monte Carlo simulations, we show that a
given or desired perturbation strength caused by an realistic absorbing inhomogeneity of a certain absorption
and volume can be approximately mimicked by a small totally absorbing object of a so-called Equivalent Black
Volume (Equivalence Relation). This concept can be useful to design realistic inhomogeneous phantoms using
a set of black objects with different volumes. Further, it permits to grade physiological or pathological changes
on a reproducible scale of equivalent black volumes, thus facilitating the performance assessment of clinical
instruments. We have also provided a plot to derive the Equivalent Black Volume yielding the same effect of a
realistic absorption object.
The use of Intralipid 20% was recently suggested as a diusive reference standard for tissue simulating phantoms.
We herein extend previously obtained results to other fat emulsions, specically Intralipid 10%, Intralipid 30%,
Lipovenoes 10%, Lipovenoes 20%, Lipofundin S 10%, and Lipofundin S 20%. Of particular importance for
practical applications, our measurements carried out at a wavelength of 751 nm show the following features.
First, batch-to-batch variations of the optical properties of these products are less than 2 % similarly to Intralipid
20%. Second, the absorption coecient of Intralipid, Lipovenoes, and Lipofundin S are very similar and their
measured values are within the experimental errors. Third, the reduced scattering of Intralipid 20%, Lipovenoes
20%, and Lipofundin S 20% are similar and their measured values are within 5%. Forth, the reduced scattering
coecient of Intralipid 10% and Intralipid 30% can be scaled from that of Intralipid 20% with an error of 9%
and 2%, respectively. A similar scaling property is valid for Lipovenoes and Lipofundin S.
In this work, based on our previously proposed perturbation theory for the diffusion equation, we present
new theoretical results in time and frequency domains. More specifically, we have developed a fourth order
perturbation theory of the diffusion equation for absorbing defects. The method of Padé Approximants is
used to extend the validity of the proposed theory to a wider range of absorbing contrasts between defects
and background medium. The results of the theory are validated by comparisons with Monte Carlo
simulations. In the frequency domain, the discrepancy between theoretical and Monte Carlo results for
amplitude (AC) data are less than 10% up to an absorption contrast of Δμa ≤ 0.2 mm-1, whereas the
discrepancy of phase data is less than 1° up to Δμa ≤ 0.1 mm-1. In the time domain, the average
discrepancy is around 2-3% up to Δμa ≤ 0.06 mm-1. The proposed method is an effective and fast forwardproblem
solver that has the potential to find general applicability in a number of situations.
We present a multi-laboratory comparison of several independent forward solvers used for photon migration
through layered media. Two main categories of forward solvers are presented: Monte Carlo procedures and
solutions of the diffusion equation for the time domain. For Monte Carlo we have included four independent
codes. For the solutions of the diffusion equation, we have presented: two semi-analytical approaches based
on the Green's function method and one solution obtained with the finite element method. The comparisons
between the different time-dependent solutions were performed for a two-layer medium.
We propose the use of a retrieval operator for biomedical applications in near-infrared spectroscopy. The proposed
retrieval operator is based on the "Optimal Estimation" method. The main characteristic of this method relates
to the possibility to include prior information both on target and on forward model parameters of the inversion
procedure. The possibility of the retrieval operator to elaborate a-priori information can in principle be a benefit
for the whole retrieval procedure. This means that a larger number of target parameters can be retrieved, or that
a better accuracy can be achieved in retrieving the target parameters. The final goal of this inversion procedure is
to have an improved estimate of the target parameters. The procedure has been tested on time-resolved simulated
experiments obtained with a Monte Carlo code. The results obtained show that an improved performance of
the inversion procedure is achieved when prior information on target and forward model parameters is available.
With the use of a priori information on target parameters we have in average a lower difference between the
retrieved values of the parameters and their true values, and the error bars determined by the inversion procedure
on the retrieved parameters are significantly lower. At the same time a good estimate of the errors on the forward
model parameters can significantly improve the retrieval of the target parameters.
A reference standard for tissue-simulating phantoms, i.e., a phantom with well known and stable optical properties,
reproducible, and easy to be found, would be very useful for many applications based on measurements of
diffused light. Although many tissue-equivalent phantoms have been proposed, to our knowledge none of them
has been characterized sufficiently well to be suggested as a reference standard. Based on the results of measurements
of optical properties we carried out at visible and NIR wavelengths, the use of Intralipid 20% diluted
in water as diffusive medium, and of India ink as absorber, is here suggested as a first step towards a diffusive
reference standard for tissue-simulating phantoms. As for Intralipid 20%, measurements carried out on samples
from nine different batches with expiry dates spreading over ten years showed surprisingly small batch-to-batch
variations. For the reduced scattering coefficient the maximum deviation from the value averaged over the nine
batches was of about 2%, and the results for the absorption coefficient were very close to those for pure water.
As for India ink measurements on samples from different batches and from five different brands showed large
inter-brand and inter-batch variations for both the absorption and the extinction coefficient. On the contrary,
small variations have been observed for the ratio between the absorption and the extinction coefficient. Intralipid
20% and Indian ink can be therefore easily mixed to obtain liquid phantoms with well known optical properties.
This phantom can be a first step towards a reference standard for optical tissue phantoms.
In this review we present the instrumental and theoretical developments for functional diffuse reflectance spectroscopy at
small source-detector distances. We proposed the possibility to perform photon migration measurements at null or small
inter-fiber distances demonstrating the improvement of this novel approach in terms of achievable contrast, spatial
resolution and number of detected photons. We developed a novel system to perform time-resolved diffuse reflectance
measurement at small source detector separation based on a single photon avalanche photodiode (SPAD) operated in fast
time gated mode and a broadband fiber laser. By means of time gating it is possible to detect longer lived photons
neglecting initial ones. We show results both on homogeneous and inhomogeneous tissue phantoms demonstrating a
dynamic range of 7 orders of magnitude and a temporal range of 6 nanoseconds. Furthermore, this approach proved
valuable to detect brain activity.
In this work we studied the accuracy of a non-linear fitting procedure, based on the Levenberg-Marquardt algorithm,
for time-resolved measurements to retrieve the absorption and the reduced scattering coefficients of
an absorbing diffusive medium. This procedure is suitable for retrieving optical properties in a wider range of
situations (e.g. solid samples, reflectance geometry), with respect to the linear inversion procedures recently presented
for both CW and time domain measurements. By means of both analytical and numerical (Monte Carlo)
simulations, we quantified the influence of photon counts, temporal sampling, analytical model, background and
instrument response function on the accuracy in the estimation of the optical properties. Furthermore, we validated
our results with preliminary measurements on calibrated diffusive solutions. The main source of error that
affects the accuracy of the absorption and reduced scattering coefficients retrieved by the non-linear procedure
appears to be the analytical model adopted in the inversion procedure.
A hybrid heuristic time dependent analytical solution of the radiative transfer
equation for the slab geometry is derived. Comparisons with the results of Monte Carlo
simulations have shown an excellent behavior of the model in describing photon migration
at short distances and early times where the solution of the diffusion equation is subjected to
strong approximations.
In this work we focused on time-resolved measurements in diffusive media performed at small (few millimeters)
source-detector distances in reflectance geometry. This configuration has been predicted to have better contrast,
better spatial resolution, and lower noise than the typical measurements performed at few centimeters. In our
instrumental set-up we exploited a fast-gating (rise-time < 400 ps) front-end electronics enabling a silicon Single-
Photon Avalanche Diode (SPAD) for time-correlated single-photon counting. By means of this detector, we can
acquire "late" photons of the diffused light collected 2 mm apart from the injection point. This is possible
because the fast gated SPAD rejects the huge amount of "early" photons which otherwise would saturate the detection electronic chain. The time resolution of the set-up is 100 ps. The instrument has been validated on both homogeneous and inhomogeneous (high absorbing inclusion at different depths inside) tissue phantoms with different optical properties. We obtained diffused time-resolved curves with dynamic ranges of about 107. Moreover, we demonstrated good agreement between the measured time-resolved contrasts and those calculated by Monte Carlo numerical simulations.
We show the performance of a proposed perturbation theory of the diffusion equation for studying light
propagation in optically heterogeneous media, i.e. characterized by a distribution of the absorption and the
reduced scattering coefficient. In different geometries (cylindrical, slab, layered), we study the change of
continuous wave intensity due to the presence of focal absorption perturbations. The results obtained with
fourth order perturbation theory show a clear improved accuracy with respect to first order calculations for
a range of the absorption contrasts of interest in the field of near infrared spectroscopy and diffuse optical
tomography. The method of Padè Approximants is used to extend the limits of the proposed perturbation
theory to a wider range of absorption contrasts. For validation of the theory, we show comparison with
Monte Carlo simulations.
KEYWORDS: Scattering, Absorption, Monte Carlo methods, Optical properties, Data modeling, Picosecond phenomena, Signal to noise ratio, Near infrared, Photon counting, Geometrical optics
In this work we studied the accuracy of a non-linear fitting procedure, based on the Levenberg-Marquardt algorithm,
for time-resolved measurements to retrieve the absorption and the reduced scattering coefficients of
an absorbing diffusive medium. This procedure is suitable for retrieving optical properties in a wider range of
situations (e.g. solid samples, reflectance geometry), with respect to the linear inversion procedures recently
presented for both CW and time domain measurements. By means of both analytical and numerical (Monte
Carlo) simulations, we quantified the influence of photon counts, temporal sampling, analytical model, background
and instrument response function on the accuracy in the estimation of the optical properties. Also a new
analytical model to describe light propagation in diffusive media based on the Radiative Transport Equation has
been considered. The main source of error that affects the accuracy of the absorption and reduced scattering
coefficients retrieved by the non-linear procedure appears to be the analytical model adopted in the inversion
procedure.
We performed reflectance measurements with a time-resolved white-light spectroscopy system to monitor concentrations changes in a two-layer liquid phantom with optical properties similar to human tissues. By varying the concentrations of three inks with different spectral features, we changed the absorption coefficient of the upper and lower layer to simulate either haemodynamics changes in the muscle covered by adipose layer, or functional brain activation with systemic response in the scalp. Data were analyzed by a time-resolved spectrally constrained fitting method based on a homogeneous model of photon diffusion. Although this approach is based on a homogeneous model and employs a single 2cm source-detector distance, the technique is able to monitor changes in the lower layer, while it is scarcely affected by variation in the upper layer. Preliminary in vivo measurements have been performed on one healthy volunteer to monitor oxy- and deoxy-haemoglobin changes in the muscle during arterial occlusion and in the brain during a motor task. Even if the overall sensitivity of the technique is reduced, in vivo results are in general agreement with the findings of dedicated system for tissue oximetry.
We demonstrate the feasibility of time-resolved diffuse reflectance at small source-detector separations using a
single-photon avalanche diode (SPAD) operated in time-gated mode. Photon time distributions at an interfiber
distance of 0.2 cm were obtained on tissue phantoms with a reduced scattering coefficient of 10 cm-1, and
an absorption coefficient of 0.1 cm-1, with a dynamic range of 106 and collecting photons at arrival times up
to 4 ns. By time-gating the initial photons, carrying information mainly from superficial layers, it is possible
to detect longer lived photons that have explored deeper depths even at almost null interfiber distances. The
proposed approach should provide higher number of photons at any arrival time, higher contrast, and better
spatial resolution as compared to longer interfiber distances.
In spite of many progresses achieved both with theories and with experiments in studying light propagation through
diffusive media, a reliable method for accurate measurements of the optical properties of diffusive media at NIR
wavelengths is, in our opinion, still missing. It is therefore difficult to create a reference diffusive medium. We describe
two methods in the CW and time domain to calibrate the reduced scattering coefficient of a liquid diffusive medium and
the absorption coefficient of an absorber with a standard error smaller than 2% for both the coefficients.
The paper addresses the problem of extending conventional Monte Carlo procedures to cases of multiple scattering in media with suspensions of non-spherical or chiral particles. Extinction coefficients of the media depend on polarization of radiation. Along the propagation path polarization of radiation changes, unless the field is polarized according to one of two particular modes. The relationship between these modes and the elements of the amplitude scattering matrix for the type of particle is shown by means of a simple formalism, tested with reference to simple shapes and orientation of the particles. Some possibilities for extending Monte Carlo procedures are suggested. A case of small chiral spheres is considered.
McCART is a numerical procedure to solve the radiative transfer equation for light propagation through the atmosphere especially developed to study the effect of the atmosphere on the response of hyperspectral sensors for remote sensing of the earth's surface. McCART is based on a single Monte Carlo simulation run for a reference layered plane non-absorbing atmosphere and a plane ground with uniform reflectance. The spectral response of the sensor for a given distribution of ground reflectance and for a specific profile of scattering and absorption properties of the atmosphere is obtained in a short time from the results of the Monte Carlo simulation, making use of scaling relationships and of symmetry properties. The response includes the effects of adjacent pixels. The results can be used to establish the limits of applicability of approximate algorithms for the processing and analysis of hyperspectral images. The algorithm can be also used to develop procedures of atmospheric compensation.
The paper addresses the problem of extending conventional Monte Carlo procedures to cases of multiple scattering in media with suspensions of non-spherical or chiral particles. Extinction coefficients of the media depend on polarization of radiation. Along the propagation path polarization of radiation changes, unless the field is polarized according to one of two particular modes. The relationship between these modes and the elements of the amplitude scattering matrix for the type of particle is shown by means of a simple formalism, tested with reference to simple shapes and orientation of the particles. Some possibilities for extending Monte Carlo procedures are suggested. A case of small chiral spheres is considered.
Fausto Acernese, Paolo Amico, N. Arnaud, Saverio Avino, D. Babusci, Regis Barille, Fabrizio Barone, L. Barsotti, M. Barsuglia, F. Beauville, M. Bizouard, C. Boccara, Francois Bondu, L. Bosi, C. Bradaschia, S. Braccini, Alain Brillet, V. Brisson, L. Brocco, Damir Buskulic, G. Calamai, Enrico Calloni, E. Campagna, F. Cavalier, G. Cella, Eric Chassande-Mottin, Frederic Cleva, T. Cokelaer, J.-P. Coulon, Elena Cuoco, Vincenzino Dattilo, M. Davier, Rosario De Rosa, Luciano Di Fiore, A. Di Virgilio, B. Dujardin, Antonio Eleuteri, Daniel Enard, I. Ferrante, F. Fidecaro, I. Fiori, Raffaele Flaminio, J.-D. Fournier, S. Frasca, Franco Frasconi, Andreas Freise, Luca Gammaitoni, Alberto Gennai, Adalberto Giazotto, Gianfranco Giordano, Lara Giordano, G. Guidi, H. Heitmann, P. Hello, P. Heusse, L. Holloway, S. Kreckelbergh, Paolo La Penna, Vincent Loriette, Magali Loupias, G. Losurdo, Jean-Marie Mackowski, E. Majorana, Catherine Man, E. Marchetti, Frederique Marion, Fabrizio Martelli, Alain Masserot, Louis Massonnet, Massimo Mazzoni, Leopoldo Milano, J. Moreau, F. Moreau, Nazario Morgado, F. Mornet, Benoit Mours, J. Pacheco, A. Pai, C. Palomba, Federico Paoletti, Silvio Pardi, R. Passaquieti, D. Passuello, B. Perniola, Laurent Pinard, R. Poggiani, Michele Punturo, P. Puppo, Ketevan Qipiani, J. Ramonet, P. Rapagnani, V. Reita, Alban Remillieux, F. Ricci, Iolanda Ricciardi, Guido Russo, Salvatore Solimeno, Ruagero Stanga, E. Tournefier, F. Travasso, Herve Trinquet, Didier Verkindt, Flavio Vetrano, Oliver Veziant, A. Vicere, J.-Y. Vinet, H. Vocca, Michel Yvert
The French-Italian interferometric gravitational wave detector VIRGO is currently being commissioned. Its principal instrument is a Michelson interferometer with 3 km long optical cavities in the arms and a power-recycling mirror. This paper gives an overview of the present status of the system. We report on the presently attained sensitivity and the system’s performance during the recent commissioning runs.
F. Beauville, D. Buskulic, R. Flaminio, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, M. Yvert, Regis Barille, Vincenzino Dattilo, Daniel Enard, Franco Frasconi, Alberto Gennai, Paolo La Penna, Magali Loupias, Federico Paoletti, L. Bracci, Giovanni Calamai, E. Campagna, G. Conforto, E. Cuoco, I. Fiori, G. Guidi, G. Losurdo, Fabrizio Martelli, Massimo Mazzoni, B. Perniola, Ruagero Stanga, Flavio Vetrano, A. Vicere, D. Babusci, Gianfranco Giordano, Jean-Marie Mackowski, Nazario Morgado, Laurent Pinard, Alban Remillieux, Fausto Acernese, Fabrizio Barone, Enrico Calloni, Rosario De Rosa, Luciano Di Fiore, Antonio Eleuteri, Leopoldo Milano, Ketevan Qipiani, Iolanda Ricciardi, G. Russo, Salvatore Solimeno, M. Varvella, Francois Bondu, Alain Brillet, Eric Chassande-Mottin, Frederic Cleva, T. Cokelaer, J.-P. Coulon, B. Dujardin, J.-D. Fournier, H. Heitmann, Catherine Man, F. Mornet, J. Pacheco, A. Pai, Herve Trinquet, J.-Y. Vinet, N. Arnaud, M. Barsuglia, M. Bizouard, V. Brisson, F. Cavalier, M. Davier, P. Hello, P. Heusse, S. Kreckelberg, A. Claude Boccara, Vincent Loriette, J. Moreau, V. Reita, P. Amico, L. Bosi, Luca Gammaitoni, M. Punturo, F. Travasso, H. Vocca, L. Barsotti, S. Braccini, C. Bradaschia, G. Cella, C. Corda, A. Di Virgilio, I. Ferrante, F. Fidecaro, Adalberto Giazotto, E. Majorana, L. Holloway, R. Passaquieti, D. Passuello, R. Poggiani, A. Toncelli, M. Tonelli, L. Brocco, S. Frasca, C. Palomba, P. Puppo, P. Rapagnani, F. Ricci
The goal of the VIRGO program is to build a giant Michelson type interferometer (3 kilometer long arms) to detect gravitational waves. Large optical components (350 mm in diameter), having extremely low loss at 1064 nm, are needed. Today, the Ion beam Sputtering is the only deposition technique able to produce optical components with such performances.
Consequently, a large ion beam sputtering deposition system was built to coat large optics up to 700 mm in diameter. The performances of this coater are described in term of layer uniformity on large scale and optical losses (absorption and scattering characterization).
The VIRGO interferometer needs six main mirrors. The first set was ready in June 2002 and its installation is in progress on the VIRGO site (Italy). The optical performances of this first set are discussed. The requirements at 1064 nm are all satisfied. Indeed, the absorption level is close to 1 ppm (part per million), the scattering is lower than 5 ppm and the R.M.S. wavefront of these optics is lower than 8 nm on 150 mm in diameter. Finally, some solutions are proposed to further improve these performance, especially the absorption level (lower than 0.1 ppm) and the mechanical quality factor Q of the mirrors (thermal noise reduction).
Photon migration through diffusive two and three-layered slabs has been studied making use of the diffusion equation, of Monte Carlo simulations and of experiments. We have obtained analytical solutions of the diffusion equation for the diffuse reflectance and transmittance both in the time domain and in the continuous wave domain. The mean pathlength spent by received photons inside each diffusive layer has also been determined by the analytical solutions, by Monte Carlo simulations and by experiments. The results obtained show that the theory proposed is suitable for describing photon migration in diffusive layered media. The analytical solutions have been also used in inversion procedures for retrieving the optical properties of a two-layered slab.
A procedure for retrieving the optical properties of a two-layered diffusive medium based on an exact analytical solution of the time dependent diffusion equation and on multidistance reflectance data is presented. The method overcomes some limitations of previously developed procedures. Five parameters have been always fitted: the
absorption and the reduced scattering coefficient of both layers and the thickness of the first layer. The results obtained have shown that this procedure does not require an initial guess for the unknown optical parameters fitted, whilst the start value for the thickness of the first layer needs to be estimated within an error of about 50%. Time resolved measurements of diffuse reflectance have been generated with Monte Carlo simulations. A particular attention has been devoted to determine the optical properties of the muscle with the subcutaneous fat layer.
The method consists in measuring the perturbation provoked by a small volume (0.2-1 ml) of tissue on light propagating through a medium of known optical properties. The absorption and the reduced scattering coefficient of the medium are retrieved from multidistance continuous wave measurements of transmittance. The inversion procedure is based on the solution of the diffusion equation obtained with a perturbative approach. The method has been validated with Monte Carlo results. Experimental results are reported for various kind of tissue. The results obtained shows that the method is particularly effective for low absorbing tissues.
An exact solution of the time dependent diffusion equation for a layered diffusive medium has been obtained by using a method based on the decomposition of the fluence rate in a series of eigenfunctions. Making use of this exact analytical solution inversion procedures have been implemented to retrieve the optical properties of the medium. Time resolved measurements of diffuse reflectance have been generated with Monte Carlo simulations. Inversion procedures have been carried out both for a single time resolved measurement and for multi-distance time resolved measurements. The characteristics of both procedures have been investigated. For the case of a two-layered medium the fitting procedure carried out on a single measurement showed that it is impossible to retrieve correctly all the optical parameters of the layered medium. The inversion procedure correctly retrieves the absorption coefficient of the second layer and the reduced scattering coefficient of the first layer. A significant improvement is obtained by using multi-distance measurements. A particular attention has been devoted to determine the optical properties of muscle with the subcutaneous fat layer.
A method to measure the diffusion coefficient of homogeneous and layered media, based on multi-distance measurements of time-resolved reflectance is proposed. The diffusion coefficient is retrieved by fitting procedures on the logarithm of the ratio of two reflectances measured at two different source-receiver distances. The inversion procedure uses analytical models derived from the diffusion equation and it is not affected by the boundary conditions used. For layered media the inversion procedure retrieves the diffusion coefficient of the first layer. The proposed procedure is simpler than others usually employed and also provides a reliable criterion for retrieval of information on the layered structure of the diffusive medium.
Some comparison between the results of 3D FEM and 3D Monte Carlo calculations of light propagation inside highly scattering cylindrical optical phantoms are presented. The temporal profiles of transmitted ? Dirac pulses through the cylindrical phantoms have been calculated for different source-detector angles. The comparisons have been carried out in time-domain and for both homogeneous and inhomogeneous cylindrical phantoms; in the latter case some absorbing cylinders were included inside a scattering cylinder. Refractive index mismatch between the phantoms and the surrounding medium was taken into account. Some comparison with experimental results are also shown.
The characteristics of the light transmitted through diffusing media have been studied by using the diffusion approximation of the radiative transfer equation. Making use of the partial-current-boundary condition an analytical expression for the angular dependence of the specific intensity emerging from a diffusing medium has been obtained. The analytical expression gives results in excellent agreement with Monte Carlo simulations for the slab geometry. The limits of validity of the theory have been investigated. Making use of the diffusion equation and of the extrapolated boundary condition, an heuristic analytical expression for the time-resolved reflectance has also been obtained assuming the photon flux as being simply proportional to the fluence rate. The proposed expression is simpler with respect to other commonly used expressions and seems to give better results when used to retrieve the optical properties from time-resolved measurements.
The scattering and the absorption coefficients of tissue can provide important information about the physiological condition of tissue. Living bodies have a complex structure, therefore in most cases tissue cannot be regarded as a homogeneous medium. In some cases biological tissue have layered structures (head, skin, bone, etc.), consequently in order to measure the optical properties in vivo it is necessary to formulate the photon migration in layered media. Making use of the diffusion equation a theoretical time domain model for photon migration through a highly scattering layered slab has been elaborated. A pencil pulsed light beam is normally incident upon the surface of the first diffusing layer. The effect of the refractive index mismatch with the external medium is taken into account and proper boundary conditions between the diffusing layers are considered. Analytical solutions of the fluence rate inside the layers have been obtained. A Monte Carlo program for the photon migration through a two or a three layered slab has been also developed. The results obtained by using the analytical solution and Monte Carlo simulations are compared and presented. The main goal of this work is the future application of the model on retrieving the optical properties of layered media.
A comparison among different techniques used for breast imaging has been carried out by using a Monte Carlo (MC) code to simulate confocal scanning on a diffusing slab containing absorbing inhomogeneities. The MC code evaluated the temporal point spread function (TPSF) for many positions of the source- receiver system with respect to the inhomogeneity. Each TPSF was fitted using the diffusion equation solution for a homogeneous slab. The information contained in each TPSF was summarized in three parameters: the absorption coefficient, the reduced scattering coefficient and the amplitude factor. An image was obtained plotting each of these parameters. To simulate the time gating technique the analytical functions obtained from the fit were used to evaluate the energy received within short gating times. To simulate the frequency domain technique the Fourier transform of the analytical function was calculated. The results obtained from simulations showed that a good estimation of the dimension of an absorbing inhomogeneity can be retrieved from the images obtained either from continuous wave domain, or time domain, or frequency domain measurements. The better contrast and the independence of the image quality on absorption properties of the diffusing medium indicates that the time gating technique is the one producing the best image quality.
The single scattering properties (extinction coefficient and scattering function at small forward scattering angles) of bovine and swine brain were obtained from transmissometric measurements on thin slices of tissues at l=633 nm. Large differences between the optical properties of white and gray matter were observed, whereas minor differences were found between bovine and swine samples. For gray matter, values between 10 and 30 mm−1 were obtained for the extinction coefficient. The scattering function was strongly forward peaked, indicating a highly anisotropic scattering. For white matter, values between 100 and 250 mm−1 were measured for the extinction coefficient. These values were so large that it was impossible to obtain a sample thin enough to measure the scattering function in single scattering conditions.
The absorption and the reduced scattering coefficients of living tissues were obtained from measurements of time-resolved reflectance at near-IR wavelengths. The inversion procedure was based on the temporal spread function for a semi-infinite medium given by the diffusion approximation. Measurements showed significant variations between the optical parameters measured on different organs and different volunteers. The single scattering properties (extinction coefficient and scattering function at small forward scattering angles) of bovine and swine brain were obtained from transmissometric measurements on thin slices of tissues. Large differences between the optical properites of white and grey matter were observed, whereas minor differences were found between bovine and swine samples.
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