On the extinction of radiation by a homogeneous but spatially correlated random medium

Possible Error in Reflection Pulse Oximeter Readings as a Result of Applied Pressure

Pulse oximetry is one of the most widely used techniques in modern medicine. In pulse oximetry, photoplethysmography (PPG) signals are measured at two different wavelengths and converted into the parameter Gamma, which is used to calculate the oxygen saturation of arterial blood. Although most pulse oximetry sensors are based on transmission geometry, the reflection mode is required for different form factors such as the forehead or wrists. In reflection oximetry, local pressure is applied to the measurement surface. We investigated the relationship between applied pressure and Gamma and found that for the reflection mode, Gamma tends to increase with increasing applied pressure. To explain this, we described the PPG signal in terms of two alternative models: a volumetric model and a Scattering-Driven Model (SDM). We assumed that the application of external pressure results in a decrease in local blood flow. We showed that only SDM correctly qualitatively describes Gamma as a function of the decrease in blood flow. We concluded that both described models coexist and that the relative influence of each depends on the measurement geometry and blood perfusion in the skin.

In situ analysis and imaging of aromatic amidine at varying ligand densities in solid phase

We report the development of a fast and accurate fluorescence-based assay for amidine linked to cellulose membranes and Sepharose gel. The assay is founded on the glyoxal reaction, which involves reaction of an amidine group with glyoxal and an aromatic aldehyde, leading to the formation of a fluorophore that can be analyzed and quantified by fluorescence spectroscopy and imaging. While the assay has been reported previously for aromatic amidine estimation in solution phase, here we describe its adaptation and application to amidine linked to diverse forms of solid matrices, particularly benzamidine Sepharose and benzamidine-linked cellulose membranes. These functionalized porous matrices find important application in purification of serine proteases. The efficacy of a protein separation device is determined by, among other factors, the ligand (amidine) density. Hence, a sensitive and reproducible method for amidine quantitation in solid phase is needed. The glyoxal reaction was carried out on microbead-sized Sepharose gel and cellulose membranes. Calibration curves were developed for each phase, which established linearity in the range of 0-0.45 μmol per mL amidine for free amidine in solution, 0-0.45 μmol amidine per mL Sepharose gel, and 0-0.48 μmol per mL cellulose membrane. The assay showed high accuracy (~ 3.4% error), precision (RSD < 2%), and reproducibility. Finally, we show how this fluorescent labeling (glyoxal) method can provide a tool for imaging membranes and ligand distribution through confocal laser scanning microscopy. Graphical abstract.

Generalized time-independent correlation transport equation with static background: influence of anomalous transport on the field autocorrelation function

A generalized time-independent correlation transport equation (GCTE) is proposed for the field autocorrelation function. The GCTE generalizes various models for anomalous transport of photons and takes into account the possible presence of a static background. In a tutorial example, the GCTE is solved for a homogeneous semi-infinite medium in reflectance configuration through Monte Carlo simulations. The chosen anomalous photon transport model also includes the classic and the "generalized" Lambert-Beer's law (depending on the choice of parameters). A numerical algorithm allowing generation of the related anomalous random photon steps is also given. The clear influence of anomalous transport on the field autocorrelation function is shown and discussed for the proposed specific examples by comparing the general results with the classical case (Lambert-Beer's law).

Spatially Resolved Spectral Powder Analysis: Experiments and Modeling

Understanding the behavior of light in granular media is necessary for determining the sample size, shape, and weight when probing using fiber optic setups. This is required for a correct estimate of the active pharmaceutical ingredient content in a pharmaceutical blend via near-infrared spectroscopy. Several strategies to describe the behavior of light in granular and turbid media exist. A common approach is the Monte-Carlo simulation of individual photons and their description using mean free path lengths for scattering and absorption. In this work, we chose a complementary method by approximating these parameters via real physical counterparts, i.e., the particle size, shape, and density and the resulting chord lengths. Additionally, the wavelength dependence of refractive indices is incorporated. The obtained results were compared with those obtained in an experimental setup that included the SAM-Spec Felin probe head by Indatech for detecting spatially resolved spectra of samples. Our method facilitates the interpretation of the acquired experimental results by contrasting the optical response, the physical particle attributes, and the simulation results.

Correlated fractional counting processes on a finite-time interval

We present some correlated fractional counting processes on a finite-time interval. This will be done by considering a slight generalization of the processes in Borges et al. (2012). The main case concerns a class of space-time fractional Poisson processes and, when the correlation parameter is equal to 0, the univariate distributions coincide with those of the space-time fractional Poisson process in Orsingher and Polito (2012). On the one hand, when we consider the time fractional Poisson process, the multivariate finite-dimensional distributions are different from those presented for the renewal process in Politi et al. (2011). We also consider a case concerning a class of fractional negative binomial processes.

Correlated fractional counting processes on a finite-time interval

We present some correlated fractional counting processes on a finite-time interval. This will be done by considering a slight generalization of the processes in Borges et al. (2012). The main case concerns a class of space-time fractional Poisson processes and, when the correlation parameter is equal to 0, the univariate distributions coincide with those of the space-time fractional Poisson process in Orsingher and Polito (2012). On the one hand, when we consider the time fractional Poisson process, the multivariate finite-dimensional distributions are different from those presented for the renewal process in Politi et al. (2011). We also consider a case concerning a class of fractional negative binomial processes.

Facile multi-dimensional profiling of chemical gradients at the millimetre scale

Tomography with a LCD/LED screen as the source of light enables multi-dimensional reconstruction of non-homogeneous samples.

A literature review and novel theoretical approach on the optical properties of whole blood

Optical property measurements on blood are influenced by a large variety of factors of both physical and methodological origin. The aim of this review is to list these factors of influence and to provide the reader with optical property spectra (250–2,500 nm) for whole blood that can be used in the practice of biomedical optics (tabulated in the appendix). Hereto, we perform a critical examination and selection of the available optical property spectra of blood in literature, from which we compile average spectra for the absorption coefficient (μ_a), scattering coefficient (μ_s) and scattering anisotropy (g). From this, we calculate the reduced scattering coefficient (μ_s′) and the effective attenuation coefficient (μ_eff). In the compilation of μ_a and μ_s, we incorporate the influences of absorption flattening and dependent scattering (i.e. spatial correlations between positions of red blood cells), respectively. For the influence of dependent scattering on μ_s, we present a novel, theoretically derived formula that can be used for practical rescaling of μ_s to other haematocrits. Since the measurement of the scattering properties of blood has been proven to be challenging, we apply an alternative, theoretical approach to calculate spectra for μ_s and g. Hereto, we combine Kramers–Kronig analysis with analytical scattering theory, extended with Percus–Yevick structure factors that take into account the effect of dependent scattering in whole blood. We argue that our calculated spectra may provide a better estimation for μ_s and g (and hence μ_s′ and μ_eff) than the compiled spectra from literature for wavelengths between 300 and 600 nm.

Light diffusion in quenched disorder: role of step correlations

We present a theoretical and experimental study of light transport in disordered media with strongly heterogeneous distribution of scatterers formed via nonscattering regions. Step correlations induced by quenched disorder are found to prevent diffusivity from diverging with increasing heterogeneity scale, contrary to expectations from annealed models. Spectral diffusivity is measured for a porous ceramic where nanopores act as scatterers and macropores render their distribution heterogeneous. Results agree well with Monte Carlo simulations and a proposed analytical model.

Comparative analysis of radiative transfer approaches for calculation of plane transmittance and diffuse attenuation coefficient of plane-parallel light scattering layers

We present an analysis of a number of different approximations for the plane transmittance Tp and diffuse attenuation coefficient Kd of a semi-infinite, unbounded, plane-parallel, and optically homogeneous layer. The maximally wide optical conditions (from the full absorption to the full scattering and from the fully forward to the fully backward scattering) were considered. The approximations were analyzed from the point of view of their physical limitations and closeness to the numerical solution of the radiative transfer equation for the plane transmittance. The main criterion for inclusion of the models for analysis was the possibility of practical use, i.e., approximations were well parameterized and included only easily measured or estimated parameters. A detailed analysis of errors for different Tp and Kd models showed that the two-stream radiative transfer Ben-David model yields the best results over all optical conditions and depths. However, the quasi-single-scattering and polynomial Gordon's approximations proved to be the best for the depths close to zero.

Holey random walks: optics of heterogeneous turbid composites

We present a probabilistic theory of random walks in turbid media with nonscattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics, and void spacings can be analytically predicted. The theory is validated using Monte Carlo simulations of light transport in heterogeneous systems in the form of random sphere packings and good agreement is found. The role of step correlations is discussed and differences between unbounded and bounded systems are investigated. Our results are relevant to the optics of heterogeneous systems in general and represent an important step forward in the understanding of media with strong (fractal) heterogeneity in particular.

Turbulence effect on cloud radiation

The effect of turbulent clustering of water droplets on radiative transfer is investigated by means of both a three-dimensional direct numerical simulation of particle-laden homogeneous isotropic turbulence and a radiative transfer simulation based on a Monte Carlo photon tracing method. The results show that turbulent clustering causes the formation of void regions of droplets and hence increases the direct transmittance. This effect decreases as the turbulent Reynolds number increases and is estimated to be negligibly small under the conditions in real clouds.

On the extinction of radiation by a homogeneous but spatially correlated random medium: comment

Some extinction laws for radiation transmitted through inhomogeneous random media were discussed by Kostinski [J. Opt. Soc. Am. A 18, 1929 (2001)] by means of a complicated use of concepts of statistical theory of fluids. We show that these extinction laws are readily obtained in terms of classical probability theory. The validity of exponential extinction laws for large observation distances (as compared with the size of inhomogeneities of a medium) is proven and emphasized. It is shown that Kostinski's results turn out to be applicable to small observation distances only, for which the concept of extinction law is hardly applicable.