Average Photon Path Length Research Articles

Estimation of Photon Path Length and Penetration Depth in Articular Cartilage Zonal Architecture Over the Therapeutic Window.

The key characteristics of light propagation are the average penetration depth, average maximum penetration depth, average maximum lateral spread, and average path length of photons. These parameters depend on tissue optical properties and, thus, on the pathological state of the tissue. Hence, they could provide diagnostic information on tissue integrity. This study investigates these parameters for articular cartilage which has a complex structure. We utilize Monte Carlo simulation to simulate photon trajectories in articular cartilage and estimate the average values of the light propagation parameters (penetration depth, maximum penetration depth, maximum lateral spread, and path length) in the spectral band of 400-1400 nm based on the optical properties of articular cartilage zonal layers and bulk tissue. Our findings suggest that photons in the visible band probe a localized small volume of articular cartilage superficial and middle zones, while those in the NIR band penetrate deeper into the tissue and have larger lateral spread. In addition, we demonstrate that a simple model of articular cartilage tissue, based on the optical properties of the bulk tissue, is capable to provide an accurate description of the light-tissue interaction in articular cartilage. The results indicate that as the photons in the spectral band of 400-1400 nm can reach the full depth of articular cartilage matrix, they can provide viable information on its pathological state. Therefore, diffuse optical spectroscopy holds significant importance for objectively assessing articular cartilage health. In this study, for the first time, we estimate the light propagation parameters in articular cartilage.

Evolution of transmitted depolarization in diffusely scattering media.

We performed Mueller matrix Monte Carlo simulations of the propagation of optical radiation in diffusely scattering media for collimated incidence and report the results as a function of thickness and the angle subtended by the detector. For sufficiently small thickness, a fraction of the radiation does not undergo any scattering events and is emitted at zero angle. Thus, for a very small detector angle, the measured signal will indicate mostly the attenuation of the coherent contribution, while for larger angles, the diffuse scattering radiation will contribute significantly more. The degree to which the radiation is depolarized thus depends on the angle subtended by the detector. A three-stream model-where the coherent radiation, the forward diffusely scattered radiation, and the backward scattered radiation are propagated according to the differential Mueller matrix formalism-is introduced and describes the results from the Monte Carlo simulations and the results of measurements well. This scatter-based model for depolarization in diffusely scattering media is an alternative to that based upon elementary fluctuation theory applied to a single propagation stream. Results for average photon path length, determined from the Monte Carlo simulations, suggest that applying fluctuation theory to photon path length may unify the two approaches.

Random laser materials: from ultrahigh efficiency to very low threshold (Anderson localization)

Random lasers hold the premise for cheap coherent light sources that can be miniaturized and molded into any shape and used for speckle-free imaging in biology, remote sensing, display technology, encrypting, cancer detection and distributed amplification. However, they require improvements specifically in terms of efficiency and low emission threshold. This work details for the first time a strategy for increasing the efficiency of a random laser that consists in using smaller particles, trapped between large particles to serve as absorption and gain centers whereas the large particles control mainly the light diffusion into the sample. A record slope efficiency of more than 50% was achieved using yttrium vanadate particles with mean particle size of 54 μm by optimizing the distribution of the polydispersed particles. In addition, random lasing with very low emission threshold (0.24 mJ/cm2) is also reported in a strongly disordered optical medium that is in the transition regime to Anderson localization composed by a colloidal suspension of core–shell TiO2@Silica nanoparticles in ethanol solution of rhodamine 6G. A promising method called fraction of absorbed pump power allowed us to infer the emission threshold for localized modes (peaks mode). The classical super-fluorescence band (ASE) of the random laser was measured separately by collecting the emission at the back of the samples, showing a linear dependence with pumping fluence without gain depletion. The intensity of peaks during Anderson transition is approximately equal within a broad frequency range, indicating suppression of the interaction between the peak modes. The random lasers have been characterized by measurements of backscattering cone, absorption and reflection measurement, transport mean free path, average photon path length and fill fractions.

Analysis of the average photon path length between two consecutive reflections from the cavity walls.

In this paper a general theoretical analysis of the average photon path length between two consecutive photon reflections from the cavity walls has been presented. The presented analysis relies only on the energy conservation law and the assumption of the uniform photon distribution within the cavity volume. The obtained general result coincides with the solution previously obtained but under more stringent conditions.

Photodegradation by a Heterogeneous Mixture of Micro-Sized Anatase and Truncated Rhomboid Anatase Hollow Spheres

TiO2 has attracted immense attention because of its unique properties, which include excellent photostability, ecofriendliness, and low cost. It has a wide range of applications in photocatalysis, dye-sensitized solar cells (DSSCs), lithium-ion storage, and electrochromic devices. TiO2 is the most studied photocatalyst because of the high oxidation capacity of its holes. A general photocatalytic procedure involves three main processes: irradiation-induced formation of electrons and holes, bulk diffusion of electrons and holes to the surface, and a surface reaction of the photogenerated carriers with the pollutant. Increasing the light harvesting, reducing the charge recombination, and increasing the surface reactivity are three methods to improve photocatalytic efficiency. To increase light harvesting, TiO2 has been treated by using a photosensitive material or doped to extend its light absorbance into the visible-light region. However, such additional treatment also causes thermal or crystal instability and the trapping of carriers, which considerably reduces efficiency. However, Mie scattering by a submicron structure increases the average photon path-length, which markedly increases light harvesting. A hollow sphere structure with a strong scattering effect and high surface area was used to enhance photocatalytic activity. To reduce the recombination of electrons and holes in the photocatalytic process, heterogeneous structures have been extensively adopted against self-recombination. Generally, photoexcited electrons are transferred to the interface of the heterogeneous structure, which results in the efficient separation of electrons and holes. Commercial P25 (particles comprised of 75% anatase and 25% rutile) is an effective photocatalyst owing to the synergy between anatase and rutile. Additionally, our group has reported an excellent photocatalyst that is effective over a wide range of pH values, which was formed by mixing microand nano-sized anatases. Anatase of different sizes has different flat-band states. Mixing TiO2 particles with various band positions facilitates the transfer of electrons therein, which results in the separation of electrons and holes and greatly improves the photocatalytic performance. Additionally, the atomic arrangement and Ti coordination at the surface strongly influence the transfer of photoexcited carriers at the surface and the adsorption/desorption between the photocatalyst and the pollutant molecules. Numerous studies have reported that anatase TiO2 with exposed {001} facets exhibits excellent photocatalytic activity. This study attempts to elucidate the details of the photocatalytic reaction. The aforementioned three strategies are used to improve the photocatalytic efficiency. Highly uniform hollow anatase TiO2 submicron spheres with exposed {001} and {101} Highly uniform hollow spheres were assembled from truncated rhomboid anatase TiO2 nanoparticles (HS), which were synthesized from the hydrothermal treatment of a NaF solution by using amorphous TiO2 spheres as a precursor and template. The submicron hollow spheres with highly photocatalytic active surfaces exhibited excellent photocatalytic behavior. In this investigation, the factors that enhanced the photocatalytic performance were examined in terms of light harvesting, photoefficiency, and reaction activity. The photocatalytic performance was increased by a factor of approximately 1.5 for the scattering structure of submicron hollow spheres than that of nanofragments of submicron hollow sphere powder. The rate constant of anatase TiO2 with specific photoactive surfaces at {001} and {101} was approximately six times higher than that of randomly exposed TiO2 particles. Furthermore, a heterogeneous mixture of the submicron hollow spheres and micro-sized anatase TiO2 (HS@micro-sized TiO2) prohibited electron–hole recombination in the catalyst during the degradation reaction. The rate constant for the heterojunction system was 3.4 times greater than that of the individual constituents. The rate constant for HS@micro-sized TiO2 (k=0.175 min ) was 1.8 times larger than that of commercial P25 (k=0.099 min ). HS@micro-sized TiO2 is a promising photocatalytic material.

Determination of the effect of source intensity profile on speckle contrast using coherent spatial frequency domain imaging

Laser Speckle Imaging (LSI) is fast, noninvasive technique to image particle dynamics in scattering media such as biological tissue. While LSI measurements are independent of the overall intensity of the laser source, we find that spatial variations in the laser source profile can impact measured flow rates. This occurs due to differences in average photon path length across the profile, and is of significant concern because all lasers have some degree of natural Gaussian profile in addition to artifacts potentially caused by projecting optics. Two in vivo measurement are performed to show that flow rates differ based on location with respect to the beam profile. A quantitative analysis is then done through a speckle contrast forward model generated within a coherent Spatial Frequency Domain Imaging (cSFDI) formalism. The model predicts remitted speckle contrast as a function of spatial frequency, optical properties, and scattering dynamics. Comparison with experimental speckle contrast images were done using liquid phantoms with known optical properties for three common beam shapes. cSFDI is found to accurately predict speckle contrast for all beam shapes to within 5% root mean square error. Suggestions for improving beam homogeneity are given, including a widening of the natural beam Gaussian, proper diffusing glass spreading, and flat top shaping using microlens arrays.

The PANDA time-of-propagation disc DIRC

A novel Cherenkov detector, a time-of-propagation (TOP) disc DIRC, is proposed for particle identification at the PANDA experiment at the future FAIR facility. It measures Cherenkov light that is generated and internally reflected in a 2 cm thick fused silica plate. The Cherenkov angle is reconstructed from a time-of-propagation measurement at the rim of the disc of individual Cherenkov photons with a resolution of better than 50 ps. Dichroic mirrors at the rim of the disc fulfil two purposes. They allow for a selection of certain wavelength bands and thus are used to reduce dispersive smearing, and they enlarge the average photon path length by reflection and thus improve the separation power of the detector. A reconstruction algorithm has been developed to assign the detected photons to a given particle trajectory. Using a likelihood method, the algorithm calculates particle type probabilities for each track. The detector is expected to separate pions and kaons up to a momentum of ∼ 4 GeV/c. Additional focussing elements at the rim of the disc are proposed to enhance the signal to background separation of the detector.

Remote Sensing of Cloud-Top Pressure Using Moderately Resolved Measurements within the Oxygen A Band—A Sensitivity Study

AbstractReflected solar radiation measured by the Medium Resolution Imaging Spectrometer (MERIS) on the Environmental Satellite (Envisat) is currently used within the European Space Agency’s ground segment for the retrieval of cloud-top pressure. The algorithm is based on the analysis of the gaseous absorption of solar radiation in the oxygen A band at 761 nm. The strength of absorption is directly related to the average photon pathlength, which is mainly determined by the cloud-top pressure. However, it additionally depends on surface and cloud properties, like cloud thickness and microphysics. The interpretation of the measurements is further complicated by the temperature dependence of the absorption line shapes and the sensitivity to the spectral properties of the spectrometer like spectral position and width. This paper is focused on results of sensitivity studies using the Matrix Operator Model (MOMO) radiative transfer model that examine the most important parameters affecting the measurements of MERIS or similar instruments. The cloud-top pressure retrieval scheme is briefly presented. An analysis of the information content and the degrees of freedom of measurements within the oxygen A band is included in this study.

The Retrieval of Land Surface Pressure from MERIS Measurements in the Oxygen A Band

AbstractMeasurements of the Medium-Resolution Imaging Spectrometer (MERIS) on the Environmental Satellite (Envisat) are used for the retrieval of surface pressure above land and ice surfaces. The algorithm is based on the exploitation of gaseous absorption in the oxygen A band at 762 nm. The strength of absorption is directly related to the average photon pathlength, which in clear-sky cases above bright surfaces is mainly determined by the surface pressure, with minor influences from scattering at aerosols.Sensitivity studies regarding the influences of aerosol optical thickness and scale height and the temperature profile on the measured radiances are presented. Additionally, the sensitivity of the retrieval to the accuracy of the spectral characterization of MERIS is quantified. The algorithm for the retrieval of surface pressure (SPFUB) is presented and validated against surface pressure maps constructed from ECMWF sea level pressure forecasts in combination with digital elevation model data. The accuracy of SPFUB was found to be within 10 hPa above ice surfaces at Greenland and 15 hPa above desert and mountain scenes in northern Africa and southwest Asia. In a case study above Greenland the accuracy of SPFUB could be enhanced to be better than 3 hPa by spatial averaging over areas of 40 km × 40 km.

Noninvasive Characterization of Pharmaceutical Solids by Diode Laser Oxygen Spectroscopy

Characterization of solid pharmaceuticals, ranging from monitoring of solid-state reactions to understanding tablet dissolution, is of great interest for pharmaceutical science. The quality of the finished product highly depends on knowledge about the pharmaceutical materials used and the different unit operations involved in manufacturing of pharmaceuticals. Thus, availability of appropriate and reliable tools for measurements of physical and chemical properties of drug materials in situ during chemical and physical processing is a key for optimized processing. In early stages of pharmaceutical development a whole range of techniques for characterization of the solid state is available, addressing, for example, particle size and shape, density, porosity, calorimetry, thermo-mechanical properties, specific area, and crystallinity. However, most of these techniques are slow and not well suited for fast laboratory-based or process applications. Process analytical technology (PAT) is a term describing a holistic approach to pharmaceutical manufacturing based on in-depth understanding through advanced process sensors and modeling tools. In order to succeed with this, new tools are needed, e.g., with capability to directly measure physico-chemical attributes in situ of the mechanical process. In this context, tools based on spectroscopic techniques offer obvious advantages owing to their speed, compactness, versatility, and ability to perform noninvasive analysis. By employing the spectroscopic technique referred to as gas in scattering media absorption spectroscopy (GASMAS), it is possible to extract information related to gas dispersed within highly scattering (turbid) materials. In our case, the key is contrast between the sharp (GHz) absorption features of molecular oxygen located around 760 nm and the broad absorption features related to tablet bulk material. The technique is based on high-resolution diode laser absorption spectroscopy, and its main principle is illustrated in Fig. 1. Light is injected into a highly scattering sample, often utilizing optical fibers. The actual path length distribution of transmitted photons will depend on the scattering properties of the sample. Due to significant multiple scattering, the average photon path length greatly exceeds sample dimensions. For example, the average path length of photons that have traveled through a pharmaceutical tablet typically exceeds 10 cm. During passages through air-filled pores, photons in resonance with an absorption line in the A-band of molecular oxygen can be absorbed. Oxygen absorption can be distinguished from bulk absorption due to the extremely narrow absorption features (GHz) exhibited by free gases. To resolve such narrow features, high-resolution spectroscopy must be employed. The resulting absorption signal depends on both the oxygen content and the scattering properties (photons path lengths) of the sample. Indirectly, it is thus related to mechanical properties such as porosity and particle size. The GASMAS technique has previously been used to study the gas content in, for example, polystyrene foam, wheat flour, granulated salt, wood materials, fruit, and human sinuses. Gas exchange dynamics has been studied by placing samples of wood and fruit in nitrogen atmospheres and monitoring the re-invasion of oxygen. In this paper we show the potential of using GASMAS for determination of physical and structural parameters of pharmaceutical solids. We present results from a study of pharmaceutical tablets made from two different sieve fractions (particle size distributions) and with different compression forces. In addition, the prospects of a broader use of this technique for pharmaceutical analysis are discussed.

Energy resolution and absolute detection efficiency for LSO crystals: A comparison between Monte Carlo simulation and experimental data

Non-proportionality between energy deposition and scintillation light production in a scintillator and transport of scintillation photons in the detector have been introduced in a Geant4-based simulation code. Simulation and experimental results were compared for samples of LSO detectors: absolute detector efficiency and energy resolution obtained from simulation are consistent with the experimental data. We also studied the average path length of scintillation photons in the detector and its contribution to the time resolution.

Cloud‐top pressure retrieval using the oxygen A‐band in the IRS‐3 MOS instrument

Backscattered solar radiation as measured by MOS (Modular Optoelectronical Scanner) on the IRS3 (Indian Remote sensing Satellite 3) has been used in an algorithm to retrieve cloud top pressure. The algorithm uses a radiance ratio between absorbing channels in the Oxygen‐A absorption band at 761 nm and a window channel at 750 nm. The ratios are directly related to the average photon path length, which is mainly determined by the cloud top pressure. This paper presents the principles of the retrieval scheme, results of a sensitivity study and a first validation using radiosondes.

Monte Carlo Simulation of Near Infrared Reflectance Spectroscopy in the Wavelength Range from 1000 nm to 1900 nm

We have calculated the characteristics of reflected near infrared light, which is incident on the skin surface, scattered in the skin tissue and detected, in the wavelength range from 1000 nm to 1900 nm. We have used a Monte Carlo method to calculate the propagation path, the average photon visit depth, the average photon path length, etc. for the cases of short source-detector distances, to which the isotropic scattering approximation cannot be applied. An experiment to validate the simulation results was also conducted using a liquid phantom.

Optical path-length spectroscopy of incipient caries lesions in relation to quantitative light-induced fluorescence and lesion characteristics.

A basic understanding of the light-scattering processes that take place inside the dental tissue (either sound or carious) is obtained both with measurements of the photon path-length distribution of light inside such media and with Monte Carlo simulations. Furthermore, the following is investigated: the correlations between different momenta of the photon path-length distribution of light inside caries lesions, the fluorescence loss determined with quantitative light-induced fluorescence, and/or the demineralization and depth of caries lesions determined with transversal microradiography. It is concluded that (i) the light paths inside both carious and sound enamel are considerably influenced by the refractive-index contrast at the tooth surface; (ii) contrary to a previous hypothesis, the fluorescence loss is larger in lesions in which the average photon path length is longer; (iii) very good correlations are obtained between the optical characteristics and the physical parameters of lesions when the optical measurements are performed such that there is high refractive contrast at the tooth surface.

Cloud modulation of zenith sky oxygen photon path lengths over Boulder, Colorado: Measurement versus model

Cloudy sky average photon path lengths were measured using the gamma band of oxygen near 628 nm on many days over Boulder, Colorado, using a zenith‐looking spectrograph with a resolution of 0.8 nm. The approach allows accurate measurement of the average photon path length. Days characterized by relatively extensive cloud cover are examined here, which exhibit very large path length variations as the cloud fields overhead evolve. The ability of a plane parallel line‐by‐line model with a single uniform cloud layer to predict the measured O2 path lengths has been tested by constraining the model to the (independently) observed surface irradiance. Overall, its performance is quite good, which demonstrates that the relationship between the diffuse transmission by clouds and the average photon path length is consistent with plane parallel radiative transfer calculations for the conditions studied. Thus large errors in the cloud radiative transfer of such models, as suggested by some recent cloud absorption measurements, are not supported by this study. Furthermore, direct observations in the blue and red spectral regions do not support even a 1% differential absorption between these spectral regions.

Measurement of the average path length of photons in samples by self-attenuation of X-rays

For homogeneous samples a relation between the average path length of photons detected in full-energy peaks in the spectra of X- and gamma-rays and the counting efficiency is derived for an arbitrary sample-detector geometry. An experimental method of measuring the average path length in the samples is presented. The results of such measurements are compared to the calculated average path lengths and discussed in terms of self-attenuation factors.

Photon transport in luminescent solar concentrators

The theory of radiative energy transfer in the stationary state in a reflecting luminescent layer is applied to solve the problem of photon transport in planar single dye luminescent solar concentrators. Efficiency yields of reabsorption and reemission processes are investigated. The optical efficiency of the collector is increased by secondary and higher reemission processes, but decreased by the reabsorption of photons transported through the concentrator. The average optical path length of luminescent photons is introduced, and the transported spectral photon density at the edges is calculated and determined experimentally. The results permit the conclusion that the mean photon transport length is proportional to the square root of surface area of the concentrator for all geometries.

Multiple-scattering transmission and an effective average photon path length of a plane-parallel beam in a homogeneous medium

A two-stream radiative transfer model is used to derive expressions for the multiple-scattered transmitted flux (including single-scattering contributions) and the total effective average photon path length on transmission of a normally incident plane-parallel beam on a homogeneous layer characterized by the optical depth, the single-scattering albedo, and the asymmetry parameter of the scatterers. The results are simple analytical expressions that are useful for modifying the Beer-Lambert transmission law for a thick scattering medium in which the multiple-scattering contribution to the transmission is not negligible.

Average photon path-length in isotropically scattering finite atmospheres

The determination of the average path-length of photons in a finite isotropically scattering plane-parallel homogeneous atmosphere is discussed. To solve this problem we have used the kernel approximation method which easily allows us to find the derivatives of the intensity with respect to optical depth, optical thickness and albedo of single scattering.

Average photon path-length of radiation emerging from finite atmospheres

The determination of the average path-length of photons emerging from a finite planeparallel atmosphere with molecular scattering is discussed. We examine the effects of polarisation on the average path-length of the emergent radiation by comparing the results with those obtained for the atmosphere where the scattering obeys the scalar Rayleigh function. Only the axial radiation field is considered for both cases.