Estimation of optical properties of turbid media: experimental comparison of spatially and temporally resolved reflectance methods

We compare two methods for the optical characterization of turbid media. The estimates of the absorption and reduced scattering coefficients (mu(a) and mu(')(s)) by a spatially resolved method and a time-resolved method are performed on tissue-like phantoms. Aqueous suspension of microspheres and Intralipid are used as scattering media with the addition of ink as an absorber. mu(')(s) is first measured on weakly absorbing media. The robustness of these measurements is then tested with respect to a variation of mu(a). The spatially resolved method gave more accurate estimates for mu(')(s) whereas the time-resolved method gave better results for mu(a) estimates.     

Scaling method for fast Monte Carlo simulation of diffuse reflectance spectra from multilayered turbid media

A scaling Monte Carlo method has been developed to calculate diffuse reflectance from multilayered media with a wide range of optical properties in the ultraviolet-visible wavelength range. This multilayered scaling method employs the photon trajectory information generated from a single baseline Monte Carlo simulation of a homogeneous medium to scale the exit distance and exit weight of photons for a new set of optical properties in the multilayered medium. The scaling method is particularly suited to simulating diffuse reflectance spectra or creating a Monte Carlo database to extract optical properties of layered media, both of which are demonstrated in this paper. Particularly, it was found that the root-mean-square error (RMSE) between scaled diffuse reflectance, for which the anisotropy factor and refractive index in the baseline simulation were, respectively, 0.9 and 1.338, and independently simulated diffuse reflectance was less than or equal to 5% for source-detector separations from 200 to 1500 microm when the anisotropy factor of the top layer in a two-layered epithelial tissue model was varied from 0.8 to 0.99; in contrast, the RMSE was always less than 5% for all separations (from 0 to 1500 microm) when the anisotropy factor of the bottom layer was varied from 0.7 to 0.99. When the refractive index of either layer in the two-layered tissue model was varied from 1.3 to 1.4, the RMSE was less than 10%. The scaling method can reduce computation time by more than 2 orders of magnitude compared with independent Monte Carlo simulations.     

Static and dynamic properties of highly turbid media determined by spatially resolved diffusive-wave spectroscopy

We show that spatially resolved backscattering can be used for simultaneous measurements of static and dynamic properties of highly turbid media. The spatial variation of the backscattered intensity gives access to the transport men free path. The decay of the temporal intensity-intensity correlation function depends on the point of observation. This property can be used to probe complex dynamics with several time scales. The implementation of the method and the data analysis are tested on concentrated suspensions of polystyrene spheres.     

Experimental and simulated angular profiles of fluorescence and diffuse reflectance emission from turbid media

Given the wavelength dependence of sample optical properties and the selective sampling of surface emission angles by noncontact imaging systems, differences in angular profiles due to excitation angle and optical properties can distort relative emission intensities acquired at different wavelengths. To investigate this potentiality, angular profiles of diffuse reflectance and fluorescence emission from turbid media were evaluated experimentally and by Monte Carlo simulation for a range of incident excitation angles and sample optical properties. For emission collected within the limits of a semi-infinite excitation region, normalized angular emission profiles are symmetric, roughly Lambertian, and only weakly dependent on sample optical properties for fluorescence at all excitation angles and for diffuse reflectance at small excitation angles relative to the surface normal. Fluorescence and diffuse reflectance within the emission plane orthogonal to the oblique component of the excitation also possess this symmetric form. Diffuse reflectance within the incidence plane is biased away from the excitation source for large excitation angles. The degree of bias depends on the scattering anisotropy and albedo of the sample and results from the correlation between photon directions upon entrance and emission. Given the strong dependence of the diffuse reflectance angular emission profile shape on incident excitation angle and sample optical properties, excitation and collection geometry has the potential to induce distortions within diffuse reflectance spectra unrelated to tissue characteristics.     

Semi-analytical Monte Carlo simulation for time-resolved light propagating in multilayered turbid media

In this study, a Monte Carlo (MC) method for time-resolved light scattering from multilayered turbid media (SMCML) has been developed. This method is particularly suitable for simulating light backscattering from layered media and receiving the time-resolved signal in a finite sensor area, such as ocean detection, photomedicine and photobiology. The classical semi-analytical MC method requires the scattering events to be located in a single-layer medium. To address the multilayer problem, the energy loss mechanism of photons propagating in tissue was analyzed in this study. According to the energy contribution to the detector, only photons that contribute significantly were considered. Simulations were conducted for stochastic turbid media with different optical parameters. Temporal profiles of the echo signal were obtained with a satisfactory convergence. Compared to the classical MC method, the SMCML method can dramatically reduce the computation time by more than two orders of magnitude.     

Photomodulated reflectance and transmittance: optical characterisation of novel semiconductor materials and device structures

Photomodulation spectroscopy, in reflection and transmission modes, is presented here as a powerful non-destructive optical technique for the investigation of fundamental physical properties of new semiconductor materials and complex micro- and nano-structures. The abilities of photoreflectance and phototransmittance in application to many kinds of semiconductor structures are demonstrated. The following aspects are discussed: (1) separation of the optical response and built-in electric field determination in different depths of the sample by a selection of the pump beam wavelength; (2) electric field in δ-doped structures by an application of a fast Fourier transformation; (3) electron concentration dependence of the band gap related transitions in wurtzite GaN epitaxial layers; (4) comparison of different spectroscopic techniques used for investigations of InGaSb/GaSb quantum wells within 1.5-2 μm spectral region; (5) quantum well intermixing effects in InGaAsP/InP 1.55-μm laser structures; (6) photomodulation spectroscopy of self-assembled quantum dots.     

Real-time absorption and scattering characterization of slab-shaped turbid samples obtained by a combination of angular and spatially resolved measurements

We present a fast and accurate method for real-time determination of the absorption coefficient, the scattering coefficient, and the anisotropy factor of thin turbid samples by using simple continuous-wave noncoherent light sources. The three optical properties are extracted from recordings of angularly resolved transmittance in addition to spatially resolved diffuse reflectance and transmittance. The applied multivariate calibration and prediction techniques are based on multiple polynomial regression in combination with a Newton--Raphson algorithm. The numerical test results based on Monte Carlo simulations showed mean prediction errors of approximately 0.5% for all three optical properties within ranges typical for biological media. Preliminary experimental results are also presented yielding errors of approximately 5%. Thus the presented methods show a substantial potential for simultaneous absorption and scattering characterization of turbid media.     

Spectrophotometer for measuring spectral reflectance and transmittance

The development of a computer-controlled spectrophotometer that enables measurement of spectral transmittance, reflectance, and optical loss of thin-film specimens is discussed. We also describe the design and testing procedure of the spectrophotometer, incorporating test sample performance data. In the visible region the overall photometric accuracy is verified to be 0.1% and 0.2% for transmittance and reflectance, respectively. The wavelength scale is accurate to within 0.5 nm with a reproducibility of 0.1 nm.     

Simple algorithm for the measurement of absorption coefficients of a two-layered medium by spatially resolved and time-resolved reflectance

An inversion procedure for the recovery of absorption coefficients of a two-layered semi-infinite diffusive medium by use of time-resolved reflectance measured at two different source-detector distances is proposed. The inversion procedure is based on the property of the photon diffusion equation; i.e., the solution of the diffusion equation for the time-resolved reflectance measured at a longer source--detector distance coincides with that measured at a shorter one by a proper temporal, spatial, and intensity transformation. This inversion procedure, used together with the results of one set of Monte Carlo simulations, is validated as working well when the values of the scattering coefficients of the two layers and the thickness of the first layer are within a range of interest in tissue optics.     

Dedicated spectrophotometer for localized transmittance and reflectance measurements

A dedicated spectrophotometer is built to achieve localized transmittance and reflectance measurements. The spatial resolution can be chosen from 100 microm to 2 mm, the spectral resolution from 0.5 to 5 nm, and the spectral range from 400 to 1700 nm. This apparatus can be used to study the index and thickness uniformity on single layers to determine and optimize the characteristics of the deposition chamber. It can also be used to measure the spatial variations of optical properties of intended nonuniform coatings such as linear variable filters.     

Hyperspectral diffuse reflectance imaging for rapid, noncontact measurement of the optical properties of turbid materials

We present a method and technique of using hyperspectral diffuse reflectance for rapid determination of the optical properties of turbid media. A hyperspectral imaging system in line scanning mode was used to acquire spatial diffuse reflectance profiles from liquid phantoms made up of absorbing dyes and fat emulsion scatterers over the spectral range of 450-1000 nm instantaneously. The hyperspectral reflectance data were analyzed by using a steady-state diffusion approximation model for semi-infinite homogeneous media. A calibration procedure was developed to compensate the nonuniform instrument response of the imaging system, and a curve-fitting algorithm was used to extract absorption and reduced scattering coefficients (mua and mus', respectively) for the phantoms in the wavelength range from 530 to 900 nm. The hyperspectral imaging system gave good measures of mua and mus' for the phantoms with average fitting errors of 12% and 7%, respectively. The hyperspectral imaging technique is fast, noncontact, and easy to use, which makes it especially suitable for measurement of the optical properties of turbid liquid and solid foods.     

Scattering and absorption cross sections of light diffusing materials retrieved from reflectance and transmittance spectra of collimated radiation

Four-flux radiative transfer models have been extensively used to describe reflectance and transmittance (R&T) spectra of light scattering and absorbing (S&A) media. Solutions to the differential equations corresponding to the collimated fluxes are obtained by subsequent application of boundary conditions. Explicit expressions for the collimated R&T of light are reported, when considering a light S&A medium contained between two glass slides, an experimental arrangement which is appropriate for liquid suspensions and viscous matrices containing solid particles. A spectral simulated annealing method is applied to retrieve, from measured R&T spectra of collimated light under normal incident radiation, the scattering and absorption coefficients of the composite medium. First, the accuracy of the method is established by applying it to synthetic collimated R&T data. Secondly, we apply the method to experimental data and use it to determine the S&A coefficients of a layer of TiO₂ particles dispersed in a PVP/water matrix.     

Investigation of two-layered turbid media with time-resolved reflectance

Light propagation in two-layered turbid media that have an infinitely thick second layer is investigated with time-resolved reflectance. We used a solution of the diffusion equation for this geometry to show that it is possible to derive the absorption and the reduced scattering coefficients of both layers if the relative reflectance is measured in the time domain at two distances and if the thickness of the first layer is known. Solutions of the diffusion equation for semi-infinite and homogeneous turbid media are also applied to fit the reflectance from the two-layered turbid media in the time and the frequency domains. It is found that the absorption coefficient of the second layer can be more precisely derived for matched than for mismatched boundary conditions. In the frequency domain, its determination is further improved if phase and modulation data are used instead of phase and steady-state reflectance data. Measurements of the time-resolved reflectance were performed on solid two-layered tissue phantoms that confirmed the theoretical results.     

Multiple path analysis of reflectance from turbid media

A novel method to calculate the reflectance of light from a turbid medium is presented. The method takes an approach similar to that of the Beer-Lambert law, where the intensity of light is attenuated by an exponential factor involving the path length and the absorption coefficient. Due to scatter, however, there are many path lengths; in the present method all possible path lengths are weighted by their probabilities and summed over. A path length probability density is derived by considering a photon random walk through the medium. The result is a simple expression for the reflectance based on the physical properties of the medium.     

Determination of the thickness of metal coatings on granular diamond materials by spatially resolved optical methods

The embedding of surface-modified granulates into metallic matrices is a promising way to optimize the interface matrix/granulate in respect to mechanical and thermal properties. In the case of surface modification by coating, a reliable determination of the coating thickness on granulates is desirable, since the interface properties may depend on it to a critical extent. This paper proposes a simple method to determine the thickness of transparent metal coatings on diamond substrates. Diamond granulates with grain sizes between 100 and 120 μm were coated with molybdenum in an intermixing device which allows reasonable film uniformity on granulates. The deposition method was single source DC magnetron sputtering with argon as working gas. By comparing the transmission of the uncoated and coated diamonds with an optical scanner, the coating thickness could be determined from the known extinction coefficient. A good correlation between the measured film thicknesses and the deposition time was achieved. It can be concluded therefore, that the presented method is a viable and cost-efficient way for the determination of the average thickness of transparent metallic coatings on a sample of transparent granular substrates, with an estimated minimum and maximum measurable thickness of 2.5 nm and 15 nm respectively for molybdenum.     

Spatial shift of spatially modulated light projected on turbid media

This work extends modulated imaging, a recently developed technique based on the projection of structured light on a turbid medium that is able to measure optical properties of the high-scattering medium and perform tomography. We observe that structured light obliquely projected on a turbid medium undergoes a spatial shift during propagation. We propose a method to measure the spatial phase shift of a sinusoidal fringe pattern projected in a turbid medium, and we present a model derived from the diffusion approximation to describe the light propagation. Experimental validation by measurements performed on liquid phantoms is presented.     

Solid state spatially resolved 1H and 19F nuclear magnetic resonance spectroscopy of dental materials by stray-field imaging

As part of a program to evaluate the use of stray-field magnetic resonance microimaging (STRAFI) in dental materials research spatially resolved nuclear magnetic resonance (NMR) for solid dental cements has been investigated. By applying a quadrature echo pulse sequence to a specimen positioned in the stray-field of a NMR spectrometer superconducting magnet the magnetic resonance within a thin slice was obtained. The specimen was stepped through the field in 500 m increments to record ¹ and ¹⁹F profiles and T₂ values at each point. The specimens were fully cured cylinders made from four types of restorative material (glass ionomer, resin modified glass ionomer, compomer, composite). The values for F¹⁹T₂ varied with material type and reflected the nature of the matrix structure. For all materials containing ¹⁹F in the glass two values were calculated for ¹⁹F T₂, one short and one long. These were relatively invariant. Solid state magic angle spinning (MAS)-NMR showed that they came from the glass. This suggests that a proportion of the element is relatively mobile (in a glass phase) and the remainder is more tightly bound (in a compound dispersed in the glass). This demonstration, that NMR microimaging of both ¹H and ¹⁹F in solid dental cements is possible, opens up exciting new possibilities for investigating the distribution of these elements (in particular fluorine) in solid dental materials. ©©1999©Kluwer Academic Publishers