Determination of g and mu using multiply scattered light in turbid media

Compact setup to determine size and concentration of spherical particles in a turbid medium

We propose a compact setup to determine the size and concentration of spherical particles in a turbid medium. A pair of plane mirrors is used to multifold the undeviated laser beam, and measure it at a detector placed close to the sample, to determine the interaction coefficient. The size of particles is uniquely determined by comparison of the scattered light from the medium, measured at two separate detectors placed at two different angular positions, with that from Monte Carlo simulations. The methodology is verified using measurements with turbid samples comprising polystyrene spheres.

Simultaneous recovery of a full set of optical properties in turbid media using incomplete P5 approximation to CW radiance

Traditional methods for determining the optical properties of turbid media are implemented in diffusive regimes, where the scattering coefficient μ_s and anisotropy factor g are inseparable due to the similarity relation for anisotropy scattering. Determining μ_s and g in addition to the absorption coefficient μ_a normally requires measurements using thin samples or media of low scattering, which are inappropriate for in vivo applications. In this work, we propose an analytical method to simultaneously recover μ_a, μ_s, and g based on the incomplete P5 approximation (P5_in) to the continuous wave (CW) radiative transport equation. The proposed method was verified using both simulated and experimental data with the relative errors less than 6.6%, 11.6%, and 8.2% for μ_a ranging 0.0071-0.0168  mm^-1, μ_s ranging 2.35-8.47  mm^-1, and g ranging 0.61-0.81, respectively. Since the P5_in-based radiance method can be easily implemented with several measurements, it is expected to be used for recovering a full set of the optical properties in vivo.

Photon diffusion near the point-of-entry in anisotropically scattering turbid media

From astronomy to cell biology, the manner in which light propagates in turbid media has been of central importance for many decades. However, light propagation near the point-of-entry in turbid media has never been analytically described, until now. Here we report a straightforward and accurate method that overcomes this longstanding, unsolved problem in radiative transport. Our theory properly treats anisotropic photon scattering events and takes the specific form of the phase function into account. As a result, our method correctly predicts the spatially dependent diffuse reflectance of light near the point-of-entry for any arbitrary phase function. We demonstrate that the theory is in excellent agreement with both experimental results and Monte Carlo simulations for several commonly used phase functions.

Scattering-phase theorem: anomalous diffraction by forward-peaked scattering media

The scattering-phase theorem states that the values of scattering and reduced scattering coefficients of the bulk random media are proportional to the variance of the phase and the variance of the phase gradient, respectively, of the phase map of light passing through one thin slice of the medium. We report a new derivation of the scattering phase theorem and provide the correct form of the relation between the variance of phase gradient and the reduced scattering coefficient. We show the scattering-phase theorem is the consequence of anomalous diffraction by a thin slice of forward-peaked scattering media. A new set of scattering-phase relations with relaxed requirement on the thickness of the slice are provided. The condition for the scattering-phase theorem to be valid is discussed and illustrated with simulated data. The scattering-phase theorem is then applied to determine the scattering coefficient μs, the reduced scattering coefficient μ's, and the anisotropy factor g for polystyrene sphere and Intralipid-20% suspensions with excellent accuracy from quantitative phase imaging of respective thin slices. The spatially-resolved μs, μ's and g maps obtained via such a scattering-phase relationship may find general applications in the characterization of the optical property of homogeneous and heterogeneous random media.

Sensitivity of spatially resolved reflectance signals to coincident variations in tissue optical properties

Canonical correlation analysis, a multivariate statistical technique, was used to investigate the degree of association between tissue optical properties and spatially resolved reflectance signals. Monte Carlo modeling was employed to simulate signals corresponding to different combinations of optical properties and these data sets were fed as input to statistical analysis. The results show that it is possible to adjust the separation and angular orientation of source and detector fibers such that the effect of a particular optical property will be augmented among coincident variations in other properties. The trends observed exhibit differences when compared with a conventional univariate sensitivity analysis in which only a single property is varied whereas all other parameters of interest are kept constant.

Determination of the optical properties of turbid media using relative interstitial radiance measurements: Monte Carlo study, experimental validation, and sensitivity analysis

Interstitial quantification of the optical properties of tissue is important in biomedicine for both treatment planning of minimally invasive laser therapies and optical spectroscopic characterization of tissues, for example, prostate cancer. In a previous study, we analyzed a method first demonstrated by Dickey et al., [Phys. Med. Biol. 46, 2359 (2001)] to utilize relative interstitial steady-state radiance measurements for recovering the optical properties of turbid media. The uniqueness of point radiance measurements were demonstrated in a forward sense, and strategies were suggested for improving performance under noisy experimental conditions. In this work, we test our previous conclusions by fitting the P3 approximation for radiance to Monte Carlo predictions and experimental data in tissue-simulating phantoms. Fits are performed at: 1. a single sensor position (0.5 or 1 cm), 2. two sensor positions (0.5 and 1 cm), and 3. a single sensor position (0.5 or 1 cm) with input knowledge of the sample's effective attenuation coefficient. The results demonstrate that single sensor radiance measurements can be used to retrieve optical properties to within approximately 20%, provided the transport albedo is greater than approximately 0.9. Furthermore, compared to the single sensor fits, employing radiance data at two sensor positions did not significantly improve the accuracy of recovered optical properties. However, with knowledge of the effective attenuation coefficient of the medium, optical properties can be retrieved experimentally to within approximately 10% for an albedo greater or equal to 0.5.

Backscattered stokes vectors of turbid media: anisotropy factor and reduced scattering coefficient estimation

Optical characterization of biological tissues is of real interest to improve medical diagnosis and in particular in the detection of precancerous tissues. The reduced scattering coefficient micro's and the absorption coefficient microa are the most commonly retrieved coefficients. Some methods also allow to obtain the anisotropy factor g, but only few of them are non-invasive. We propose a new non-invasive method allowing the estimation of the anisotropy factor and the reduced scattering coefficient. This method is based on the image analysis of the Q-element of Stokes vector backscattered from the turbid medium. These Q-element images show specific patterns depending on g, and micro's is determined by the size of the patterns. Therefore the use of Fourier Descriptors (FD) on simulated and experimental data, to discriminate the specific geometrical features of the Q-element, enabled us to determine the anisotropy factor and the scattering coefficient.

Light scattering regimes along the optical axis in turbid media

We inject an angularly collimated laser beam into a scattering medium of a nondairy creamer-water solution and examine the distribution of the scattered light along the optical axis as a function of the source-detector spacing. The experimental and simulated data obtained from a Monte Carlo simulation suggest four regimes characterizing the transition from unscattered to diffusive light. We compare the data also with theoretical predictions based on a first-order scattering theory for regions close to the source, and with diffusionlike theories for larger source-detector spacings. We demonstrate the impact of the measurement process and the effect of the unavoidable absorption of photons by the detection fiber on the light distribution inside the medium. We show that the range of validity of these theories can depend on the experimental parameters such as the diameter and acceptance angle of the detection fiber.

Nonperturbative retrieval of the scattering strength in one-dimensional media

We examine several approaches on how to use the transmission and reflection amplitudes as functions of the modulation frequency of the laser's intensity to reconstruct the position-dependent scattering coefficient for a simple turbid medium. We explore the region where the contrast between the coefficient and its spatially averaged value is large enough such that perturbative methods fail. We show that in the case of a transillumination geometry, the knowledge of the transmission profile alone is not sufficient for unique image reconstruction, whereas the reflection spectrum allows for a complete inversion. We demonstrate the invertibility for media sampled at only a few positions.

Velocity half-sphere model for multiple light scattering in turbid media

We extend the traditional diffusion theory by distinguishing between the energy radiance in the forward and backward directions at each point in space. This approach leads to a new effective source for the diffusion equation that is nonzero for an anisotropic light source. It differs significantly from the diffusion theory for short source-detector spacings. We derive an analytical solution for the two lowest-order velocity moments of the radiance.