Vertex/propagator model for least-scattered photons traversing a turbid medium

The least-scattered photons that arrive at a detector through highly scattering tissues have the potential to image internal structures, functions, and status with high imaging resolution. In contrast, optical diffusing tomography is based on the use of the late-arriving photons, which have been diffusely scattered, leading to very low imaging resolution. A good model of the early-arriving photons, i.e., the least-scattered photons, may have a significant effect on the development of imaging algorithms and a further understanding of imaging mechanisms within current high-resolution optical-imaging techniques. We describe a vertex/propagator approach that attempts to find the probabilities for least-scattered photons traversing a scattering medium, based on analytical expressions for photon histories. The basic mathematical derivations for the model are outlined, and the results are discussed and found to be in very good agreement with those from the Monte Carlo simulations.     

Experimental determination of the boundary condition for diffuse photons in a homogeneous turbid medium

We present a simple experimental method that permits an empirical determination of the effective boundary condition and the extrapolated end point for the diffuse photon density in a homogeneous turbid medium.     

Statistical properties of the penetration of photons into a semi-infinite turbid medium: a random-walk analysis

Statistical properties of the expected amount of time spent by a photon at different depths of a semi-infinite turbid medium are derived with formalism based on the continuous-time random walk. The formalism is applied to the study of both cw and time-gated experiments. Earlier analytical results relating to cw experiments are reproduced with a single approximation, rather than the more complicated approach used in earlier research based on the discrete-time random walk. The distribution of the occupancy of different depths in a time-gated experiment is found to have a convenient scaling form.     

Spatial coherence of forward-scattered light in a turbid medium

We study spatially coherent forward-scattered light propagating in a turbid medium of moderate optical depth (0-9 mean free paths). Coherent detection was achieved by using a tilted heterodyne geometry, which desensitizes coherent detection of the attenuated incident light. We show that the degree of spatial coherence is significantly higher for light scattered only once in comparison with that for multiply scattered light and that it approaches a small constant value for large numbers of scattering events.     

Effect of diffraction on early-arriving photons during femtosecond laser transillumination of highly scattering media of biological significance

Early-arriving photons of 100-fs laser pulses transmitted through highly scattering media have been detected by a streak camera. Because of their partial spatial coherence, they are affected by diffraction from small hidden discontinuities. The experimental data of the patterns are analyzed with Fresnel diffraction theory and then corrected accordingly. Submillimeter hidden objects were scanned and imaged. Diffraction correction resulted in a significantly improved contrast in the hidden object's image.     

Analytical method for localizing a fluorescent inclusion in a turbid medium

We describe a novel method for localizing a fluorescent inclusion in a homogeneous turbid medium through the use of time-resolved techniques. Based on the calculation of the mean time of the fluorescence curves, the method does not require a priori knowledge of either the fluorescence lifetime or the mean time of the instrument response function since it adopts a differential processing approach. Theoretical expressions were validated and experiments for assessing the accuracy of localization were carried out on liquid optical phantoms with a small fluorescent inclusion. The illumination and detection optical fibers were immersed in the medium to achieve infinite medium geometry as required by the model used. The experimental setup consisted of a time-correlated single-photon counting system. Submillimeter accuracy was achieved for the localization of the inclusion.     

Ultrafast optical Kerr gate imaging in a poly-disperse turbid medium

The influence of the size parameter of the scatterers on ultrafast optical Kerr gate (OKG) imaging is investigated in highly scattering poly-disperse turbid media. The results show that in a poly-disperse turbid medium, which in our case, is a suspension of two different sized mono-disperse microspheres, the temporal and spatial behaviors of the light pulses transmitted through it are dominated by the smaller microspheres. The contrasts of the OKG images for the poly-disperse microsphere sample are closer to the contrasts of the OKG images for the smaller sized mono-disperse microsphere sample.     

Backscattering target detection in a turbid medium by polarization discrimination

We describe a method for increasing target contrast within a turbid medium by means of the polarization state of the scattered light. The backscattered Mueller matrices for various concentrations of 0.1-mum spherical scatterers were measured with and without a painted metal target. Simple discrimination based on detecting cross-polarized intensities is shown to be more effective than the use of total intensity information. As a result, the choice of polarization state is dictated primarily by the requirement to maximize depolarization at the target. This in general means that circularly polarized light is the optimum choice.     

Null detection of ballistic photons for locating objects buried in turbid media

We describe an optical system in which a vibration induced to a laser probe beam combined with a half-blocked photodiode allows determination of the position and width of objects buried in turbid media. Our system is based on the detection of an AC signal which drastically decreases under the presence of an obstructing buried object. We describe the technique and include experimental results showing that the system is capable of detecting 2?mm wide objects buried at depths up to 3?cm from the front surface of a sample simulating scattering properties of soft tissue.     

Absorption distribution of an optical beam focused into a turbid medium

The focusing of light into a turbid medium was studied with Monte Carlo simulations. Focusing was found to have a significant effect on the absorption distribution in turbid media when the depth of the focal point (the distance between the focal point and the surface of the turbid media) was less than or comparable with the transport mean free path. Focusing could significantly increase the peak absorption and narrow the absorption distribution. As the depth of the focal point increased, the peak absorption decreased, and the depth of peak absorption increased initially but quickly reached a plateau that was less than the transport mean free path. A refractive-index-mismatched boundary between the ambient medium and the turbid medium deteriorated the focusing effect, increased the absorption near the boundary, lowered the peak absorption, and broadened the absorption distribution.     

Modeling the diffuse reflectance due to a narrow beam incident on a turbid medium

We present a model for the diffuse reflectance when a continuous beam is incident normally on a half space composed of a uniform scattering and absorbing medium. This model is the result of an asymptotic analysis of the radiative transport equation for strong scattering, weak absorption, and a narrow beam width. Through comparison with the diffuse reflectance computed using the numerical solution of the radiative transport equation, we show that this diffuse reflectance model gives results that are accurate for small source--detector separation distances.     

Theory of a fixed scatterer embedded in a turbid medium: numerical results

Based on a previous theory of diffuse photon density waves by Furutsu [J. Opt. Soc. Am. A 15, 1371 (1998)], several sets of figures are prepared to detect a fixed scatterer (object) embedded in a turbid layer, such as a tumor in tissue, with a source and a detector placed independently along the boundaries on different sides. The relative total intensity of the wave is introduced such that it is reduced to 1 in the case of no scatterer and usually less than that, owing to a shadowing by the scatterer. Sets of curves are presented to demonstrate shadow images of the scatterer observed along the layer boundaries depending on the scatterer's location.     

Statistical detection and imaging of objects hidden in turbid media using ballistic photons

We exploit recent advances in active high-resolution imaging through scattering media with ballistic photons. We derive the fundamental limits on the accuracy of the estimated parameters of a mathematical model that describes such an imaging scenario and compare the performance of ballistic and conventional imaging systems. This model is later used to derive optimal single-pixel statistical tests for detecting objects hidden in turbid media. To improve the detection rate of the aforementioned single-pixel detectors, we develop a multiscale algorithm based on the generalized likelihood ratio test framework. Moreover, considering the effect of diffraction, we derive a lower bound on the achievable spatial resolution of the proposed imaging systems. Furthermore, we present the first experimental ballistic scanner that directly takes advantage of novel adaptive sampling and reconstruction techniques.     

Image contrast enhancement for two-photon fluorescence microscopy in a turbid medium

Image contrast enhancement is investigated for two-photon excitation fluorescence images of a microscopic sample that is buried underneath a turbid medium. The image contrast, which deteriorates rapidly with sample depth because of scattering loss, is enhanced by an increase in the average excitation power of the focused Gaussian (the TEM(00) mode) beam according to a compensation relation that has been derived by use of a Monte Carlo analysis of the scattering problem. A correct increase in the excitation power results in a detected fluorescence signal that remains invariant with sample depth. The scheme is demonstrated on images of DAPI-stained nuclei cells viewed underneath a suspension of 0.105-mum-diameter polystyrene spheres.     

Determination of target depth in a turbid medium with polarization-dependent transmitted signals

We demonstrate a novel method for target depth determination in a turbid medium with experiments and Monte Carlo simulations. This method relies on the strong dependence of transmitted co-polarized intensity on target depth. Such a dependence originates from the inclusion of certain diffuse photons in the co-polarized intensity. A target of stronger scattering located closer to the transmitter results in stronger photon divergence and hence weaker co-polarized intensity at the receiver of a finite aperture. On the other hand, the degree of polarization (DOP) carries only information about ballistic and snake photons. It is weakly dependent on the target depth. The DOP data can be used as a reference of absolute scattering strength in the turbid system. Our experimental and Monte Carlo simulation results show the feasibility of the proposed target depth determination method. Meanwhile, it is shown that an appropriate time-gating process could help in improving the accuracy of target depth. In addition, the results show that the proposed method has quite large applicable ranges of scattering coefficient and absorption coefficient.     

Simple approximate formula for the reflection function of a homogeneous, semi-infinite turbid medium

A simple, approximate analytical formula is proposed for the reflection function of a semi-infinite, homogeneous particulate layer. It is assumed that the zenith angle of the viewing direction is equal to zero (thus corresponding to the case of nadir observations), whereas the light incidence direction is arbitrary. The formula yields accurate results for incidence-zenith angles less than approximately 85 degrees and can be useful in analyzing satellite nadir observations of optically thick clouds.     

Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium

We have examined the possibility of determining the optical properties of a two-layer medium by using a diffusion approximation radiation transport model [Appl. Opt. 37, 779 (1998)]. Continuous-wave and frequency-domain (FD) low-noise Monte Carlo (MC) data were fitted to the model. Marquardt-Levenberg and a simulated annealing algorithm were used and compared as optimization techniques. Our particular choice of optical properties for the two-layer model was consistent with skin and underlying fat in the presence of an exogenous chromophore [Appl. Opt. 37, 1958 (1998)]. The results are therefore specific to this set of optical properties. It was found that the cw diffusion solution could never be used to estimate all optical properties reliably. The combined cw and FD solutions could not be used to estimate some of the top-layer optical properties to an accuracy of better than 10%, although the absorption and the transport scattering coefficients of the bottom layer could be estimated to within 7% and 0.5%, respectively. No improvement was found from simultaneously fitting MC data at three different modulation frequencies. These results point to the need for a more accurate radiation transfer model at small source-detector separations.     

Propagation of diffuse light in a turbid medium with multiple spherical inhomogeneities

We develop a fast and accurate solver for the forward problem of diffusion tomography in the case of several spherical inhomogeneities. The approach allows one to take into account multiple scattering of diffuse waves between different inhomogeneities. Theoretical results are illustrated with numerical examples; excellent numerical convergence and efficiency are demonstrated. The method is generalized for the case of additional planar diffuse-nondiffuse interfaces and is therefore applicable to the half-space and slab imaging geometries.     

Radiative transfer in a turbid medium with a varying refractive index: comment

In the literature one can encounter at least two different radiative transfer equations for media with spatially varying refractive indices. These are the results of Ferwerda [J. Opt. A Pure Appl. Opt. 1, L1 (1999)] and Tualle and Tinet [Opt. Commun. 228, 33 (2003)]. Accordingly, two different diffusion approximations are derived from these two radiative transfer equations. I reconsider the derivation of the radiative transfer equation in a medium with an inhomogeneous refractive index and confirm the result of Tualle and Tinet. In the diffusion approximation, a simple analytical solution has been found for the steady-state illumination of a non-absorbing turbid medium with a varying refractive index.