Quantitative optical image reconstruction of turbid media by use of direct-current measurements

We present a detailed experimental study concerning quantitative optical property reconstruction of heterogeneous turbid media by use of absolute dc data only. We performed experiments by using tissuelike phantoms in both single-target and multitarget configurations in which variations in target size and optical contrast with the background were explored. Our results show that both scattering and absorption images can be reconstructed quantitatively by use of dc data only, whereas it was impossible to obtain such quantitative information in previously reported studies. We believe that this improvement is primarily a result of the realization of a novel data preprocessing/optimization scheme for accurately determining several critical parameters needed for reconstruction. The use of this data preprocessing/optimization scheme also eliminates the calibration reference measurement previously required for reconstruction. Experimental confirmation of this scheme is given in detail.     

Inverse hybrid technique for determining the optical properties of turbid media from integrating-sphere measurements

We have combined the Monte Carlo method with the small-angle approximation of the radiative transfer theory to derive the optical properties (the absorption coefficient, the scattering coefficient, and the anisotropy factor) of turbid materials from integrating-sphere measurements (the total transmittance and the diffuse reflectance) and the collimated transmittance. Unlike one-dimensional models, the technique accounts for the side losses of light at the edges of the sample. In addition, it enables the correction of the measured collimated signal for the contribution of multiply scattered light. On the other hand, the hybrid technique allows a significant reduction in calculation time compared with inverse methods based on a pure Monte Carlo technique. Numerical tests and experimental results from a phantom material (milk) as well as samples of biological tissue (porcine myocardium) confirmed the feasibility of applying this technique to the determination of the optical properties of turbid media.     

Optical property measurements of turbid media in a small-volume cuvette with frequency-domain photon migration

A frequency-domain photon migration (FDPM) technique is developed for quantitative measurement of the absorption and reduced scattering coefficients of highly turbid samples in a small-volume (0.45-ml) reflective cuvette. We present both an analytical model for the FDPM cuvette and its experimental verification, using calibrated phantoms and suspensions of living cells. FDPM model fits to experimental data demonstrate that the reduced scattering (mu(s)?) and absorption (mu(a)) coefficients can be derived with accuracies of 5-10% and 10-15%, respectively. Changing the cuvette wall reflectivity alters the frequency-dependent behavior of photon density waves (PDWs). For highly reflective wall boundaries (R(eff) >/= 90-95%), PDW confinement leads to substantial enhancement in both amplitude and phase compared with identical samples in infinite media. Results from experiments on microsphere suspensions are compared with predictions from Mie theory to assess the potential of this method to interpret scattering properties in terms of scatterer size and density. Optical property measurements of biological cell suspensions are reported, and the possibility of optically monitoring cell physiology in a carefully controlled environment is demonstrated.     

Haar transform analysis of photon time-of-flight measurements for quantification of optical properties in scattering media

A method to independently quantify the absorption and the scattering properties of samples based on the analysis of the Haar transform (HT) of photon time-of-flight (TOF) distributions is described. A series of reflectance photon TOF measurements were acquired from absorbing/scattering milk samples of known composition (0 < mu(a) < 0.025 mm(-1); 100 < mu(s) < 250 mm(-1)). The HT of the profiles was calculated, and the regression based on the most parsimonious subset of wavelets was determined by the genetic algorithm (GA). In addition, the utility of computing the logarithm of the profiles or of the absolute value of the wavelet coefficients before the GA was studied. Results show that the absorption coefficient could be estimated with a coefficient of variation (C.V.) of 6.7% and an r2 of 0.99 by use of the log of selected wavelets of frequency less than 800 MHz. Scattering coefficients were estimated with a C.V. of 2.3% and an r2 of 0.99 with the log of wavelets of frequency less than 400 MHz. The above results suggest that a simplified instrument based on low-frequency switches could be developed to quantify the optical properties of highly scattering media.     

Apparent and inherent optical properties of turbid estuarine waters: measurements, empirical quantification relationships, and modeling

Spectral measurements of remote-sensing reflectance (Rrs) and absorption coefficients carried out in three European estuaries (Gironde and Loire in France, Tamar in the UK) are presented and analyzed. Typical Rrs and absorption spectra are compared with typical values measured in coastal waters. The respective contributions of the water constituents, i.e., suspended sediments, colored dissolved organic matter, and phytoplankton (characterized by chlorophyll-a), are determined. The Rrs spectra are then reproduced with an optical model from the measured absorption coefficients and fitted backscattering coefficients. From Rrs ratios, empirical quantification relationships are established, reproduced, and explained from theoretical calculations. These quantification relationships were established from numerous field measurements and a reflectance model integrating the mean values of the water constituents' inherent optical properties. The model's sensitivity to the biogeochemical constituents and to their nature and composition is assessed.     

General theory of three-dimensional radiance measurements with optical microprobes

Measurements of the radiance distribution and fluence rate within turbid samples with fiber-optic radiance microprobes contain a large variable instrumental error caused by the nonuniform directional sensitivity of the microprobes. A general theory of three-dimensional radiance measurements is presented that provides correction for this error by using the independently obtained function of the angular sensitivity of the microprobes.     

Theory of equidistant three-dimensional radiance measurements with optical microprobes

Fiber-optic radiance microprobes, increasingly applied for measurements of internal light fields in living tissues, provide three-dimensional radiance distribution solids and radiant energy fluence rates at different depths of turbid samples. These data are, however, distorted because of an inherent feature of optical fibers: nonuniform angular sensitivity. Because of this property a radiance microprobe during a single measurement partly underestimates light from the envisaged direction and partly senses light from other directions. A theory of three-dimensional equidistant radiance measurements has been developed that provides correction for this instrumental error using the independently obtained function of the angular sensitivity of the microprobe. For the first time, as far as we know, the measurements performed with different radiance microprobes are comparable. An example of application is presented. The limitations of this theory and the prospects for this approach are discussed.     

Chemometric analysis of frequency-domain photon migration data: quantitative measurements of optical properties and chromophore concentrations in multicomponent turbid media

Frequency-domain photon migration (FDPM) is a widely used technique for measuring the optical properties (i.e., absorption, micro(a), and reduced scattering, micro(s)', coefficients) of turbid samples. Typically, FDPM data analysis is performed with models based on a photon diffusion equation; however, analytical solutions are difficult to obtain for many realistic geometries. Here, we describe the use of models based instead on representative samples and multivariate calibration (chemometrics). FDPM data at seven wavelengths (ranging from 674 to 956 nm) and multiple modulation frequencies (ranging from 50 to 600 MHz) were gathered from turbid samples containing mixtures of three absorbing dyes. Values for micro(a) and micro(s)' were extracted from the FDPM data in different ways, first with the diffusion theory and then with the chemometric technique of partial least squares. Dye concentrations were determined from the FDPM data by three methods, first by least-squares fits to the diffusion results and then by two chemometric approaches. The accuracy of the chemometric predictions was comparable or superior for all three dyes. Our results indicate that chemometrics can recover optical properties and dye concentrations from the frequency-dependent behavior of photon density waves, without the need for diffusion-based models. Future applications to more complicated geometries, lower-scattering samples, and simpler FDPM instrumentation are discussed.     

Collection efficiency of a single optical fiber in turbid media

If a single optical fiber is used for both delivery and collection of light, two major factors affect the measurement of collected light: (1) the light transport in the medium that describes the amount of light that returns to the fiber and (2) the light coupling to the optical fiber that depends on the angular distribution of photons entering the fiber. We focus on the importance of the latter factor and describe how the efficiency of the coupling depends on the optical properties of the medium. For highly scattering tissues, the efficiency is well predicted by the numerical aperture (NA) of the fiber. For lower scattering, such as in soft tissues, photons arrive at the fiber from deeper depths, and the coupling efficiency could increase twofold to threefold above that predicted by the NA.     

Absorbance measurements in turbid media by the photon correlation method

Optical absorption in highly turbid media was quantified by the time shift of the electric field autocorrelation function of diffused photons. The intensity autocorrelation function was analyzed by the third-order cumulant expansion and a linear relationship between the time shift and the absorber concentration was observed. The slope of the fitted line gave the molecular extinction coefficient of the absorber. The absorption spectra were also obtained from the time shift. Applicability to dual-wavelength absorption measurement is also discussed. We demonstrate for the first time, as far as we know, the feasibility of absorbance quantification in turbid media by the photon correlation method.     

Method to determine the optical properties of turbid media

A novel method to determine the optical properties, namely, absorption coefficient, scattering coefficient, and anisotropy factor of turbid solutions, single constituent or multiconstituent, is presented. Turbid solutions of milk, ink, and a mixture of both were illuminated by a laser beam and measurements were carried out in scattered light. Experimental results were matched to the corresponding results of Monte Carlo simulation to obtain the optical properties of the turbid media.     

Autocorrelation of scattered laser light for ultrasound-modulated optical tomography in dense turbid media

Based on measurement of the intensity autocorrelation function, a new method to determine the modulation depth of scattered laser light modulated by an ultrasonic wave in turbid media was applied to ultrasound-modulated optical tomography. Good signal-to-noise ratios and high sensitivities were demonstrated. Images of double optically absorbing objects buried in a highly optically scattering gel sample were obtained. The contrast was more than 10%, and the spatial resolution was approximately 2 mm.     

Noninvasive determination of the optical properties of two-layered turbid media

Light propagation in two-layered turbid media having an infinitely thick second layer is investigated in the steady-state, frequency, and time domains. A solution of the diffusion approximation to the transport equation is derived by employing the extrapolated boundary condition. We compare the reflectance calculated from this solution with that computed with Monte Carlo simulations and show good agreement. To investigate if it is possible to determine the optical coefficients of the two layers and the thickness of the first layer, the solution of the diffusion equation is fitted to reflectance data obtained from both the diffusion equation and the Monte Carlo simulations. Although it is found that it is, in principle, possible to derive the optical coefficients of the two layers and the thickness of the first layer, we concentrate on the determination of the optical coefficients, knowing the thickness of the first layer. In the frequency domain, for example, it is shown that it is sufficient to make relative measurements of the phase and the steady-state reflectance at three distances from the illumination point to obtain useful estimates of the optical coefficients. Measurements of the absolute steady-state spatially resolved reflectance performed on two-layered solid phantoms confirm the theoretical results.     

Frequency-domain optical image reconstruction in turbid media: an experimental study of single-target detectability

An experimental study of the detectability of an object embedded in optically tissue-equivalent media by frequency-domain image reconstruction is presented. The experiments were performed in an 86-mm-diameter cylindrical phantom containing an optically homogeneous cylindrical target whose absorption and scattering properties presented a 2:1 contrast with the background medium. The parameter space explored during experimentation involved object size (15-, 8-, and 4-mm targets) and location (centered, 20-mm off-centered, and 35-mm off-centered) variations. Image reconstruction was achieved with a previously reported regularized least-squares approach that incorporates finite-element solutions of the diffusion equation and Newton's method solutions of the nonlinear minimization problem. Also included during image formation were image enhancement schemes-(1) total variation minimization, (2) dual meshing, and (3) spatial low-pass filtering-which have recently been added. Quantitative measures of image quality including the size, location, and shape of the heterogeneity along with errors in its recovered optical property values are used to quantify the image reconstructions. The results show that a near 22:1 ratio of tissue thickness relative to detectable object size has been achieved with this approach in the laboratory conditions and parameter space that have been investigated.     

Ultrasound-modulated optical tomography of absorbing objects buried in dense tissue-simulating turbid media

Continuous-wave ultrasonic modulation of scattered laser light was used to image objects buried in tissue-simulating turbid media. The buried object had an absorption coefficient greater than the background turbid medium. The ultrasonic wave that was focused into the turbid media modulated the laser light that passed through the ultrasonic field. The modulated laser light that was collected by a photomultiplier tube reflected the local mechanical and optical properties in the zone of ultrasonic modulation. Objects buried in the middle plane of 5-cm-thick dense turbid media were imaged with millimeter resolution through the scanning and detecting alterations of the ultrasound-modulated optical signal. The optical properties of the dense turbid media included an absorption coefficient of 0.1 cm(-1) and a reduced scattering coefficient of 10 cm(-1) and were comparable with those of biological tissues in the visible and near-IR ranges. The dependence of the ultrasound-modulated optical signal on the off-axis distance of the detector from the optic axis and the area of the detector was studied as well.     

Monte Carlo modeling of optical coherence tomography imaging through turbid media

We combine a Monte Carlo technique with Mie theory to develop a method for simulating optical coherence tomography (OCT) imaging through homogeneous turbid media. In our model the propagating light is represented by a plane wavelet; its line propagation direction and path length in the turbid medium are determined by the Monte Carlo technique, and the process of scattering by small particles is computed according to Mie theory. Incorporated into the model is the numerical phase function obtained with Mie theory. The effect of phase function on simulation is also illustrated. Based on this improved Monte Carlo technique, OCT imaging is directly simulated and phase information is recorded. Speckles, resolution, and coherence gating are discussed. The simulation results show that axial and transversal resolutions decrease as probing depth increases. Adapting a light source with a low coherence improves the resolution. The selection of an appropriate coherence length involves a trade-off between intensity and resolution.     

Effect of refractive index on the measurement of optical properties in turbid media

Continuous-wave measurement-based methods offer a rapid cost-effective way to determine optical properties in turbid media. This method requires a measure of the refractive index of the medium, which is often unknown a priori. Whereas previous studies have reported that the refractive index has little impact on the measurement of optical properties, here we show a significant effect of refractive indices on measurements, using both simulations and experiments. In addition we propose a noniterative method to determine the refractive index of the medium. This method can also provide an optimal initial guess of the optical properties for the standard iterative method for determining optical properties in turbid media. Our method is confirmed by simulations and experiments with latex spheres and Intralipid suspensions.