Optical Properties Of Turbid Media Research Articles

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.

Information content of point radiance measurements in turbid media: implications for interstitial optical property quantification

Motivated by a recent report by Dickey et al. [Phys. Med. Biol. 46, 2359 (2001)], who demonstrated optical property retrieval by using relative radiance measurements at a single position, we investigate the uniqueness of relative radiance measurements for quantifying the optical properties of turbid media by studying the solutions of the diffusion and P3 approximations of the Boltzmann transfer equation for a point source. Using the P3 approximation, we investigate the potential of radiance measurements for optical property recovery by examining the optical property response surface for point radiance information. We further derive first-order similarity relations for relative point radiance measurements and use these expressions to examine analytically the effects of noise on optical property retrieval over a wide range of optical properties typical of biological tissue. Finally, optimal experimental configurations are studied and explicit conditions for uniqueness derived that suggest potential strategies for improving optical property recovery. It is expected that point radiance measurements will prove valuable for both on-line treatment planning of minimally invasive laser therapies and optical characterization of tissues.

In vitro measurements of optical properties of porcine brain using a novel compact device

Knowledge of the optical properties of tissues can be applied in numerous medical and scientific fields, including cancer diagnostics and therapy. There are many different ways of determining the optical properties of turbid media. The paper describes measurements of the optical properties of porcine brain tissue using novel instrumentation for simultaneous absorption and scattering characterisation of small turbid samples. Integrating sphere measurements are widely used as a reference method for determination of the optical properties of relatively thin turbid samples. However, this technique is associated with bulky equipment, complicated measuring techniques, interference compensation techniques and inconvenient sample handling. It is believed that the sphere for some applications can be replaced by a new, compact device, called the combined angular and spatially resolved head sensor, to measure the optical properties of thin turbid samples. The results compare very well with data obtained with an integrating sphere for well-defined samples. The instrument was shown to be accurate to within 12% for microa and 1% for micro's in measurements of intralipid-ink samples. The corresponding variations of data were 17% and 2%, respectively. The reduced scattering coefficient for porcine white matter was measured to be 100 cm(-1) at 633 nm, and the value for coagulated brain tissue was 65 cm(-1). The corresponding absorption coefficients were 2 and 3 cm(-1), respectively.

Characterization of spatial and temporal variations in the optical properties of tissuelike media with diffuse reflectance imaging.

We describe a method to characterize spatial or temporal changes in the optical properties of turbid media using diffuse reflectance images acquired under broad-beam illumination conditions. We performed experiments on liquid phantoms whose absorption (mu(a)) and reduced scattering (mu(s)') coefficients were representative of those of biological tissues in the near infrared. We found that the relative diffuse reflectance R depends on mu(a) and mu(s)' only through the ratio mu(a)/mu(s)' and that dependence can be well described with an analytical expression previously reported in the literature [S. L. Jacques, Kluwer Academic Dordrecht (1996)]. We have found that this expression for R deviates from experimental values by no more than 8% for various illumination and detection angles within the range 0 degrees-30 degrees. Therefore, this analytical expression for R holds with good approximation even if the investigated medium presents curved or irregular surfaces. Using this expression, it is possible to translate spatial or temporal changes in the relative diffuse reflectance from a turbid medium into quantitative estimates of the corresponding changes of (mu(a)/mu(s)')(1/2). In the case of media with optical properties similar to those of tissue in the near infrared, we found that the changes mu(a)/mu(s)' should occur over a volume approximately 2 mm deep and 4 mm x 4 mm wide to apply this expression.

Experimental and computational aspects of optical property determination of turbid media using frequency-domain laser infrared photothermal radiometry (abstract)

In this work, the optical and thermal properties of tissue-like materials are measured using frequency-domain infrared photothermal radiometry. This technique is better suited for quantitative multi-parameter optical measurements than the widely used pulsed photothermal radiometry (PPTR), due to the availability of two independent signal channels, amplitude and phase, and the superior signal-to-noise ratio provided by synchronous lock-in detection. A rigorous three-dimensional thermal-wave formulation with a three-dimensional diffuse and coherent photon density-wave source is applied to data from model phantoms. The combined theoretical, experimental, and computational methodology shows good promise with regard to its analytical ability to measure optical properties of turbid media uniquely, as compared to PPTR, which exhibits uniqueness problems. From data sets obtained using calibrated test phantoms, the reduced optical scattering and absorption coefficients were found to be within 20% and 10%, respectively, from the independently derived values using Mie theory and spectrophotometric measurements.

Theoretical, experimental, and computational aspects of optical property determination of turbid media by using frequency-domain laser infrared photothermal radiometry

In this work, the optical and thermal properties of tissuelike materials are measured by using frequency-domain infrared photothermal radiometry. This technique is better suited for quantitative multiparameter optical measurements than the widely used pulsed-laser photothermal radiometry (PPTR) because of the availability of two independent signal channels, amplitude and phase, and the superior signal-to-noise ratio provided by synchronous lock-in detection. A rigorous three-dimensional (3-D) thermal-wave formulation with a 3-D diffuse and coherent photon-density-wave source is applied to data from model phantoms. The combined theoretical, experimental, and computational methodology shows good promise with regard to its analytical ability to measure optical properties of turbid media uniquely, as compared with PPTR, which exhibits uniqueness problems. From data sets obtained by using calibrated test phantoms, the reduced optical scattering and absorption coefficients were found to be within 20% and 10%, respectively, of the values independently derived by using Mie theory and spectrophotometric measurements.

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.

Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy

Near-infrared (NIR) optical properties of turbid media, e.g., tissue, can be accurately quantified noninvasively using methods based on diffuse reflectance or transmittance, such as frequency domain photon migration (FDPM). Factors which govern the accuracy and sensitivity of FDPM-measured optical properties include instrument performance, the light propagation model, and fitting algorithms used to calculate optical properties from measured data. In this article, we characterize instrument, model, and fitting uncertaintics of an FDPM system designed for clinical use and investigate how each of these factors affects the quantification of NIR absorption (μa) and reduced scattering (μs′) parameters in tissue phantoms. The instrument is based on a 500 MHz, multiwavelength platform that sweeps through 201 discrete frequencies in as little as 675 ms. Phase and amplitude of intensity modulated light launched into tissue, i.e., diffuse photon density waves (PDW), are measured with an accuracy of ±0.30° and ±3.5%, while phase and amplitude precision are ±0.025° and ±0.20%, respectively. At this level of instrument uncertainty, simultaneous fitting of frequency-dependent phase and amplitude nonlinear model functions derived from a photon diffusion approximation provides an accurate and robust strategy for determining optical properties from FDPM data, especially for media with high absorption. In an optical property range that is characteristic of most human tissues in the NIR (5×10−3<μa<5×10−2 mm−1, 0.5<μs′<2 mm−1), we theoretically and experimentally demonstrate that the multifrequency, simultaneous-fit approach allows μa and μs′ to be quantified with an accuracy of ±5% and ±3%, respectively. Although exceptionally high levels of precision can be obtained using this approach (<1% of the estimated absorption and scattering values), we show that the absolute accuracy of optical property measurements is highly dependent on specific factors associated with instrument performance, model function relevance, and details of the fitting strategy used to calculate μa and μs′.

Quantitative microspectrophotometry in turbid media

We present a new technique to determine the scattering coefficient, the absorption coefficient, and the anisotropy factor in turbid media on a microscopic level. To this end, a microspectrophotometer was used to obtain transmission measurements at different solid angles. To extract the optical properties from phantom materials (liquid and solid) and biological tissue (bovine liver) an inverse Monte Carlo algorithm was used. The results obtained with the new microspectrophotometric technique agreed within one standard deviation with the values from Mie theory and within less than 10% with the data derived from conventional spectroscopic measurements. The results suggest that this new method is a valid tool to determine the optical properties of turbid media on a microscopic level.

High-precision frequency-domain measurements of the optical properties of turbid media

We report high-precision measurements of the absorption and the reduced scattering coefficients for turbid media. Using a frequency-domain measurement technique for a point-source infinite-medium geometry, we find that the standard deviations of multiple measurements of the absorption coefficient mu(a) and the reduced scattering coefficient mu(s)(?) are less than 0.6%, and three independently derived values for mu(a) and mu(s)(?) agree to better than 1%. Measurements of mu(a) agree with measurements of a nonscattering medium to within 1.2%. To obtain high precision requires attention to proper conditions for the spherical photon-density wave model, the detection linearity, and the ratio of the absorption rate to the source modulation rate. Frequency-domain amplitude and phase measurements deviate from fitted curves by 0.1% and 0.06 degrees rms, respectively.

Photon-density wave correlation spectroscopy detects large-scale fluctuations in turbid media

We study the fluctuations in the photon-density wave parameters [average intensity (dc), modulation amplitude, and phase] caused by macroscopic fluctuations in the optical properties of turbid media. We present both a theoretical analysis based on diffusion theory and its experimental verification on a strongly scattering suspension containing absorbing particles (1--1.6 mm effective diameter) in turbulent motion. The photon-density waves are induced by the laser diode output (750 nm), which is intensity-modulated at 110 MHz. The dc, amplitude, and phase are acquired with an acquisition time per data point of 8 ms, which corresponds to a frequency bandwidth of 62.5 Hz. We have found that in the presence of the absorbing particles, the dc and phase average values and power spectra are in good agreement with our theoretical predictions. We have verified that our instrument can extend the measured frequency band up to the kHz region, which is appropriate for the study of fluctuations of optical parameters in biological tissues.

Measurement of tissue optical properties by time-resolved detection of laser-induced transient stress

We report on a technique utilizing time-resolved detection of laser-induced stress transients for the measurement of optical properties in turbid media specifically suitable for biological tissues. The method was tested initially in nonscattering absorbing media so that it could be compared with spectrophotometry. The basis of this method is provided by the conditions of temporal stress confinement in the irradiated volume where the pressure generated in tissues heated instantly by laser pulses is proportional to the absorbed laser energy density, and the exponential profile of the initial stress distribution in the irradiated volume corresponds to the z-axial distribution of the absorbed laser fluence. Planar thermoelastic waves can propagate in water-containing media with minimal distortion, and their axial profiles can be detected by an acoustic transducer with sufficient temporal resolution. The acoustic waves induced by 14-ns laser pulses in nonscattering media, turbid gels, and tissues were measured by a piezoelectric transducer with a 3-ns response time. Temporal profiles of stress transients yielded z-axial distributions of the absorbed laser energy in turbid and opaque media, provided that the speed of sound in these media was known. The absorption and effective scattering coefficients of beef liver, dog prostate, and human aortic atheroma at three wavelengths, 1064 nm (in near infrared), 532 nm (visible), and 355 nm (near UV), were deduced from laser-induced stress profiles with additional measurements of total diffuse reflectance.

Detection and characterization of optical inhomogeneities with diffuse photon density waves: a signal-to-noise analysis

Diffusing photons provide information about the optical properties of turbid media. In biological tissues these optical properties may be correlated to physiological parameters, enabling one to probe effectively the physiological states of tissue for abnormalities such as tumors and hemorrhages. We show that positional uncertainty in the source and detector lead to significant random errors that degrade the optical information available from diffusing photons. We investigate the limits for the detection, localization, and characterization of optical inhomogeneities by using diffusing photons as a probe. Although detection is sufficient for tumor screening, full characterization of the optical properties is desirable for specification of the tumor. Our findings in model breast systems with realistic signal-to-noise ratios indicate that tumors as small as 0.3 cm in diameter can be unambiguously detected; however, simultaneous determination of tumor size and optical properties is possible only if its diameter is of the order of 1.0 cm or larger. On the other hand, if a priori information about the size (optical properties) is available, then the optical properties (size) of tumors as small as 0.3 cm in diameter can be determined.

Frequency-domain optical imaging of absorption and scattering distributions by a Born iterative method.

We presents a Born; iterative method, for reconstructing optical properties of turbid media by means of frequency-domain data. The approach is based on iterative solution of a linear perturbation equation, which is derived from the integral from of the Helmholtz wave equation for photon-density waves in each iteration the total field and the associated weight matrix are recalculated based on the previous reconstructed image. We then obtain a new estimate by solving the updated perturbation equation. The forward solution, also based on a Helmholtz equation, is obtained by a multigrid finite difference method. The inversion is carried out through a Tikhonov regularized optimization process by the conjugate gradient descent method. Using this method, we first reconstruct the distribution of the complex wave numbers in a test medium, from which the absorption and the scattering distributions are then derived. Simulation results with two-dimensional test media have shown that this method can yield quantitatively (in terms of coefficient valued) as well as qualitatively (in terms of object location and shape) accurate reconstructions of absorption and scattering distributions in cases in which the first-order Born approximation cannot work well. Both full-angle and limited-angle measurement schemes have been simulated to examine the effect of the location of detectors and sources. The robustness of the algorithm to noise has also been evaluated.

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.

Determination of the optical properties of turbid media from a single Monte Carlo simulation

We describe a fast, accurate method for determination of the optical coefficients of `semi-infinite' and `infinite' turbid media. For the particular case of time-resolved reflectance from a biological medium, we show that a single Monte Carlo simulation can be used to fit the data and to derive the absorption and reduced scattering coefficients. Tests with independent Monte Carlo simulations showed that the errors in the deduced absorption and reduced scattering coefficients are smaller than 1% and 2%, respectively.

Optical properties of thick, turbid media from picosecond time-resolved light scattering measurements

A computational and experimental investigation is reported regarding the feasibility of determining optical properties of turbid media from picosecond (PS) time-resolved light scattering measurements in conjunction with diffusion theory predictions, Monte Carlo simulations, and other appropriate optical measurements. Picosecond time-resolved transmission measurements were performed using aqueous latex particle suspensions with and without absorbing dye. Monte Carlo simulations were also performed to aid in determining limitations of the approach as well as suitable measurement parameters. The system of interest was an optically thick plane-parallel, homogeneous slab consisting of an absorbing, anisotropic scattering medium subject to collimated, pulsed incident radiation. The results of comparing Monte Carlo and diffusion theory predictions showed that important pulse parameters, such as long-time asymptotic log slope and RMS pulse width, are given by diffusion theory analytical expressions with enough accuracy to be useful for determining the unknown optical properties of the medium from time-resolved scattering measurements. These findings were verified using PS time-resolved transmission measurements on aqueous latex particle suspensions. It was also found that the albedo criterion for application of diffusion theory to time-dependent scattering may be much less restrictive than is usually reported (weak absorption or albedo near one is not necessary).

Determining the optical properties of turbid media by using the adding–doubling method

A method is described for finding the optical properties (scattering, absorption, and scattering anisotropy) of a slab of turbid material by using total reflection, unscattered transmission, and total transmission measurements. This method is applicable to homogeneous turbid slabs with any optical thickness,albedo, or phase function. The slab may have a different index of refraction from its surroundings and may or may not be bounded by glass. The optical properties are obtained by iterating an adding-doubling solution of the radiative transport equation until the calculated values of the reflection and transmission match the measured ones. Exhaustive numerical tests show that the intrinsic error in the method is < 3% when four quadrature points are used.

An inverse problem in a three-dimensional radiative transfer

In a series of papers (cf. Bellmanet al., 1965a, b; Kagiwadaet al., 1975), an estimation of optical properties of turbid media has been made, in the least-squared sense, with the aid of quasi-linearization and invariant imbedding. Recently, an extension of the above procedure to the three-dimensional case with horizontally inhomogeneous albedo of the underlying surface has been attempted (Ueno, 1982). From computational aspects the numerical evaluation is not so easy, even by means of high-speed electronic computers. In the present paper it is shown that the latin-square algorithm is a useful estimate for the least-squares inference of the optical properties of turbid media bounded by an inhomogeneous reflecting surface.

Optical properties of turbid media with specularly reflecting boundaries: applications to biological problems

The optical properties of turbid media are formulated in terms of the diffusion equation approximation to linear transport theory. In particular the important effects of specular reflection at bounding surfaces are accurately accounted for by means of explicit boundary conditions at these surfaces. Applications of these results to two problems of biological interest are made. In one a simple multiple scattering model of a leaf is shown to account well for its measured optical properties. In another a method is proposed for finding accurate absorption spectra of pigment-containing cells.