Visible spectral dependence of the scattering and absorption coefficients of pigmented coatings from inversion of diffuse reflectance spectra

A spectral-projected gradient method and an extension of the Kubelka-Munk theory are applied to obtain the relevant parameters of the theory from measured diffuse reflectance spectra of pigmented samples illuminated with visible diffuse radiation. The initial estimate of the spectral dependence of the parameters, required by a recursive spectral-projected gradient method, was obtained by use of direct measurements and up-to-date theoretical estimates. We then tested the consistency of the Kubelka-Munk theory by repeating the procedure with samples of different thicknesses.     

Angular distribution of diffuse reflectance in biological tissue

We measured angular-resolved diffuse reflectance in tissue samples of different anisotropic characteristics. Experimental measurements were compared with theoretical results based on the diffusion approximation. The results indicated that the angular distribution in isotropic tissue was the same as in isotropic phantoms. Under normal incidence, the measured angular profiles of diffuse reflectance approached the Lambertian distribution when the evaluation location was far away from the incident point. The skewed angular profiles observed under oblique incidence could be explained using the diffuse model. The anisotropic tissue structures in muscle showed clear effects on the measurements especially at locations close to the light incidence. However, when measuring across the muscle fiber orientations, the results were in good agreement with those obtained in isotropic samples.     

A new optical coefficient of biological tissue that determines the diffuse reflectance light distribution on the tissue surface

When a light beam is incident normally upon a tissue, the spatial distribution of diffuse reflectance on the tissue surface is affected by the optical properties of the tissue. The purpose of this paper is to find the relationship between the spatial distribution of diffuse reflectance on the tissue surface and optical properties of the tissue. The diffuse reflected light distribution is found to be determined mainly by a new optical coefficient μ_as. A qualitative relationship between μ_as and the diffuse reflected light distribution was developed by Monte Carlo simulations. Measurements of the diffuse reflected light distribution on solutions of Intralipid-10% with added ink confirm the Monte Carlo simulations. The new optical coefficient μ_as was measured from several tissue examples by the qualitative relationship. The value of μ_as was useful for determining the components of the tissue.     

Determination of Kubelka-Munk scattering and absorption coefficients by diffuse illumination

The Kubelka-Munk theory, although it provides an equation that relates the reflection of a sample under diffuse illumination to certain of its properties, does not take boundary reflectance into account. Boundary reflection is always present because there is always a difference between the refractive indices of the sample and of the surrounding medium. We describe how a half-sphere is used to achieve diffuse illumination, and we present and exemplify equations that correct for boundary reflection with measurements of four composite restorative dental materials. The refractive index of the sample is measured with a matching technique that employs a glycerol-water mixture. Edge loss errors are estimated.     

Optical diffuse reflectance accessory for measurements of skin tissue by near-infrared spectroscopy

An optimized accessory for measuring the diffuse reflectance spectra of human skin tissue in the near-infrared spectral range is presented. The device includes an on-axis ellipsoidal collecting mirror with efficient illumination optics for small sampling areas of bulky body specimens. The optical design is supported by the results of a Monte Carlo simulation study of the reflectance characteristics of skin tissue. Because the results evolved from efforts to measure blood glucose noninvasively, the main emphasis is placed on the long-wavelength near-infrared range where sufficient penetration depth for radiation into tissue is still available. The accessory is applied for in vivo diffuse reflectance measurements.     

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.     

Comparative evaluation of two simple diffuse reflectance models for biological tissue applications

We present a comparative evaluation of two simple diffuse reflectance models for biological tissue applications. One model is based on a widely accepted and used in biomedical optics implementation of diffusion theory, and the other one is based on a semiempirical approach derived from basic physical principles. We test the models on tissue phantoms and on human skin, utilizing a standard six-around-one optical fiber probe for light delivery and collection. We show that both models are suitable for use with an optical fiber probe and illustrate the potential, applicability, and validity range of the models.     

Design and testing of a white-light, steady-state diffuse reflectance spectrometer for determination of optical properties of highly scattering systems

We present a steady-state radially resolved diffuse reflectance spectrometer capable of measuring the absorption and transport scattering spectra of tissue-simulating phantoms over an adjustable 170-nm wavelength interval in the visible and near infrared. Measurements in a variety of phantoms are demonstrated over the relevant range of tissue optical properties, and the accuracy of the instrument is found to be approximately 10% in both scattering and absorption. Monte Carlo simulations designed to test the accuracy of the instrument are presented that support the experimental findings.     

Multispectral diffuse optical tomography with absorption and scattering spectral constraints

We present a new method to simultaneously reconstruct the images of oxyhemoglobin, deoxyhemoglobin, and water concentrations, as well as the volume fraction images of the scattering particles using continuous wave multispectral diffuse optical tomography with the absorption and scattering spectral prior constraints. In this method, the nonlinear relationship between the reduced scattering coefficient and the volume fraction and the size of the particles is linearized, allowing direct reconstruction of the volume fraction of scattering particles in tissues. The method is validated by a series of numerical simulations, phantom experiments, and in vivo clinical experiments. The initial clinical results indicate that the volume fraction of scattering particles in a malignant tumor is higher than that in a benign tumor.     

Optical characterization of biological tissues: determining absorption and scattering coefficients

We have measured the spectra of diffuse reflection and the total and collimated transmission of the mucous membrane of the stomach in the normal state by the methods of integrating spheres and single scattering in a wavelength range from 350 to 750 nm. The optical characteristics of this biological tissue were determined by solving the inverse scattering problem using the Kubelka-Munk three-flux model and the diffusion method. A comparative analysis of the results is presented.     

Determination of tissue optical properties from diffuse reflectance profiles by multivariate calibration

We describe a method for determining the reduced scattering and absorption coefficients of turbid biological media from the spatially resolved diffuse reflectance. A Sugeno Fuzzy Inference System in conjunction with data preprocessing techniques is employed to perform multivariate calibration and prediction on reflectance data generated by Monte Carlo simulations. The preprocessing consists of either a principal component analysis or a new, extended curve-fitting procedure originating from diffusion theory. Prediction tests on reflectance data with absorption coefficients between 0.04 and 0.06 mm(-1) and reduced scattering coefficients between 0.45 and 0.99 mm(-1) show the root-mean-square error of this method to be 0.25% for both coefficients. With reference to practical applications, we also describe how the prediction accuracy is affected by using relative instead of absolute reflectance data, by imposing measurement noise on the reflectance data, and by changing the number and the position of detectors.     

Determination of the optical coefficients of biological tissue by neural network

A system that incorporated a laser source and a CCD camera was used to measure spatially-resolved steady-state diffuse reflectance. Monte Carlo simulations and experiments in tissue phantoms were used to train a neural network that characterizes the reflectance data on a turbid medium. The neural network was used to extract the optical properties (scattering and absorption coefficients) of biological tissue. The accuracy of the neural network was investigated and validated. Tests on tissue-simulation phantoms showed the relative errors of this technique to be 3% for the reduced scattering coefficient and 9% for the absorption coefficients. The optical properties of human skin were also measured in vivo at 633 nm. For human skin tissue it was found that our results were in good agreement with their reference values.     

Clinical determination of tissue optical properties by endoscopic spatially resolved reflectometry

A noninvasive method to measure the optical properties of a diffusing and absorbing medium is described. Based on the spatially resolved measurement of diffuse reflectance at the sample surface, this method is particularly suitable for investigating the in vivo optical properties of biological tissues endoscopically in a clinical context. The sensitivity of the measurement is discussed, and two optical probes for two different clinical applications are presented. Preliminary measurements are performed on a nonbiological medium, which illustrate the possibilities of the proposed method. Finally, we report on in vivo measurements of the optical properties of the human esophageal wall at 630 nm.     

A feature parameter of optical diffuse reflectance on normal and malignant human breast tissue

Light that is delivered to the tissue surface undergoes multiple elastic scattering and absorption; part of it returns to the surface as optical diffuse reflectance, carrying quantitative information on the structure and composition of the measured tissue. In this paper, we utilized a well tested and publicly available Monte Carlo simulation software to simulate optical diffuse reflectance on normal and malignant human breast tissue in the visible wavelength region 450–650 nm. Based on the Monte Carlo simulation results, we discovered a feature parameter of optical diffuse reflectance on the simulated tissue surface. Normal and malignant human breast tissue may be discriminated by the value of the feature parameter. The values of the feature parameter are shown for normal and malignant human breast tissue in the visible wavelength region 450–650 nm. Experiments with tissue phantoms showed that the feature parameter is correlated to the component of the phantom. So the feature parameter is useful for the non-invasive optical diagnosis of biological tissue.     

In vivo determination of local skin optical properties and photon path length by use of spatially resolved diffuse reflectance with applications in laser Doppler flowmetry

Methods for local photon path length and optical properties estimation, based on measured and simulated diffuse reflectance within 2 mm from the light source, are proposed and evaluated in vivo on Caucasian human skin. The accuracy of the methods was good (2%-7%) for path length and reduced scattering but poor for absorption estimation. Reduced scattering and absorption were systematically lower in the fingertip than in the forearm skin (633 nm). A maximum intrasite and interindividual variation of approximately 35% in an average photon path length was found. The methodology was applied in laser Doppler flowmetry, where path-length normalization of the estimated perfusion removed the optical property dependency.     

Fiber-optic probe for noninvasive real-time determination of tissue optical properties at multiple wavelengths

We present a compact, fast, and versatile fiber-optic probe system for real-time determination of tissue optical properties from spatially resolved continuous-wave diffuse reflectance measurements. The system collects one set of reflectance data from six source-detector distances at four arbitrary wavelengths with a maximum overall sampling rate of 100 Hz. Multivariate calibration techniques based on two-dimensional polynomial fitting are employed to extract and display the absorption and reduced scattering coefficients in real-time mode. The four wavelengths of the current configuration are 660, 785, 805, and 974 nm, respectively. Cross-validation tests on a 6 x 7 calibration matrix of Intralipid-dye phantoms showed that the mean prediction error at, e.g., 785 nm was 2.8% for the absorption coefficient and 1.3% for the reduced scattering coefficient. The errors are relative to the range of the optical properties of the phantoms at 785 nm, which were 0-0.3/cm for the absorption coefficient and 6-16/cm for the reduced scattering coefficient. Finally, we also present and discuss results from preliminary skin tissue measurements.