Optical tomography in the presence of void regions

There is a growing interest in the use of near-infrared spectroscopy for the noninvasive determination of the oxygenation level within biological tissue. Stemming from this application, there has been further research in the use of this technique for obtaining tomographic images of the neonatal head, with the view of determining the levels of oxygenated and deoxygenated blood within the brain. Owing to computational complexity, methods used for numerical modeling of photon transfer within tissue have usually been limited to the diffusion approximation of the Boltzmann transport equation. The diffusion approximation, however, is not valid in regions of low scatter, such as the cerebrospinal fluid. Methods have been proposed for dealing with nonscattering regions within diffusing materials through the use of a radiosity-diffusion model. Currently, this new model assumes prior knowledge of the void region location; therefore it is instructive to examine the errors introduced in applying a simple diffusion-based reconstruction scheme in cases in which there exists a nonscattering region. We present reconstructed images of objects that contain a nonscattering region within a diffusive material. Here the forward data is calculated with the radiosity-diffusion model, and the inverse problem is solved with either the radiosity-diffusion model or the diffusion-only model. The reconstructed images show that even in the presence of only a thin nonscattering layer, a diffusion-only reconstruction will fail. When a radiosity-diffusion model is used for image reconstruction, together with a priori information about the position of the nonscattering region, the quality of the reconstructed image is considerably improved. The accuracy of the reconstructed images depends largely on the position of the anomaly with respect to the nonscattering region as well as the thickness of the nonscattering region.     

Linear single-step image reconstruction in the presence of nonscattering regions

There is growing interest in the use of near-infrared spectroscopy for the noninvasive determination of the oxygenation level within biological tissue. Stemming from this application, there has been further research in using this technique for obtaining tomographic images of the neonatal head, with the view of determining the level of oxygenated and deoxygenated blood within the brain. Because of computational complexity, methods used for numerical modeling of photon transfer within tissue have usually been limited to the diffusion approximation of the Boltzmann transport equation. The diffusion approximation, however, is not valid in regions of low scatter, such as the cerebrospinal fluid. Methods have been proposed for dealing with nonscattering regions within diffusing materials through the use of a radiosity-diffusion model. Currently, this new model assumes prior knowledge of the void region; therefore it is instructive to examine the errors introduced in applying a simple diffusion-based reconstruction scheme in cases where a nonscattering region exists. We present reconstructed images, using linear algorithms, of models that contain a nonscattering region within a diffusing material. The forward data are calculated by using the radiosity-diffusion model, and the inverse problem is solved by using either the radiosity-diffusion model or the diffusion-only model. When using data from a model containing a clear layer and reconstructing with the correct model, one can reconstruct the anomaly, but the qualitative accuracy and the position of the reconstructed anomaly depend on the size and the position of the clear regions. If the inverse model has no information about the clear regions (i.e., it is a purely diffusing model), an anomaly can be reconstructed, but the resulting image has very poor qualitative accuracy and poor localization of the anomaly. The errors in quantitative and localization accuracies depend on the size and location of the clear regions.     

Quantitative reconstruction of refractive index distribution and imaging of glucose concentration by using diffusing light

We show that a two-step reconstruction method can be adapted to improve the quantitative accuracy of the refractive index reconstruction in phase-contrast diffuse optical tomography (PCDOT). We also describe the possibility of imaging tissue glucose concentration with PCDOT. In this two-step method, we first use our existing finite-element reconstruction algorithm to recover the position and shape of a target. We then use the position and size of the target as a priori information to reconstruct a single value of the refractive index within the target and background regions using a region reconstruction method. Due to the extremely low contrast available in the refractive index reconstruction, we incorporate a data normalization scheme into the two-step reconstruction to combat the associated low signal-to-noise ratio. Through a series of phantom experiments we find that this two-step reconstruction method can considerably improve the quantitative accuracy of the refractive index reconstruction. The results show that the relative error of the reconstructed refractive index is reduced from 20% to within 1.5%. We also demonstrate the possibility of PCDOT for recovering glucose concentration using these phantom experiments.     

Experimental test of a perturbation model for time-resolved imaging in diffusive media

We report what to our knowledge is a novel perturbation approach for time-resolved transmittance imaging in diffusive media, based on the diffusion approximation with extrapolated boundary conditions. The model relies on the method of Padé approximants and consists of a nonlinear approximation of time-resolved transmittance curves in the presence of an inclusion. The proposed model is intended to extend the range of applicability of perturbation models when applied to inclusions that are non-point-like. We test the model on different tissue phantoms with scattering only, absorbing only, and both scattering and absorbing inclusions. Maps of the optical properties are displayed, and the results are compared with those obtained by means of the usual linear approximation of time-resolved transmittance curves. We found that the nonlinear approach gives a better prediction for absolute values of the scattering and absorption coefficients of inclusions, when the inclusion optical properties are higher than the surrounding background. Furthermore, better-resolved spots and a reduced cross talk between the two parameters are found in the reconstructed maps. Because the range of the optical properties spanned by the considered phantoms covers the values expected for optical mammography, the application of the reported reconstruction method to in vivo images of a breast appears promising from a diagnostic viewpoint.     

Time-resolved diffuse optical tomographic imaging for the provision of both anatomical and functional information about biological tissue

We present in vivo images of near-infrared (NIR) diffuse optical tomography (DOT) of human lower legs and forearm to validate the dual functions of a time-resolved (TR) NIR DOT in clinical diagnosis, i.e., to provide anatomical and functional information simultaneously. The NIR DOT system is composed of time-correlated single-photon-counting channels, and the image reconstruction algorithm is based on the modified generalized pulsed spectral technique, which effectively incorporates the TR data with reasonable computation time. The reconstructed scattering images of both the lower legs and the forearm revealed their anatomies, in which the bones were clearly distinguished from the muscles. In the absorption images, some of the blood vessels were observable. In the functional imaging, a subject was requested to do handgripping exercise to stimulate physiological changes in the forearm tissue. The images of oxyhemoglobin, deoxyhemoglobin, and total hemoglobin concentration changes in the forearm were obtained from the differential images of the absorption at three wavelengths between the exercise and the rest states, which were reconstructed with a differential imaging scheme. These images showed increases in both blood volume and oxyhemoglobin concentration in the arteries and simultaneously showed hypoxia in the corresponding muscles. All the results have demonstrated the capability of TR NIR DOT by reconstruction of the absolute images of the scattering and the absorption with a high spatial resolution that finally provided both the anatomical and functional information inside bulky biological tissues.     

Three-dimensional optical tomography: resolution in small-object imaging

Near-infrared (NIR) optical tomography provide estimates of the internal distribution of optical absorption and transport scattering from boundary measurement of light propagation within biological tissue. Although this is a truly three-dimensional (3D) imaging problem, most research to date has concentrated on two-dimensional modeling and image reconstruction. More recently, 3D imaging algorithms are demonstrating better estimation of the light propagation within the imaging region and are providing the basis of more accurate image construction algorithms. As 3D methods emerge, it will become increasingly important to evaluate their resolution, contrast, and localization of optical property heterogeneity. We present a concise study of 3D reconstructed resolution of a small, low-contrast, absorbing and scattering anomaly as it is placed in different locations within a cylindrical phantom. The object is an 8-mm-diameter cylinder, which represents a typical small target that needs to be resolved in NIR mammographic imaging. The best resolution and contrast is observed when the object is located near the periphery of the imaging region (12-22 mm from the edge) and is also positioned within the multiple measurement planes, with the most accurate results seen for the scatter image when the anomaly is at 17 mm from the edge. Furthermore, the accuracy of quantitative imaging is increased to almost 100% of the target values when a priori information regarding the internal structure of imaging domain is utilized.     

提高时域乳腺光学层析成像质量的方法

时域乳腺光学层析成像技术可以有效重建乳腺组织的光学参数,实现乳腺癌的早期检测.为了提高重建图像的性能,针对图像重建过程中吸收系数和约化散射系数的雅克比矩阵间的量级差异,提出了一种有效的雅克比矩阵标定方法;为了克服不适定性因素对重建图像质量的影响,引入了图像分割技术实现对雅克比矩阵有效降维.实验数据的相关验证表明,上述两种方法可有效提高重建图像的质量.     

Experimental determination of photon propagation in highly absorbing and scattering media

Optical imaging and tomography in tissues can facilitate the quantitative study of several important chromophores and fluorophores. Several theoretical models have been validated for diffuse photon propagation in highly scattering and low-absorbing media that describe the optical appearance of tissues in the near-infrared (NIR) region. However, these models are not generally applicable to quantitative optical investigations in the visible because of the significantly higher tissue absorption in this spectral region compared with that in the NIR. We performed photon measurements through highly scattering and absorbing media for ratios of the absorption coefficient to the reduced scattering coefficient ranging approximately from zero to one. We examined experimentally the performance of the absorption-dependent diffusion coefficient defined by Aronson and Corngold [J. Opt. Soc. Am. A 16, 1066 (1999)] for quantitative estimations of photon propagation in the low- and high-absorption regimes. Through steady-state measurements we verified that the transmitted intensity is well described by the diffusion equation by considering a modified diffusion coefficient with a nonlinear dependence on the absorption. This study confirms that simple analytical solutions based on the diffusion approximation are suitable even for high-absorption regimes and shows that diffusion-approximation-based models are valid for quantitative measurements and tomographic imaging of tissues in the visible.     

Estimation of chest-wall-induced diffused wave distortion with the assistance of ultrasound

The chest-wall layer underneath breast tissue consists of muscles and bones, which induce distortion in near-infrared diffused waves measured at distant source--detector pairs when reflection geometry is used. A priori information on chest-wall depth obtained from coregistered real-time ultrasound can be used to assist in the removal of distant measurements. We applied Monte Carlo simulation to a simple two-layer model consisting of breast tissue and a chest wall to investigate chest-wall-induced distortion. The Monte Carlo method indicates that, when more than 50% of the received photons travel through the breast tissue layer before being detected, the detected signal may be useful for image reconstruction. The results of phantom experiments obtained from the two-layer model further validate the distortion problem and demonstrate imaging improvement after distant measurements have been filtered out. Clinical examples have shown similar imaging improvements on reconstructed absorption maps. Clinical data obtained from 20 patients with the chest-wall depths of less than 2 cm from the skin surface suggest that the cutoff distances of distorted measurements are largely related to the chest-wall depth and are relatively independent of the optical properties of tissue.     

Refractive-index profiling of embedded microstructures in optical materials

We describe use of a phase-sensitive low-coherence reflectometer to measure spatial variation of refractive index in optical materials. The described interferometric technique is demonstrated to be a valuable tool to profile the refractive index of optical elements such as integrated waveguides and photowritten optical microstructures. As an example, a refractive-index profile is mapped of a microstructure written in a microscope glass slide with an ultrashort-pulse laser.     

Geometrical-optics approximation of forward scattering by gradient-index spheres

By means of geometrical optics we present an approximation method for acceleration of the computation of the scattering intensity distribution within a forward angular range (0-60 degrees ) for gradient-index spheres illuminated by a plane wave. The incident angle of reflected light is determined by the scattering angle, thus improving the approximation accuracy. The scattering angle and the optical path length are numerically integrated by a general-purpose integrator. With some special index models, the scattering angle and the optical path length can be expressed by a unique function and the calculation is faster. This method is proved effective for transparent particles with size parameters greater than 50. It fails to give good approximation results at scattering angles whose refractive rays are in the backward direction. For different index models, the geometrical-optics approximation is effective only for forward angles, typically those less than 60 degrees or when the refractive-index difference of a particle is less than a certain value.     

Refractive-index changes caused by proton radiation in silicate optical glasses

We have studied experimentally, by using a differential interferometric technique, the effect of proton radiation on the refractive index of commercial (Schott) silicate crown glasses, BK7 and LaK9, and their radiation-resistant counterparts. The strongest effect was observed for the radiation-hard lanthanum crown LaK9G15: At a 0.65-Mrad dose the index change was approximately 3 x 10(-5). Radiation-hard glasses are used in optical systems operating in radiation environments because they prevent spectral transmission degradation in the visible. However, such glasses are not protected against radiation-induced refractive-index perturbations, and a diffraction-limited optical system based on such glasses may fail owing to radiation-induced aberrations.     

Extraction of the refractive index profile of thin transparent conductive oxide films from the analysis of reflectance optical spectra

In the direction of growth of fabricated films, the material near the free surface as well as the interface with the substrate exhibits properties which are different from those of the material in the bulk. The resulting spatial inhomogeneity of the refractive index influences positions and values of the extrema of optical spectra. We exploit this to derive the profile of the refractive index by developing a theoretical approach. In the calculations, taking the derived profile into account, we attain a good reproduction of the experimental Transmittance and Reflectance spectra from approximately 1 to 4 eV, the region of relatively weak refractive-index dispersion.     

Optical imaging: three-dimensional approximation and perturbation approaches for time-domain data

The reconstruction method presented here is based on diffusion approximation for light propagation in turbid media and on a minimization strategy for the output-least-squares problem. A perturbation approach is introduced for the optical properties. Here we can strongly reduce the number of free variables of the inverse problem by exploiting a priori information such as the search for single inhomogeneities within a relatively homogeneous object, a typical situation for breast cancer detection. We achieve higher accuracy and a considerable reduction in computational effort by solving a parabolic differential equation for a perturbation density, i.e., the difference between the photon density in an inhomogeneous object and the density in the homogeneous case being given by an analytic expression. The calculations are performed by a two-dimensional finite-element-method algorithm. However, as a time-dependent correction factor is applied, the three-dimensional situation is well approximated. The method was successfully tested by use of the University of Pennsylvania standard data set. Data noise was generated and taken into account in a modified data set. The influence of different noise on the reconstruction results is discussed.     

Direct reconstruction of complex refractive index distribution from boundary measurement of intensity and normal derivative of intensity

We present an optical tomographic reconstruction method to recover the complex refractive index distribution from boundary measurements based on intensity, which are the logarithm of intensity and normal derivative of intensity. The method, which is iterative, repeatedly implements the forward propagation equation for light amplitude, the Helmholtz equation, and computes appropriate sensitivity matrices for these measurements. The sensitivity matrices are computed by solving the forward propagation equation for light and its adjoint. The results of numerical experiments show that the data types ln(I) and partial differential I/ partial differential n reconstructed, respectively, the imaginary and the real part of the object refractive index distribution. Moreover, the imaginary part of the refractive index reconstructed from partial differential I/ partial differential n and the real part from ln(I) failed to show the object's inhomogeneity. The value of the propagation constant, k, used in our simulations was 50, and this value resulted in smoothing of the reconstructed inhomogeneities. Thus we have shown that it is possible to reconstruct the complex refractive index distribution directly from the measured intensity without having to first find the light amplitude, as is done in most of the currently available reconstruction algorithms of diffraction tomography.     

Scaling property of the diffusion equation for light in a turbid medium with varying refractive index

A spatially varying refractive index leads to the bending of photon paths in a medium, which complicates the Monte Carlo modeling of a photon random walk. We show that the process of photon diffusion in a turbid medium with varying refractive index and curved photon paths can be mapped to the diffusion process in a medium with straight photon paths and modified optical properties. Specifically, the diffusion coefficient, the absorption, and the refractive index of the second medium should differ from the corresponding properties of the first medium by the factor of the squared refractive index of the first medium. The specific intensity of light in the second medium will then be equal to the specific intensity in the first medium divided by the same factor, which also means that the photon density distributions in the two media will be identical. In a Monte Carlo simulation the scaling property suggests that two different algorithms can be used to obtain the photon density distribution, namely, the algorithm with curved photon paths and given optical properties and the algorithm with straight photon paths and modified optical properties.     

Sensing properties of asymmetric double-layer-covered tapered fibers

A novel, to our knowledge, device based on a tapered optical fiber with a double-layer deposition including a metallic media is presented, and its properties are studied. The main novelty of the device consists of the introduction of a dielectric layer, whereas the systems depicted in the literature are simply metal-coated tapered fibers. The presence of the dielectric layer permits one to tune the response of the device to the refractive index of the surrounding medium. We have proved the suitability of this scheme for refractive-index sensing by depicting two measurement modes, namely, total power attenuation and spectral transmittance.     

Tomographic reconstruction of three-dimensional refractive index fields by use of a regularized phase-tracking technique and a polynomial approximation method

We present a complete data-processing procedure for quantitative reconstruction of three-dimensional (3D) refractive index fields from limited multidirectional interferometric data. The proposed procedure includes two parts: (1) extraction of the projection data from limited multidirectional interferograms by a regularized phase-tracking technique and wavefront fitting and (2) reconstruction of the 3D refractive index fields by a modified polynomial approximation method. It has been shown that the procedure gives a satisfactory solution to the reconstruction issue in interferometric tomography, from the initial projection data extraction to the final image reconstruction. Computer simulation and experimental results are both presented.     

Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation,phantom, and clinical results

Three-dimensional (3D), multiwavelength near-infrared tomography has the potential to provide new physiological information about biological tissue function and pathological transformation. Fast and reliable measurements of multiwavelength data from multiple planes over a region of interest, together with adequate model-based nonlinear image reconstruction, form the major components of successful estimation of internal optical properties of the region. These images can then be used to examine the concentration of chromophores such as hemoglobin, deoxyhemoglobin, water, and lipids that in turn can serve to identify and characterize abnormalities located deep within the domain. We introduce and discuss a 3D modeling method and image reconstruction algorithm that is currently in place. Reconstructed images of optical properties are presented from simulated data, measured phantoms, and clinical data acquired from a breast cancer patient. It is shown that, with a relatively fast 3D inversion algorithm, useful images of optical absorption and scatter can be calculated with good separation and localization in all cases. It is also shown that, by use of the calculated optical absorption over a range of wavelengths, the oxygen saturation distribution of a tissue under investigation can be deduced from oxygenated and deoxygenated hemoglobin maps. With this method the reconstructed tumor from the breast cancer patient was found to have a higher oxy-deoxy hemoglobin concentration and also a higher oxygen saturation level than the background, indicating a ductal carcinoma that corresponds well to histology findings.     

In vivo breast imaging with diffuse optical tomography based on higher-order diffusion equations

We report on in vivo absorption and scattering imaging of a human breast cyst and implant, using a reconstruction algorithm based on our third-order diffusion equations. To validate these in vivo images, a series of phantom experiments were conducted, in which we used low-absorbing and low-scattering heterogeneities to mimic a breast cyst or implant. These heterogeneities or targets were composed of pure water or a mixture of water and very dilute Intralipid (0.05% and 0.1%). The phantom experiment confirmed the quantitative imaging capability of our improved algorithm for reconstructing heterogeneities where the conventional diffusion approximation is inadequate. Pilot clinical results from female volunteers indicate that enhanced diffuse optical tomography can quantitatively image findings such as breast cysts or implants in which the absorption and scattering coefficients are usually low.