Active constrained truncated Newton method for simple-bound optical tomography

In the past, nonlinear unconstrained optimization of the optical imaging problem has focused on Newton-Raphson techniques. Besides requiring expensive computation of the Jacobian, the unconstrained minimization with Tikhonov regularization can pose significant storage problems for large-scale reconstructions, involving a large number of unknowns necessary for realization of optical imaging. We formulate the inverse optical imaging problem as both simple-bound constrained and unconstrained minimization problems in order to illustrate the reduction in computational time and storage associated with constrained image reconstructions. The forward simulator of excitation and generated fluorescence, consisting of the Galerkin finite-element formulation, is used in an inverse algorithm to find the spatial distribution of absorption and lifetime that minimizes the difference between predicted and synthetic frequency-domain measurements. The inverse approach employs the truncated Newton method with trust region and a modification of automatic reverse differentiation to speed the computation of the optimization problem. The reconstruction results confirm that the physically based, constrained minimization with efficient optimization schemes may offer a more logical approach to the large-scale optical imaging problem than unconstrained minimization with regularization.     

Dual-mesh optical tomography reconstruction method with a depth correction that uses a priori ultrasound information

A dual-mesh reconstruction method with a depth correction for near-infrared diffused wave imaging with ultrasound localization is demonstrated by use of phantoms and clinical cancer cases. Column normalization is applied to the weight matrix obtained from the Born approximation to correct the depth-dependent problem in the reconstructed absorption maps as well as in the total hemoglobin concentration maps. With the depth correction, more uniform absorption maps for target layers at different depths are obtained from the phantoms, and the correlation between the reconstructed hemoglobin concentration maps of deeply located, large cancers and the histological microvessel density counts are dramatically improved.     

Image reconstruction in optical tomography in the presence of coupling errors

Image reconstruction in optical tomography is a nonlinear and generally ill- posed inverse problem. Noise in the measured surface data can give rise to substantial artifacts in the recovered volume images of optical coefficients. Apart from random shot noise caused by the limited number of photons detected at the measurement site, another class of systematic noise is associated with losses specific to individual source and detector locations. A common cause for such losses in data acquisition systems based on fiber-optic light delivery is the imperfect coupling between the fiber tips and the skin of the patient because of air gaps or surface moisture. Thus the term coupling errors was coined for this type of data noise. However, source and detector specific errors can also occur in noncontact measurement systems not using fiber-optic delivery, for example, owing to local skin pigmentation, hair and hair follicles, or instrumentation calibration errors. Often it is not possible to quantify coupling effects in a way that allows us to remove them from the data or incorporate them into the light transport model. We present an alternative method of eliminating coupling errors by regarding the complex-valued coupling factors for each source and detector as unknowns in the reconstruction process and recovering them simultaneously with the images of absorption and scattering. Our method takes into account the possibility that coupling effects have an influence on both the amplitude and the phase shift of the measurements. Reconstructions from simulated and experimental phantom data are presented, which show that including the coupling coefficients in the reconstruction greatly improves the recovery of absorption and scattering images.     

A reconstruction method for diffuse optical tomography by grouping of source-detector configuration

Image reconstruction for diffusion optical tomography often involves repeatedly solving the forward problem, wherein the diffusion equation is typically utilized to describe the light propagation. However, the diffusion equation may not be valid in regions of either high absorption or low scatter. In this paper, a new method is proposed to improve the forward model. This method is based on the modelling error between the Monte Carlo method and the diffusion equation. To further improve the efficiency of image reconstruction, we propose the grouping strategy of source-detector configuration. Simulation results demonstrate that the proposed method can significantly speed up the reconstruction process with the high reconstruction quality.     

Image restoration method based on Hilbert transform for full-field optical coherence tomography

A full-field optical coherence tomography (FF-OCT) system utilizing a simple but novel image restoration method suitable for a high-speed system is demonstrated. An en-face image is retrieved from only two phase-shifted interference fringe images through using the mathematical Hilbert transform. With a thermal light source, a high-resolution FF-OCT system having axial and transverse resolutions of 1 and 2.2 microm, respectively, was implemented. The feasibility of the proposed scheme is confirmed by presenting the obtained en-face images of biological samples such as a piece of garlic and a gold beetle. The proposed method is robust to the error in the amount of the phase shift and does not leave residual fringes. The use of just two interference images and the strong immunity to phase errors provide great advantages in the imaging speed and the system design flexibility of a high-speed high-resolution FF-OCT system.     

Comparison of reconstruction algorithms for optical diffraction tomography

A recently developed inverse scattering algorithm [A. J. Devaney and M. Dennison, Inverse Probl., 19, 855 (2003) and M. Dennison and A. J. Devaney, Inverse Probl., 20, 1307 (2004)] is described and applied in a computer simulation study of optical diffraction tomography (ODT). The new algorithm is superior to standard ODT reconstruction algorithms, such as the filtered backpropagation algorithm, in applications employing a limited number of scattering experiments (the so-called limited-view case) and also in cases where multiple scattering occurs between the object being interrogated and the (known) background in which the object is embedded. The new algorithm is compared and contrasted with the filtered backpropagation algorithm in a computer simulation of ODT of weakly inhomogeneous cylindrical objects being interrogated in a limited number of scattering experiments employing incident plane waves. Our study has potential applications in biomedical imaging and tomographic microscopy.     

Non-interferometric methods of phase estimation for application in optical tomography

Abstract

We describe here two non-interferometric methods for the estimation of the phase of transmitted wavefronts through refracting objects. The phase of the wavefronts obtained is used to reconstruct either the refractive index distribution of the objects or their contours. Refraction corrected reconstructions are obtained by the application of an iterative loop incorporating digital ray tracing for forward propagation and a modified filtered back projection (FBP) for reconstruction. The FBP is modified to take into account non-straight path propagation of light through the object. When the iteration stagnates, the difference between the projection data and an estimate of it obtained by ray tracing through the final reconstruction is reconstructed using a diffraction tomography algorithm. The reconstruction so obtained, viewed as a correction term, is added to the estimate of the object from the loop to obtain an improved final refractive index reconstruction.     

Linear and nonlinear reconstruction for optical tomography of phantoms with nonscattering regions

Most research in optical imaging incorrectly assumes that light transport in nonscattering regions in the head may be modeled by use of the diffusion approximation. The effect of this assumption is examined in a series of experiments on tissue-equivalent phantoms. Images from cylindrical and head-shaped phantoms with and without clear regions [simulating the cerebrospinal fluid (CSF) filled ventricles] and a clear layer (simulating the CSF layer surrounding the brain) are reconstructed with linear and nonlinear reconstruction techniques. The results suggest that absorbing and scattering perturbations can be identified reliably with nonlinear reconstruction methods when the clear regions are also present in the reference data but that the quality of the image degrades considerably if the reference data does not contain these features. Linear reconstruction performs similarly to nonlinear reconstruction, provided the clear regions are present in the reference data, but otherwise linear reconstruction fails. This study supports the use of linear reconstruction for dynamic imaging but suggests that, in all cases, image quality is likely to improve if the clear regions are modeled correctly.     

Image reconstruction algorithm based on the extended regularised total least squares method for electrical capacitance tomography

Electrical capacitance tomography (ECT) is a non-invasive imaging technology that aims at the visualisation of the cross-sectional permittivity distribution of a dielectric object based on the measured capacitance data. Successful applications of ECT depend greatly on the precision and speed of the image reconstruction algorithms. ECT image reconstruction is a typical ill-posed problem, and its solution is unstable, that is, the solution is sensitive to noises in the input data. Methods that ensure the stability of a solution while enhancing the quality of the reconstructed images should be used to obtain a meaningful reconstruction result. An image reconstruction algorithm based on the regularised total least squares (TLS) method that considers the errors in both the sensitivity field matrix and the capacitance data for ECT is presented. The regularised TLS method is extended using a combination robust estimation technique and an extended stabilising functional according to the ill-posed characteristics of ECT, which transforms the image reconstruction problem into an optimisation problem. In addition, the Newton algorithm is employed to solve the objective functional. Numerical simulations indicate that the algorithm is feasible and overcomes the numerical instability of ECT image reconstruction; for the cases of the reconstructed objects considered here, the spatial resolution of the reconstructed images obtained using the algorithm is enhanced; as a result, an efficient method for ECT image reconstruction is introduced.     

Comparison of two- and three-dimensional reconstruction methods in optical tomography

We present a three-dimensional (3D) image reconstruction scheme for optical near-infrared imaging of highly scattering material. The algorithm reconstructs the spatial distribution of the optical parameters of a volume Omega from transillumination measurements on the boundary of Omega. We test the performance of the method for a cylindrical object with embedded absorbing perturbation for a number of different source and detector arrangements. Furthermore, we investigate the effect of a mismatched reconstruction, using a two-dimensional (2D) reconstruction model to image a single plane of the object from 3D tomographic data obtained in a single plane. The motivation for the application of 2D models is their advantage in speed and memory requirements. We found that the difference in the measurement data between 2D and 3D models depends greatly on the measurement type used, giving a much better agreement for mean time-of-flight data than for dc intensity data. Image artifacts that are due to data model mismatches can therefore be significantly reduced by use of mean time data.     

Rigorous and efficient grating-analysis method made easy for optical engineers

The coordinate-transformation-based differential method of Chandezon et al. [J. Opt. (Paris) 11, 235 (1980); J. Opt. Soc. Am. 72, 839 (1982)] (the C method) is one of the simplest and most versatile methods for modeling surface-relief gratings. However, to date it has been used by only a small number of people, probably because, traditionally, elementary tensor theory is used to formulate the method. We reformulate the C method without using any knowledge of tensor, thus, we hope, making the C method more accessible to optical engineers.     

Multilevel, hybrid regularization method for reconstruction of fluorescent molecular tomography

In this paper, a multilevel, hybrid regularization method is presented for fluorescent molecular tomography (FMT) based on the hp-finite element method (hp-FEM) with a continuous wave. The hybrid regularization method combines sparsity regularization and Landweber iterative regularization to improve the stability of the solution of the ill-posed inverse problem. In the first coarse mesh level, considering the fact that the fluorescent probes are sparsely distributed in the entire reconstruction region in most FMT applications, the sparse regularization method is employed to take full advantage of this sparsity. In the subsequent refined mesh levels, since the reconstruction region is reduced and the initial value of the unknown parameters is provided from the previous mesh, these mesh levels seem to be different from the first level. As a result, the Landweber iterative regularization method is applied for reconstruction. Simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom are conducted to evaluate the performance of our method. The reconstructed results show the potential and feasibility of the proposed approach.     

Unified inversion scheme that uses light scattering for morphological parameters and optical properties of aggregated aerosols

A robust scheme for characterizing chainlike aggregated aerosols by use of nonintrusive light-scattering measurements is presented. This scheme entails the selection of suitable scattering quantities and their optimal measurement angles; the development of an inversion algorithm to yield the complex refractive index of agglomerates m = n + ik, the primary particle diameter d(p), the number of primary particles per agglomerate N(p), the number density of agglomerates n(A), and the volume fraction of agglomerates f(v); and evaluation of the uncertainties of the inferred parameters that correspond to measuring uncertainties. The data-inversion algorithm is based on the exact formulation of light scattering for agglomerates that consist of primary particles in the Rayleigh limit and therefore has solid theoretical foundations. In addition, this approach yields all the desired parameters of the aggregated aerosols by using in situ light-scattering measurements with a minimum of possible uncertainties. Furthermore, the methodology developed here can be extended to aerosols with other types of morphology and optical property.     

Endoscopic optical coherence tomography with a modified microelectromechanical systems mirror for detection of bladder cancers

Experimental results of a modified micromachined microelectromechanical systems (MEMS) mirror for substantial enhancement of the transverse laser scanning performance of endoscopic optical coherence tomography (EOCT) are presented. Image distortion due to buckling of MEMS mirror in our previous designs was analyzed and found to be attributed to excessive internal stress of the transverse bimorph meshes. The modified MEMS mirror completely eliminates bimorph stress and the resultant buckling effect, which increases the wobbling-free angular optical actuation to greater than 37 degrees, exceeding the transverse laser scanning requirements for EOCT and confocal endoscopy. The new optical coherence tomography (OCT) endoscope allows for two-dimensional cross-sectional imaging that covers an area of 4.2 mm x 2.8 mm (limited by scope size) and at roughly 5 frames/s instead of the previous area size of 2.9 mm x 2.8 mm and is highly suitable for noninvasive and high-resolution imaging diagnosis of epithelial lesions in vivo. EOCT images of normal rat bladders and rat bladder cancers are compared with the same cross sections acquired with conventional bench-top OCT. The results clearly demonstrate the potential of EOCT for in vivo imaging diagnosis and precise guidance for excisional biopsy of early bladder cancers.     

Time integration of mechanical systems with elastohydrodynamic lubricated joints using Quasi‐Newton method and projection formulations

This work deals with the efficient time integration of mechanical systems with elastohydrodynamic (EHD) lubricated joints. Two novel approaches are presented. First, a projection function is used to formulate the well‐known Swift–Stieber cavitation condition and the mass‐conservative cavitation condition of Elrod as an unconstrained problem. Based on this formulation, the pressure variable from the EHD problem is added to the dynamic equations of a multi‐body system in a monolithic manner so that cavitation is solved within a global iteration. Compared with a partitioned state‐of‐the‐art formulation, where the pressure is solved locally in a nonlinear force element, this global search reduces simulation time. Second, a Quasi‐Newton method of DeGroote is applied during time integration to solve the nonlinear relation between pressure and deformation. Compared with a simplified Newton method, the calculation of the time‐consuming parts of the Jacobian are avoided, and therefore, simulation time is reduced significantly, when the Jacobian is calculated numerically. Solution strategies with the Quasi‐Newton method are presented for the partitioned formulation as well as for the new DAE formulations with projection function. Results are given for a simulation example of a rigid shaft in a flexible bearing. Copyright © 2016 John Wiley & Sons, Ltd.     

Computationally efficient method for retrieving aerosol optical depth from ATSR-2 and AATSR data

We present a robust and computationally efficient method for retrieving aerosol optical depth (AOD) from top-of-atmosphere ATSR-2 (Along-Track Scanning Radiometer) and AATSR (Advanced ATSR) reflectance data that is formulated to allow retrieval of the AOD from the 11 year archive of (A)ATSR data on the global scale. The approach uses a physical model of light scattering that requires no a priori information on the land surface. Computational efficiency is achieved by using precalculated lookup tables (LUTs) for the numerical inversion of a radiative-transfer model of the atmosphere. Estimates of AOD retrieved by the LUT approach are tested on AATSR data for a range of global land surfaces and are shown to be highly correlated with sunphotometer measurements of the AOD at 550 nm. (Pearson's correlation coefficient r(2) is 0.71.).     

A method for determining the initial elastic strains in rivetted joints and how they change during cyclic loading

N. E. Zhukov Kharkov Aviation Institute. Translated from Problemy Prochnosti, No. 2, pp. 104–108, February, 1989.     

A modified Newton‐type Koiter‐Newton method for tracing the geometrically nonlinear response of structures

The Koiter‐Newton (KN) method is a combination of local multimode polynomial approximations inspired by Koiter's initial postbuckling theory and global corrections using the standard Newton method. In the original formulation, the local polynomial approximation, called a reduced‐order model, is used to make significantly more accurate predictions compared to the standard linear prediction used in conjunction with Newton method. The correction to the exact equilibrium path relied exclusively on Newton‐Raphson method using the full model. In this paper, we proposed a modified Newton‐type KN method to trace the geometrically nonlinear response of structures. The developed predictor‐corrector strategy is applied to each predicted solution of the reduced‐order model. The reduced‐order model can be used also in the correction phase, and the exact full nonlinear model is applied only to calculate force residuals. Remainder terms in both the displacement expansion and the reduced‐order model are well considered and constantly updated during correction. The same augmented finite element model system is used for both the construction of the reduced‐order model and the iterations for correction. Hence, the developed method can be seen as a particular modified Newton method with a constant iteration matrix over the single KN step. This significantly reduces the computational cost of the method. As a side product, the method has better error control, leading to more robust step size adaptation strategies. Numerical results demonstrate the effectiveness of the method in treating nonlinear buckling problems.     

Multiphoton optical image guided spectroscopy method for characterization of collagen-based materials modified by glycation

The cross-linking with reducing sugars, known as glycation, is used to increase stiffness and strength of tissues and artificial collagen-based scaffolds. Nondestructive characterization methods that report on the structures within these materials could clarify the effects of glycation. For doing this nondestructive evaluation, we employed an in situ one-photon fluorescence as well as multiphoton microscopy method that combined two-photon fluorescence and second harmonic generation signals. We incubated collagen hydrogels with glyceraldehyde, ribose, and glucose and observed an increase in the in situ fluorescence and structural alterations within the materials during the course of glycation. The two-photon fluorescence emission maximum was observed at about 460 nm. The fluorescence emission in the one-photon excitation experiment (λ(ex) = 360 nm) was broad with peaks centered at 445 and 460 nm. The 460 nm emission component subsequently became dominant during the course of glycation with glyceraldehyde. For the ribose, in addition to the 460 nm peak, the 445 nm component persisted. The glucose glycated hydrogels exhibited broad fluorescence that did not increase significantly even after 6 weeks. As determined from measuring the fluorescence intensity at the 460 nm maximum, glycation with glyceraldehyde was faster compared to ribose and generated stronger fluorescence signals. Upon excitation of glycated samples with 330 nm light, different emission peaks were observed.     

Application of the maximum entropy method to spectral-domain optical coherence tomography for enhancing axial resolution

For the first time we applied the maximum entropy method (MEM) to spectral domain optical coherence tomography to enhance axial resolution (AR). The MEM estimates the power spectrum by fitting. For an onion with optimization of M = 70, the AR of 18.8 microm by discrete Fourier transform (DFT) was improved three times compared with peak widths. The calculation time by the MEM with M = 70 was 20 times longer than that of DFT. However, further studies are needed for practical applications, because the validity of the MEM depends on the sample structures.