On Iterative Algorithms for Quantitative Photoacoustic Tomography in the Radiative Transport Regime

In this paper, we describe the numerical reconstruction method for quantitative photoacoustic tomography (QPAT) based on the radiative transfer equation (RTE), which models light propagation more accurately than diffusion approximation (DA). We investigate the reconstruction of absorption coefficient and/or scattering coefficient of biological tissues. Given the scattering coefficient, an improved fixed-point iterative method is proposed to retrieve the absorption coefficient for its cheap computational cost. And we prove the convergence. To retrieve two coefficients simultaneously, Barzilai-Borwein (BB) method is applied. Since the reconstruction of optical coefficients involves the solution of original and adjoint RTEs in the framework of optimization, an efficient solver with high accuracy is improved from~\cite{Gao}. Simulation experiments illustrate that the improved fixed-point iterative method and the BB method are the comparative methods for QPAT in two cases.Comment: 21 pages, 44 figure

EIT Reconstruction Algorithms: Pitfalls, Challenges and Recent Developments

We review developments, issues and challenges in Electrical Impedance Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT, Manchester 2003. We focus on the necessity for three dimensional data collection and reconstruction, efficient solution of the forward problem and present and future reconstruction algorithms. We also suggest common pitfalls or ``inverse crimes'' to avoid.Comment: A review paper for the 4th Workshop on Biomedical Applications of EIT, Manchester, UK, 200

Transurethral ultrasound diffraction tomography

ReportThe potential for cost-effective tomographic imaging using ultrasound continues to be confronted with difficulties arising from the computational complexity of fully three dimensional object reconstruction in the diffraction regime. Development of fast and accurate forward and inverse models for ultrasound propagation in the biomedical frequency range of 1-10 MHz is essential for diffraction tomography to be a practical imaging modality. We have implemented a flexible, object-oriented simulation system in MATLAB for performing rapid two- and three-dimensional modeling of forward scattering using the conjugate gradient FFT method in conjunction with a fast linear adjoint approximation to the Jacobian. Nonlinear conjugate gradient inversion has been implemented and tested in both 2D and 3D, demonstrating the feasibility of the method for diffraction tomography. We have also implemented and tested several regularization schemes including L2-norm and total variation, and have used multigrid iteration in conjunction with anisotropic diffusion filtering to accelerate convergence of the inversion algorithm. Inversions of strongly scattering objects have been successfully performed in 2D and 3D, and results thereof are presented herein

Metrology of EUV Masks by EUV-Scatterometry and Finite Element Analysis

Extreme ultraviolet (EUV) lithography is seen as a main candidate for production of future generation computer technology. Due to the short wavelength of EUV light (around 13 nm) novel reflective masks have to be used in the production process. A prerequisite to meet the high quality requirements for these EUV masks is a simple and accurate method for absorber pattern profile characterization. In our previous work we demonstrated that the Finite Element Method (FEM) is very well suited for the simulation of EUV scatterometry and can be used to reconstruct EUV mask profiles from experimental scatterometric data. In this contribution we apply an indirect metrology method to periodic EUV line masks with different critical dimensions (140 nm and 540 nm) over a large range of duty cycles (1:2, ..., 1:20). We quantitatively compare the reconstructed absorber pattern parameters to values obtained from direct AFM and CD-SEM measurements. We analyze the reliability of the reconstruction for the given experimental data. For the CD of the absorber lines, the comparison shows agreement of the order of 1nm. Furthermore we discuss special numerical techniques like domain decomposition algorithms and high order finite elements and their importance for fast and accurate solution of the inverse problem.Comment: Photomask Japan 2008 / Photomask and Next-Generation Lithography Mask Technology X

Rigorous FEM-Simulation of EUV-Masks: Influence of Shape and Material Parameters

We present rigorous simulations of EUV masks with technological imperfections like side-wall angles and corner roundings. We perform an optimization of two different geometrical parameters in order to fit the numerical results to results obtained from experimental scatterometry measurements. For the numerical simulations we use an adaptive finite element approach on irregular meshes. This gives us the opportunity to model geometrical structures accurately. Moreover we comment on the use of domain decomposition techniques for EUV mask simulations. Geometric mask parameters have a great influence on the diffraction pattern. We show that using accurate simulation tools it is possible to deduce the relevant geometrical parameters of EUV masks from scatterometry measurements. This work results from a collaboration between Advanced Mask Technology Center (AMTC, mask fabrication), Physikalisch-Technische Bundesanstalt (PTB, scatterometry), Zuse Institute Berlin (ZIB), and JCMwave (numerical simulation).Comment: 8 pages, 8 figures (see original publication for images with a better resolution