Inverse scattering with a parametrized spatial spectral volume integral equation for finite scatterers

In wafer metrology, the knowledge of the photomask together with the deposition process only reveals the approximate geometry and material properties of the structures on a wafer as a priori information. With this prior information and a parametrized description of the scatterers, we demonstrate the performance of the Gauss-Newton method for the precise and noise-robust reconstruction of the actual structures, without further regularization of the inverse problem. The structures are modeled as three-dimensional finite dielectric scatterers with a uniform polygonal cross-section along their height, embedded in a planarly layered medium. A continuous parametrization in terms of the homogeneous permittivity and the vertex coordinates of the polygons is employed. By combining the global Gabor frame in the spatial spectral Maxwell solver with the consistent parametrization of the structures, the underlying linear system of the Maxwell solver inherits all the continuity properties of the parametrization. Two synthetically generated test cases demonstrate the noise-robust reconstruction of the parameters by surpassing the reconstruction capabilities of traditional imaging methods at signal-to-noise ratios up to -3 dB with geometrical errors below λ/7, where λ is the illumination wavelength. For signal-to-noise ratios of 10 dB, the geometrical parameters are reconstructed with errors of approximately λ/60 and the material properties are reconstructed with an error of around 0.03%. The continuity properties of the Maxwell solver and the use of prior information are key contributors to these results.In wafer metrology, the knowledge of the photomask together with the deposition process only reveals the approximate geometry and material properties of the structures on a wafer as a priori information. With this prior information and a parametrized description of the scatterers, we demonstrate the performance of the Gauss–Newton method for the precise and noise-robust reconstruction of the actual structures, without further regularization of the inverse problem. The structures are modeled as 3D finite dielectric scatterers with a uniform polygonal cross-section along their height, embedded in a planarly layered medium. A continuous parametrization in terms of the homogeneous permittivity and the vertex coordinates of the polygons is employed. By combining the global Gabor frame in the spatial spectral Maxwell solver with the consistent parametrization of the structures, the underlying linear system of the Maxwell solver inherits all the continuity properties of the parametrization. Two synthetically generated test cases demonstrate the noise-robust reconstruction of the parameters by surpassing the reconstruction capabilities of traditional imaging methods at signal-to-noise ratios up to −3dB with geometrical errors below 𝜆/7, where 𝜆 is the illumination wavelength. For signal-to-noise ratios of 10 dB, the geometrical parameters are reconstructed with errors of approximately 𝜆/60, and the material properties are reconstructed with errors of around 0.03%. The continuity properties of the Maxwell solver and the use of prior information are key contributors to these results

A Parallel 3D Spatial Spectral Volume Integral Equation Method for Electromagnetic Scattering from Finite Scatterers

Parallel computing for the three-dimensional spatial spectral volume integral equation method is presented for the computation of electromagnetic scattering by finite dielectric scatterers in a layered medium. The first part exploits the Gabor-frame expansion to compute the Gabor coefficients of scatterers in a parellel manner. The second part concerns the decomposition and restructuring of the matrix-vector product of this spatial spectral volume integral equation into (partially) independent components to enable parallel computing. Both capitalize on the hardware to reduce the computation time by shared-memory parallelism. Numerical experiments in the form of solving electrically large scattering problems, namely volumes up to 1300 cubic wavelengths, in combination with a large number of finite scatterers show a significant reduction in wall-clock time owing to parallel computing, while maintaining accuracy.Parallel computing for the three-dimensional spatial spectral volume integral equation method is presented for the computation of electromagnetic scattering by finite dielectric scatterers in a layered medium. The first part exploits the Gabor-frame expansion to compute the Gabor coefficients of scatterers in a parellel manner. The second part concerns the decomposition and restructuring of the matrix-vector product of this spatial spectral volume integral equation into (partially) independent components to enable parallel computing. Both capitalize on the hardware to reduce the computation time by shared-memory parallelism. Numerical experiments in the form of solving electrically large scattering problems, namely volumes up to 1300 cubic wavelengths, in combination with a large number of finite scatterers show a significant reduction in wall-clock time owing to parallel computing, while maintaining accuracy

Local normal vector field formulation for polygonal building blocks in a Gabor representation

The usage of a spatial spectral domain integralequation solver for electromagnetic scattering from dielectricobjects provides a means to execute scattering simulationsfor lithography.We consider the extension of the localnormal vector field formulation to support polygonal buildingblocks in a Gabor series representation of functions.The usage of a spatial spectral domain integral equation solver for electromagnetic scattering from dielectric objects provides a means to execute scattering simulations for lithography. We consider the extension of the local normal vector field formulation to support polygonal building blocks in a Gabor series representation of functions

Validation of the oxygen desaturation index in the diagnostic workup of obstructive sleep apnea

Introduction: Obstructive sleep apnea (OSA) is common, and diagnosis requires expensive and laborious testing to assess the apnea hypopnea index (AHI). We performed an analysis to explore the relationship between the oxygen desaturation index (ODI) as measured with pulse oximetry and the AHI in our large portable monitoring (PM) database to find an optimal cutoff value for the ODI in order to be able to exclude AHI ≥ 5 on PM. Methods: Three thousand four hundred thirteen PM recordings were randomly divided into a training set (N = 2281) and a test set (N = 1132). The optimal cutoff for the ODI to exclude an AHI ≥ 5 on PM was determined in the training set and subsequently validated in the test set. Results: Area under the curve of the ODI to exclude an AHI ≥ 5 on PM was 0.997 in the training set and 0.996 in the test set. In the training set, the optimal cutoff to predict an AHI < 5 was an ODI < 5. Using this cutoff in the test set provided a sensitivity of 97.7%, a specificity of 97.0%, a positive predictive value of 99.2%, and a negative predictive value of 91.4%. Conclusion: An ODI < 5 predicts an AHI < 5 with high sensitivity and specificity when measured simultaneously using the same oximeter during PM recording

Forearm Rotation Range of Motion and Its Velocity in Eating With Chopsticks : a Comparison Among Positions of Dish

The purpose of this study was to determine range of motion of forearm rotation and its velocity in eating. Six young students (age:20.5±0.5 years [range:20-21], 2 men and 4 women) participated in this study. To measure three-dimensional motions, we used an electromagnetic tracking device system. The first sensor was attached to the dorsal/distal of forearm with sprint, and the second sensor was attached to the dorsal/medial ulna with elastic belt. The subjects ate pickles with chopsticks. At a wooden desk with 70cm height they sat on a height-adjustable chair, so their olecranon was as high as the desk top. Three positions of a dish were measured; A: at the distance of length of distal to elbow, B: at the distance of length of the upper extremity, and C: at a middle position between A and B. The results revealed that forearm rotation, range of motion and its velocity were significantly different among three conditions (one-way repeated-measure ANOVA)(p<0.05). Characteristically the motion velocity of B was lower than C, and A was lower than C (p<0.05). Findings suggest that 1) limited forearm range of motion would decrease a burden of forearm by setting a dish at B or C than A, 2) the rotation (maximal pronation and supination: 11 and 49 degrees, respectively) was similar, to a fork (maximal pronation and supination: 10 and 51 degrees, respectively), 3) C may be efficiently operated, and 4) the system may be instructed as a good equipment for eating

Current practice patterns of outpatient management of acute pulmonary embolism: A post-hoc analysis of the YEARS study

Background: Studies have shown the safety of home treatment of patients with pulmonary embolism (PE) at low risk of adverse events. Management studi

Durability of treatment effects of the Sleep Position Trainer versus oral appliance therapy in positional OSA: 12-month follow-up of a randomized controlled trial

The Sleep Position Trainer (SPT) is a new option for treating patients with positional obstructive sleep apnea (POSA). This study investigated long-term efficacy, adherence, and quality of life during use of the SPT device compared with oral appliance therapy (OAT) in patients with POSA. This prospective, multicenter trial randomized patients with mild to moderate POSA (apnea-hypopnea index [AHI] 5-30/h) to SPT or OAT. Polysomnography was performed at baseline and after 3 and 12 months' follow-up. The primary endpoint was OSA severity; adherence, quality of life, and adverse events were also assessed. Ninety-nine patients were randomized and 58 completed the study (29 in each group). Median AHI in the SPT group decreased from 13.2/h at baseline to 7.1/h after 12 months (P < 0.001); corresponding values in the OAT group were 13.4/h and 5.0/h (P < 0.001), with no significant between-group difference (P = 1.000). Improvements throughout the study were maintained at 12 months. Long-term median adherence was also similar in the two treatment groups; the proportion of patients who used their device for ≥ 4 h for 5 days in a week was 100% in the SPT group and 97.0% in the OAT group (P = 0.598). The efficacy of SPT therapy was maintained over 12 months and was comparable to that of OAT in patients with mild to moderate POSA. Adherence was relatively high, and similar in the two groups. www.clinicaltrials.gov (NCT02045576