From cardinal spline wavelet bases to highly coherent dictionaries

Wavelet families arise by scaling and translations of a prototype function, called the mother wavelet. The construction of wavelet bases for cardinal spline spaces is generally carried out within the multi-resolution analysis scheme. Thus, the usual way of increasing the dimension of the multi-resolution subspaces is by augmenting the scaling factor. We show here that, when working on a compact interval, the identical effect can be achieved without changing the wavelet scale but reducing the translation parameter. By such a procedure we generate a redundant frame, called a dictionary, spanning the same spaces as a wavelet basis but with wavelets of broader support. We characterize the correlation of the dictionary elements by measuring their 'coherence' and produce examples illustrating the relevance of highly coherent dictionaries to problems of sparse signal representation

The trigger system of the NOMAD experiment

The NOMAD trigger system is described in the present paper. It is made up of a largearea plastic scintillator veto system, two trigger scintillator planes inside a 0.4~Tmagnetic field and their associated trigger electronics. Special features of the systemconsist of the use of proximity mesh photomultipliers which allow the trigger scintillators to operate in the magnetic field, and the use of custom-built VME moduleswhich perform the trigger logic decisions, the signal synchronisation and gate generation,event counting and livetime calculations. This paper also includes a description of each of the NOMAD triggers, with their calculated and measured rates, efficiencies and livetimes

Evaluation of freeway high occupancy vehicle lanes and ramp metering. Volume I. Final report.

Transportation Department, Office of the Assistant Secretary for Policy and International Affairs, Washington, D.C.Mode of access: Internet.Author corporate affiliation: Baugh, D., and Associates, Inc., Boston, Mass.Report covers the period Nov 1978-March 1980Subject code: HBEKSubject code: CDCMSubject code: CDKSubject code: GGOSubject code: WW*IJSubject code: X

Time frequency analysis assisted determination of ruthenium optical constants in the sub EUV spectral range 8 nm 23.75 nm

The optical constants of ruthenium in the spectral range 8 nm to 23.75 nm with their corresponding uncertainties are derived from the reflectance of a sputtered ruthenium thin film in the Extreme Ultraviolet (EUV) spectral range measured using monochromatized synchrotron radiation. This work emphasizes the correlation between structure modelling and the reconstructed optical parameters in a detailed inverse-problem optimization strategy. Complementary X-ray Reflectivity (XRR) measurements are coupled with Markov chain Monte Carlo (MCMC) based Bayesian inferences and quasi-model-independent methods to create a model factoring the sample's oxidation, contamination, and surface roughness. The sensitivity of the modelling scheme is tested and verified against contamination and oxidation. A notable approach mitigating the high dimensionality of the reconstruction problem is elaborated with the results of this work compared to two previously published datasets. The presented dataset is of high interest for the continuing development of Extreme Ultraviolet Lithography (EUVL) and EUV astronomy optical systems

Challenges of grazing emission X ray fluorescence GEXRF for the characterization of advanced nanostructured surfaces

The grazing emission X ray fluorescence GEXRF technique offers a promising approach to determining the spatial distribution of various chemical elements in nanostructures. In this paper, we present a comparison with grazing incidence small angle X ray scattering GISAXS , an established method for dimensional nanometrology, on periodic TiO2 nanostructures fabricated by a self aligned double patterning SADP process. We further test the potential of GEXRF for process control in the presence of residual chromium on the structures. The angle resolved fluorescence emission as well as the scattered radiation from the surface are collected with photon counting hybrid pixel area detectors using scanning free detection schemes. By modelling the X ray standing wave XSW field in the vicinity of and inside the nanostructure, it is possible to obtain both the angle resolved fluorescence intensities and the far field scattering intensities from the same model. The comparison also illustrates that for ensemble photon based measurement methods, accounting for roughness effects and imperfections can be essential when modelling advanced nanostructured surface