Measurements design and phenomena discrimination

The construction of measurements suitable for discriminating signal components produced by phenomena of different types is considered. The required measurements should be capable of cancelling out those signal components which are to be ignored when focusing on a phenomenon of interest. Under the hypothesis that the subspaces hosting the signal components produced by each phenomenon are complementary, their discrimination is accomplished by measurements giving rise to the appropriate oblique projector operator. The subspace onto which the operator should project is selected by nonlinear techniques in line with adaptive pursuit strategies

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

Scan Free GEXRF in the Soft X ray Range for the Investigation of Structured Nanosamples

Scan free grazing emission X ray fluorescence spectroscopy GEXRF is an established technique for the investigation of the elemental depth profiles of various samples. Recently it has been applied to investigating structured nanosamples in the tender X ray range. However, lighter elements such as oxygen, nitrogen or carbon cannot be efficiently investigated in this energy range, because of the ineffective excitation. Moreover, common CCD detectors are not able to discriminate between fluorescence lines below 1 keV. Oxygen and nitrogen are important components of insulation and passivation layers, for example, in silicon oxide or silicon nitride. In this work, scan free GEXRF is applied in proof of concept measurements for the investigation of lateral ordered 2D nanostructures in the soft X ray range. The sample investigated is a Si3N4 lamellar grating, which represents 2D periodic nanostructures as used in the semiconductor industry. The emerging two dimensional fluorescence patterns are recorded with a CMOS detector. To this end, energy dispersive spectra are obtained via single photon event evaluation. In this way, spatial and therefore angular information is obtained, while discrimination between different photon energies is enabled. The results are compared to calculations of the sample model performed by a Maxwell solver based on the finite elements method. A first measurement is carried out at the UE56 2 PGM 2 beamline at the BESSY II synchrotron radiation facility to demonstrate the feasibility of the method in the soft X ray range. Furthermore, a laser produced plasma source LPP is utilized to investigate the feasibility of this technique in the laboratory. The results from the BESSY II measurements are in good agreement with the simulations and prove the applicability of scan free GEXRF in the soft X ray range for quality control and process engineering of 2D nanostructures. The LPP results illustrate the chances and challenges concerning a transfer of the methodology to the laborator

The anisotropy in the optical constants of quartz crystals for soft X‐rays

The refractive index of a y‐cut SiO2 crystal surface is reconstructed from orientation‐dependent soft X‐ray reflectometry measurements in the energy range from 45 to 620 eV. Owing to the anisotropy of the crystal structure in the (100) and (001) directions, a significant deviation of the measured reflectance at the Si L2,3 and O K absorption edges is observed. The anisotropy in the optical constants reconstructed from these data is also confirmed by ab initio Bethe–Salpeter equation calculations for the O K edge. This new experimental data set expands the existing literature data for quartz crystal optical constants significantly, particularly in the near‐edge regions.The refractive index of a y‐cut SiO2 crystal surface is reconstructed from polarization‐dependent soft X‐ray reflectometry measurements in the energy range from 45 to 620 eV. The reconstructed anisotropy in the optical constants is also confirmed by ab initio Bethe–Salpeter equation calculations of the O K edge. imag