Spectral Decomposition of Discrepancy Kernels on the Euclidean Ball, the Special Orthogonal Group, and the Grassmannian Manifold.

To numerically approximate Borel probability measures by finite atomic measures, we study the spectral decomposition of discrepancy kernels when restricted to compact subsets of Rd. For restrictions to the Euclidean ball in odd dimensions, to the rotation group SO(3), and to the Grassmannian manifold G2,4, we compute the kernels' Fourier coefficients and determine their asymptotics. The L2-discrepancy is then expressed in the Fourier domain that enables efficient numerical minimization based on the nonequispaced fast Fourier transform. For SO(3), the nonequispaced fast Fourier transform is publicly available, and, for G2,4, the transform is derived here. We also provide numerical experiments for SO(3) and G2,4.

Compact, circular, and optically stable multipass cell for mobile laser absorption spectroscopy.

Compact and lightweight laser absorption spectrometers for accurate trace gas measurements are of great scientific and commercial importance. In these instruments, the multipass cell (MPC) represents a critical element in terms of achievable size and sensitivity. Herein, we introduce a versatile MPC concept which unifies compactness, mechanical rigidity, and optical stability. Relying on fundamental cavity design principles and modern diamond turning techniques, we have developed a segmented circular MPC that allows efficient and interference-free beam folding. A prototype cell is presented featuring up to 10 m optical path length at a total mass of less than 200 g. Incorporated in a highly compact setup without additional beam pre-shaping optics, we demonstrate a normalized noise level of low 10-4 (2σ) at 1 Hz.

Highly Selective Volatile Organic Compounds Breath Analysis Using a Broadly-Tunable Vertical-External-Cavity Surface-Emitting Laser.

A broadly tunable mid-infrared vertical-external-cavity surface-emitting laser (VECSEL) is employed in a direct absorption laser spectroscopic setup to measure breath acetone. The large wavelength coverage of more than 30 cm-1 at 3.38 µm allows, in addition to acetone, the simultaneous measurement of isoprene, ethanol, methanol, methane, and water. Despite the severe spectral interferences from water and alcohols, an unambiguous determination of acetone is demonstrated with a precision of 13 ppbv that is achieved after 5 min averaging at typical breath mean acetone levels in synthetic gas samples mimicking human breath.

Beam folding analysis and optimization of mask-enhanced toroidal multipass cells.

We present computational and experimental investigations of the beam folding properties and fringe suppression capabilities in monolithic toroidal multipass cells (MPCs) when combined with absorption masks. Coherent field simulations based on the Fresnel-Huygens theory were performed to understand the effect of multiple field truncations in such an optically semi-unstable mirror arrangement. The explicit numerical calculation of the radiation field at each reflection allows detailed optimization and performance analysis. We experimentally verified the evolving irradiance distributions and identified optimal initial field configurations. Furthermore, we suggest a proxy to estimate the noise level for specific initial conditions. These insights pave the way to a better optical performance and, thus, to even more lightweight and compact designs of this MPC type.

SIGLEC1 enables straightforward assessment of type I interferon activity in idiopathic inflammatory myopathies.

OBJECTIVE: To evaluate sialic acid binding Ig-like lectin 1 (SIGLEC1) expression on monocytes by flow cytometry as a type I interferon biomarker in idiopathic inflammatory myopathies (IIM). METHODS: We performed a retrospective analysis of adult and paediatric patients with the diagnosis of IIM. SIGLEC1 expression was assessed by flow cytometry and was compared with Physician Global Assessment or Childhood Myositis Assessment Scale disease activity scores. Mann Whitney U test and receiver operating characteristic curves were used for cross-sectional data analysis (n=96), two-level mixed-effects linear regression model for longitudinal analyses (n=26, 110 visits). Response to treatment was analysed in 14 patients within 12 months, using Wilcoxon test. SIGLEC1 was compared with interferon-stimulated gene 15/MxA status by immunohistochemical staining of muscle biopsies (n=17). RESULTS: 96 patients with adult (a) and juvenile (j) dermatomyositis (DM, n=38), antisynthetase syndrome (AS, n=19), immune-mediated necrotising myopathy (IMNM, n=8), inclusion body myositis (IBM, n=9) and overlap myositis (n=22) were included. SIGLEC1 distinguished significantly between active and inactive disease with an area under the curve of 0.92 (95% CI 0.83 to 1) in DM and correlated with disease activity longitudinally (aDM: standardised beta=0.54, p<0.001; jDM: standardised beta=-0.70, p<0.001). Response to treatment in DM was associated with a decreasing SIGLEC1 (p<0.01, Wilcoxon test). SIGLEC1 was found upregulated in 8 of 19 patients with AS, 2 of 9 patients with IBM but not in IMNM. CONCLUSION: SIGLEC1 is a candidate biomarker to assess type I interferon activity in IIM and proved useful for monitoring disease activity and response to treatment in juvenile and adult DM.

Laser driving and data processing concept for mobile trace gas sensing: Design and implementation.

High precision mobile sensing of multi-species gases is greatly demanded in a wide range of applications. Although quantum cascade laser absorption spectroscopy demonstrates excellent field-deployment capabilities for gas sensing, the implementation of this measurement technique into sensor-like portable instrumentation still remains challenging. In this paper, two crucial elements, the laser driving and data acquisition electronics, are addressed. Therefore, we exploit the benefits of the time-division multiplexed intermittent continuous wave driving concept and the real-time signal pre-processing capabilities of a commercial System-on-Chip (SoC, Red Pitaya). We describe a re-designed current driver that offers a universal solution for operating a wide range of multi-wavelength quantum cascade laser device types and allows stacking for the purpose of multiple laser configurations. Its adaptation to the various driving situations is enabled by numerous field programmable gate array (FPGA) functionalities that were developed on the SoC, such as flexible generation of a large variety of synchronized trigger signals and digital inputs/outputs (DIOs). The same SoC is used to sample the spectroscopic signal at rates up to 125 MS/s with 14-bit resolution. Additional FPGA functionalities were implemented to enable on-board averaging of consecutive spectral scans in real-time, resulting in optimized memory bandwidth and hardware resource utilisation and autonomous system operation. Thus, we demonstrate how a cost-effective, compact, and commercial SoC can successfully be adapted to obtain a fully operational research-grade laser spectrometer. The overall system performance was examined in a spectroscopic setup by analyzing low pressure absorption features of CO2 at 4.3 µm.

The impact of metalation on adsorption geometry, electronic level alignment and UV-stability of organic macrocycles on TiO2(110).

Metal complexes of the tetradentate bipyridine based macrocycle pyrphyrin (Pyr) have recently shown promise as water reduction catalysts in homogeneous photochemical water splitting reactions. In this study, the adsorption and metalation of pyrphyrin on stoichiometric TiO2(110) is investigated in ultrahigh vacuum by means of scanning tunneling microscopy, photoelectron spectroscopy, low-energy electron diffraction, and density functional theory. In a joint experimental and computational effort, the local adsorption geometry at low coverage, the long-range molecular ordering at higher coverage and the electronic structure have been determined for both the bare ligand and the cobalt-metalated Pyr molecule on TiO2. The energy level alignment of CoPyr/TiO2 supports electron injection into TiO2 upon photoexcitation of the CoPyr complex and thus renders it a potential sensitizer dye. Importantly, Co-incorporation is found to stabilize the Pyr molecule against photo-induced degradation, while the bare ligand is decomposed rapidly under continuous UV-irradiation. This interesting phenomenon is discussed in terms of additional de-excitation channels for electronically highly excited molecular states.