Uniform illumination by diffractive shaping of independent light beams

This article presents a new optical set-up for illumination of a common area with a few independent light sources. The main aim is to create a uniform light distribution of a constant shape even if one of the light sources will stop working. In such a case, the shape of the light distribution should remain unchanged, however, the total light intensity will be lower. The novelty of the proposed solution is based on the usage of a small number of the independent light sources in opposite to a well known LED arrays approach. The beam shaping is made using Dammann gratings and specially designed blazed phase diffractive gratings. The article contains the theoretical analysis and the computer simulation verified by the experiment.     

Independence,clique size and maximum degree

It was shown before that ifG is a graph of maximum degreep containing no cliques of the sizeq then the independence ratio is greater than or equal to 2 / (p +q). We shall discuss here some extreme cases of this inequality. Dedicated to Paul Erdős on his seventieth birthday     

Analysis of salazinic, norstictic, and usnic acids in Xanthoparmelia chlorochroa by ultra-performance liquid chromatography/tandem mass spectrometry

The lichen species Xanthoparmelia chlorochroa is toxic when consumed by domestic sheep, cattle, and Rocky Mountain elk. Clinical signs exhibited by poisoned animals include red urine, ataxia, and muscular weakness that rapidly progresses to recumbency. Elk are unable to recover once becoming recumbent; however, most affected cattle can recover if offered suitable feed shortly following the onset of signs. At present, the pathogenesis and specific toxin(s) are unknown. As part of an effort to elucidate the proximate toxin, a method using ultra-performance LC coupled to MS/MS with negative-ion electrospray ionization has been developed to compare salazinic, norstictic, and usnic acid concentrations in X. chlorochroa collected from locales associated with lichen poisonings. Compounds were extracted from lichen samples with acetone and sonication. The stationary phase was a Waters Acquity UPLCTM BEH Ca18 (50 x 2.1 mm; 1.7 microm particle size) column. The mobile phase consisted of an acetonitrile-water gradient. The precision of the method was confirmed by an SD below 0.4% (n=9) for triplicate samples. LOD values were 200, 100, and 50 ng/mL for salazinic, norstictic, and usnic acids, respectively.     

Highly efficient broadband double-sided Fresnel lens for THz range

Modern passive THz setups require effective optical elements with a large numerical aperture. Here we propose a new type of the optical element for THz applications, which is a broadband double-sided Fresnel-like lens with an optimized thickness. The optimization is performed to obtain a very low attenuation, low material cost, and small weight in the element media. It also provides achromatic properties for the assumed wavelength range. The experimental evaluation of the proposed diffractive lens by means of time-domain spectroscopy is presented and discussed.