Exact revision of the elliptically bent mirror theory

One of the main hurdles for nanometer focusing by a bending mirror lies in the theoretical surface errors by its approximations used for the traditional theory. The impacts of approximations and analytical corrections have been discussed, and the elliptically bent mirror theory has been described during exact mathematical analysis without any approximations. These approximations are harmful for the focusing system with bigger grazing angle, bigger mirror length, and bigger numerical aperture. The properties of equal-moment and single-moment bent mirrors have been described and discussed. Because of its obvious advantages, a single-moment bending mirror has high potential ability for nanometer focusing.     

High-aspect-ratio line focus for an x-ray laser by a deformable mirror

A high-aspect-ratio line focus is required on a plane target in x-ray laser experiments for obtaining a high gain-length product. Inherent wave-front aberrations in line-focusing optics, which consist of a cylindrical lens and a spherical lens, are discussed with respect to beam diameter. The nonuniformity of the linewidth that is due to the aberrations is also calculated by the ABCD matrix method. A deformable mirror of a continuous plate type with a diameter of 185 mm provides an adequate wave-front distribution for compensating for the wave-front aberration. The wave-front control by the deformable mirror realizes a fine linewidth of 25 mum and 18.2 mm long, corresponding to the aspect ratio of 728. The linewidth is three times the diffraction limit. The intensity distribution along the line focus is also improved.     

Electroform replication used for multiple x-ray mirror production

Work done to produce x-ray mirrors via electroform replication is reported. Several advances have been made over previous work. We have produced lower grazing incidence angle (30 min) mirrors, obtained quantitative measurements up to higher energies (6.40 keV), produced about four times as many replicas from one mandrel, and obtained angular resolutions better than other work done with replicated metal mirrors.     

Wolter type I x-ray focusing mirror using multilayer coatings

A multilayer coating is a useful addition to a mirror in the x-ray region and has been applied to normal incidence mirrors used with soft x rays. When a multilayer coating is used on grazing incidence optics, higher performance can be achieved than without it. Cr/Sc multilayers coated on a Wolter type I mirror substrate for a soft x-ray microscope are considered. The reflectivity and effective solid angle are calculated for Wolter type I mirrors with uniform and laterally graded multilayer coatings. The laterally graded multilayer mirror showed superior x-ray performance, and the multilayer tolerances were relaxed. This multilayer mirror could be especially useful in the soft x-ray microscope intended for biological applications.     

Thermal forming of glass microsheets for x-ray telescope mirror segments

We describe a technology to mass-produce ultrathin mirror substrates for x-ray telescopes of near Wolter-I geometry. Thermal glass forming is a low-cost method to produce high-throughput, spaceborne x-ray mirrors for the 0.1-200-keV energy band. These substrates can provide the collecting area envisioned for future x-ray observatories. The glass microsheets are shaped into mirror segments at high temperature by use of a guiding mandrel, without polishing. We determine the physical properties and mechanisms that elucidate the formation process and that are crucial to improve surface quality. We develop a viscodynamic model for the glass strain as the forming proceeds to find the conditions for repeatability. Thermal forming preserves the x-ray reflectance and scattering properties of the raw glass. The imaging resolution is driven by a large wavelength figure. We discuss the sources of figure errors, and we calculate the relaxation time of surface ripples.     

Reflectance of a wideband multilayer x-ray mirror at normal and grazing incidences

The reflectance of a W-B(4)C multilayer mirror, with a period thickness that increased with depth into the multilayer, was measured at near-normal incidence with synchrotron radiation and at grazing incidence with Cu Kα radiation. The period thickness increased linearly from 17.9 ? at the top of the multilayer structure to 21.9 ? at the substrate while the same ratio of nodal layer to period thickness was maintained. For a grazing angle of 80° (10° from normal incidence), the peak reflectance was 1.1% at a wavelength of 36 ?, and the reflectance profile was 1 ? wide. For Cu Kα radiation the reflectance peaked at a grazing angle of 2.4° and was 0.4° wide. Compared with a W-B(4)C multilayer mirror with a constant period thickness, the depth-graded multilayer mirror has wider reflectance profiles at near-normal and grazing incidences, resulting in larger integrated reflectances and wider fields of view.     

Construction and performance of an elliptically polarized undulator of type Apple-II

Ten years ago, an elliptically polarized undulator (EPU) with a periodic length of 56?mm was constructed at the Taiwan Light Source. It was the longest EPU at that time. An electron beam of energy 1.5?GeV and current 300?mA passes through the undulator gap and radiates variously polarized light in the soft X-ray spectral domain. This EPU was extensively used in a wide range of research fields, including inelastic scattering, spin-polarized photoemission spectroscopy, photoelectron emission microscopy, and soft X-ray scattering. In response to increased demand by users with differing experimental requirements and applications, the construction of an EPU with a period of length 46?mm is under way. This investigation describes many aspects of the magnetic design, the structural engineering, and the control system. As magnetic technology is undergoing dramatic advances, advanced mechanical devices, and mechanisms have been included in the new EPU design; this design and its differences from the earlier design are summarized here.     

Theory of reflectivity of an asymmetric mirror

By using the concept of transfer matrices and Bloch waves, we have derived a set of equations that provide insight into the operation of asymmetric Bragg reflectors that have been demonstrated to be useful in achieving high reflectivities in strained-material systems. These equations will be useful in the design of asymmetric mirrors and can be used to compare the trade-offs between the conventional, symmetric (quarter-wavelength), and asymmetric mirrors.     

Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry

We assesses the efficiency of x-ray Talbot interferometry (XTI), a technique based on the Talbot effect for measuring a wavefront gradient, in terms of how quickly it can capture a high-quality phase image with a large signal-to-noise ratio for a given incident photon number. Photon statistics cause errors in the phase of the moiré fringes and impose a detection limit on the wavefront gradient. The relation between the incident photon number and the detection limit is determined, and a figure of merit of XTI for a monochromatic cone beam is then defined. The dependence of the figure of merit on optical system parameters, such as grating pitch and position, is then discussed. The effects of varying the pattern height and linewidth of the second grating are shown for rectangular and trapezoidal teeth. Finally, we show how to design a practical cone-beam Talbot interferometer for certain boundary conditions.     

Electric field meter with a dipole antenna in an elliptically polarized electric field

A model of an electric field meter with a dipole antenna is analyzed. The model takes into account the fact that the meter incorporates other elements with a conducting surface in addition to the dipole antenna, viz.: a matching device, a signal cable, and a voltmeter. Alternative forms of the measurement equation are obtained, which differ in the error associated with the currents induced by the measured electric field on the braid of the signal cable and on the casing of the voltmeter. It is shown that this error can be eliminated partially or completely by performing additional measurements with the dipole antenna in different positions.Translated from Izmeritel'naya Tekhnika, No. 2, pp. 45–48, February, 1994.     

Synthetic RNA-protein complex shaped like an equilateral triangle

Synthetic nanostructures consisting of biomacromolecules such as nucleic acids have been constructed using bottom-up approaches. In particular, Watson-Crick base pairing has been used to construct a variety of two- and three-dimensional DNA nanostructures. Here, we show that RNA and the ribosomal protein L7Ae can form a nanostructure shaped like an equilateral triangle that consists of three proteins bound to an RNA scaffold. The construction of the complex relies on the proteins binding to kink-turn (K-turn) motifs in the RNA, which allows the RNA to bend by ～ 60° at three positions to form a triangle. Functional RNA-protein complexes constructed with this approach could have applications in nanomedicine and synthetic biology.     

Resolution of elliptically averaged small-angle scattering data

The elliptical average of small-angle scattering data requires the two-dimensional detector to be divided into concentric elliptical rings of some width with an eccentricity and orientation determined from the data. A modified scattering vector which contains the elliptical dependence is defined, and an expression is derived for the resolution of the elliptically binned data which has a form similar to that for the circularly averaged data. The optimization conditions are such that the appropriate binning width depends on the spectrometer apertures and on the eccentricity of the data.     

Generation of optical vortices with an adaptive helical mirror

Generation of optical vortices using a new design of adaptive helical mirror (AHM) is reported. The new AHM is a reflective device that can generate an optical vortex of any desired topological charge, both positive and negative, within its breakdown limits. The most fascinating feature of the AHM is that the topological charge of the optical vortex generated with it can be changed in real time by varying the excitation voltage. Generation of optical vortices up to topological charge 4 has been demonstrated. The presence of a vortex in the optical field generated with the AHM is confirmed by producing both fork and spiral fringes in an interferometric setup. Various design improvements to further enhance the performance of the reported AHM are discussed. Some of the important applications of AHM are also listed.     

Fundamental spatial resolution of an x-ray pore optic

We investigate the fundamental spatial resolution of an x-ray pore optic as a function of the pore dimensions, the photon energy, and the focal length. We achieve this by calculating the shape of the focal spot, using diffraction integrals such that the half-energy width is determined. Quantitative results are presented for the X-Ray Evolving Universe Spectroscopy (XEUS) telescope, showing that a resolution of better than 2 arc sec half-energy width is possible by use of an optic with pore sizes of approximately 0.5 mm.     

Transversely isotropic piezoelectric materials with an arbitrarily shaped boundary

Summary In this paper, a two-dimensional electro-elastic analysis is performed on transversely isotropic piezoelectric materials containing an arbitrarily shaped boundary under out-of-plane mechanical and in-plane electrical loads at infinity. General closed-formed solutions are provided in terms of complex functions by using the conformal mapping technique. Using such solutions, several numerical examples are shown by graphical representation for various arbitrarily shaped boundaries. The effects of stress concentration on arbitrarily shaped boundaries are discussed. The stress intensity factors of mode III at the cusp are computed.     

Formal convergence characteristics of elliptically constrained incremental Newton-Raphson algorithms

Numerous situations in continuum mechanics, structural stability, optimization and related fields generate problems requiring the solution of nonlinear algebraic equations. To solve such problems, a large assortment of schemes has evolved over the years. This paper will consider the formal numerical properties of the newly developed constrained type incremental Newton-Raphson operator schemes. Specifically the evaluation of the formal behavior of the elliptically constrained version is treated in detail. Note this procedure has the versatility to efficiently handle a wide range of nonlinearities including the possibilities of positive, negative, semi and indefinite tangent properties in an inherently stable manner. The formalism includes such items as determining from both a global as well as local point of view the existence, uniqueness and convergence characteristics. Also included in the developments will be the determination of the occurrence of global safety zones wherein convergence is assured. The approach taken is general enough to provide a framework to enable applications to a wide variety of constrained schemes involving continuous, piecewise continuous, closed or open constraint conditions.     

Design of an adaptive secondary mirror: a global approach

We present the mechanical and actuator design of an adaptive secondary mirror that matches the optical requirements of the active and adaptive corrections. Conceived for the particular implementation for the 6.5-m conversion of the multiple-mirror telescope, with small variations of the input parameters this study is suitable for applications for telescopes of the same class. We found that a three-layer structure, i.e., a thin deformable shell, a thick reference plate, and a third plate that acts as actuator support and heat sink, is able to provide the required mechanical stability and actuator density. We also found that a simple electromagnetic actuator can be used. This actuator, when optimized, will dissipate a typical power of a few tenths of watts.     

Asymmetric optical loop mirror: analysis of an all-optical switch

We present an analysis of the optical loop mirror in which a nonlinear optical element is asymmetrically placed in the loop. This analysis provides a general framework for the operation of a recently invented ultrafast all-optical switch known as the terahertz optical asymmetric demultiplexer. We show that a loop with small asymmetry, such as that used in the terahertz optical asymmetric demultiplexer, permits low-power ultrafast all-optical sampling and demultiplexing to be performed with a relatively slow optical nonlinearity. The size of the loop is completely irrelevant to switch operation as long as the required degree of asymmetry is accommodated. This is therefore the first low-power ultrafast all-optical switch that can be integrated on a single substrate.