The coherent radiation fraction of low‐emittance synchrotrons

In this work the coherence properties of the synchrotron radiation beam from an X‐ray undulator in a fourth‐generation storage ring are analyzed. A slightly focused X‐ray beam is simulated using a wavefront propagation through a non‐redundant array of slits and the mutual coherence function is directly obtained and compared with the Gaussian–Schell approximation. The numerical wave propagation and the approximate analytical approaches are shown to agree qualitatively, and it is also shown that, when the coherent fraction is selected by a finite aperture before the focusing element, even achromatic focusing systems like total reflection mirrors become slightly chromatic. This effect is also well accounted for in the Gaussian–Schell model. The wavefront propagation simulation through the non‐redundant array was repeated with an imperfect mirror demonstrating that, although the wavefront is distorted, its coherent length is practically unchanged.     

Design,development and first experiments on the X‐ray imaging beamline at Indus‐2 synchrotron source RRCAT,India

A full‐field hard X‐ray imaging beamline (BL‐4) was designed, developed, installed and commissioned recently at the Indus‐2 synchrotron radiation source at RRCAT, Indore, India. The bending‐magnet beamline is operated in monochromatic and white beam mode. A variety of imaging techniques are implemented such as high‐resolution radiography, propagation‐ and analyzer‐based phase contrast imaging, real‐time imaging, absorption and phase contrast tomography etc. First experiments on propagation‐based phase contrast imaging and micro‐tomography are reported.     

A microfocus X‐ray fluorescence beamline at Indus‐2 synchrotron radiation facility

A microfocus X‐ray fluorescence spectroscopy beamline (BL‐16) at the Indian synchrotron radiation facility Indus‐2 has been constructed with an experimental emphasis on environmental, archaeological, biomedical and material science applications involving heavy metal speciation and their localization. The beamline offers a combination of different analytical probes, e.g. X‐ray fluorescence mapping, X‐ray microspectroscopy and total‐external‐reflection fluorescence characterization. The beamline is installed on a bending‐magnet source with a working X‐ray energy range of 4–20 keV, enabling it to excite K‐edges of all elements from S to Nb and L‐edges from Ag to U. The optics of the beamline comprises of a double‐crystal monochromator with Si(111) symmetric and asymmetric crystals and a pair of Kirkpatrick–Baez focusing mirrors. This paper describes the performance of the beamline and its capabilities with examples of measured results.     

I18 – the microfocus spectroscopy beamline at the Diamond Light Source

The design and performance of the microfocus spectroscopy beamline at the Diamond Light Source are described. The beamline is based on a 27 mm‐period undulator to give an operable energy range between 2 and 20.7 keV, enabling it to cover the K‐edges of the elements from P to Mo and the L₃‐edges from Sr to Pu. Micro‐X‐ray fluorescence, micro‐EXAFS and micro‐X‐ray diffraction have all been achieved on the beamline with a spot size of ～3 µm. The principal optical elements of the beamline consist of a toroid mirror, a liquid‐nitrogen‐cooled double‐crystal monochromator and a pair of bimorph Kirkpatrick–Baez mirrors. The performance of the optics is compared with theoretical values and a few of the early experimental results are summarized.     

Versatility of a hard X‐ray Kirkpatrick–Baez focus characterized by ptychography

In the past decade Kirkpatrick–Baez (KB) mirrors have been established as powerful focusing systems in hard X‐ray microscopy applications. Here a ptychographic characterization of the KB focus in the dedicated nano‐imaging setup GINIX (Göttingen Instrument for Nano‐Imaging with X‐rays) at the P10 coherence beamline of the PETRA III synchrotron at HASLYLAB/DESY, Germany, is reported. More specifically, it is shown how aberrations in the KB beam, caused by imperfections in the height profile of the focusing mirrors, can be eliminated using a pinhole as a spatial filter near the focal plane. A combination of different pinhole sizes and illumination conditions of the KB setup makes the prepared optical setup well suited not only for high‐resolution ptychographic coherent X‐ray diffractive imaging but also for moderate‐resolution/large‐field‐of‐view propagation imaging in the divergent KB beam.     

Coherence and wavefront characterization of Si‐111 monochromators using double‐grating interferometry

A study of the coherence and wavefront properties of a pseudo‐channel‐cut monochromator in comparison with a double‐crystal monochromator is presented. Using a double‐grating interferometer designed for the hard X‐ray regime, the complex coherence factor was measured and the wavefront distortions at the sample position were analyzed. A transverse coherence length was found in the vertical direction that was a factor of two larger for the channel‐cut monochromator owing to its higher mechanical stability. The wavefront distortions after different optical elements in the beam, such as monochromators and mirrors, were also quantified. This work is particularly relevant for coherent diffraction imaging experiments with synchrotron sources.     

Single-nanometer focusing of hard x-rays by Kirkpatrick-Baez mirrors

We have constructed an extremely precise optical system for hard-x-ray nanofocusing in a synchrotron radiation beamline. Precision multilayer mirrors were fabricated, tested, and employed as Kirkpatrick-Baez mirrors with a novel phase error compensator. In the phase compensator, an at-wavelength wavefront error sensing method based on x-ray interferometry and an in situ phase compensator mirror, which adaptively deforms with nanometer precision, were developed to satisfy the Rayleigh criterion to achieve diffraction-limited focusing in a single-nanometer range. The performance of the optics was tested at BL29XUL of SPring-8 and was confirmed to realize a spot size of approximately 7 nm.     

相位差波前检测方法应用于平移误差检测的实验研究

相位差波前检测方法由于其结构简单,对环境要求低,测量精度较高等优点,被应用于诸多领域.本文针对拼接型天文望远镜中主镜的共相位检测问题,对相位差波前检测方法在拼接主镜各子镜间平移误差测量进行理论分析,并搭建了实验光路.实验结果表明:相位差波前检测方法对拼接镜平移误差的测量精度高于λ/20(λ为波长),满足系统对拼接平移误差的要求.     

Coherence and intensity moments of laser light

Taking the modal behaviours of the laser field into account, the coherence properties of laser light can be characterized by mode coherence functions (MCFs) and mode coherence coefficients (MCCs). Changes in laser light properties due to optical operations can be described by transformation laws for the MCFs and the MCCs. The transformation laws as well as transformation matrices for propagation in free space, phase transformations, spatial amplitude modulations and aperturizing are given. Furthermore, intensity distributions and intensity moments in the spatial and in the spatial frequency domains are expressed in terms of the MCCs. General expressions for the beam quality factors,M ²s, obtained using the intensity moments and some useful expressions for intensity moments of higher order are discussed.     

Transverse-longitudinal coherence function of a sound field for line-of-sight propagation in a turbulent atmosphere

Using the narrow-angle and Markov approximations, a formula for the transverse-longitudinal coherence function of a sound field propagating in a turbulent atmosphere with temperature and wind velocity fluctuations is derived. This function, which applies to observation points that are arbitrarily located in space, generalizes the transverse coherence function (coherence when the observation points are in a plane perpendicular to the sound propagation path), which has been studied extensively. The new result is expressed in terms of the transverse coherence function and the extinction coefficient of the mean sound field. The transverse-longitudinal coherence function of a plane sound wave is then calculated and studied in detail for the Gaussian and von Kármán spectra of temperature and wind velocity fluctuations. It is shown, for relatively small propagation distances, that the magnitude of the coherence function decreases in the longitudinal direction but remains almost constant in the transverse direction. On the other hand, for moderate and large propagation distances, the magnitude of the coherence decreases faster in the transverse direction than in the longitudinal. For some parameters of the problem, the coherence function has relatively large local maxima and minima as the transverse and longitudinal coordinates are varied. With small modifications, many results obtained in the paper can be applied to studies of electromagnetic wave propagation in a turbulent atmosphere.     

Fresnel integral in the complex form: Its new representation,interpretation, and application in problems of wave beam diffraction

A new representation for the complex Fresnel integral, allowing for its transformation into the trigonometric form, and its new interpretation based on the 2D Cornu spiral and a 3D spiral with a smooth envelope surface have been obtained. Within this representation the integral is separated into a constant part and a rapidly oscillating additive. The former is responsible for the geometrical-optical field transport, and the latter implements diffraction. This separation is exact. Based on this approach, we have proposed and implemented a new method for solving the problems of wave beam propagation in the near-field zone on a large-scale grid at large optical distortions of the wavefront, with a transport of the initial-wave amplitude and phase. The amplitude is approximated by a step or linear function, and the phase is approximated taking into account the local linear tilt and focusing of the wavefront. The physical meaning of the solutions obtained is established. The approach proposed allows one to perform regular calculations of wave field propagation in the near-field zone on a large-scale grid (up to ∼10 points within aperture) at large initial wavefront aberrations (up to ∼100λ or more).     

Performance calculations of the X‐ray powder diffraction beamline at NSLS‐II

The X‐ray Powder Diffraction (XPD) beamline at the National Synchrotron Light Source II is a multi‐purpose high‐energy X‐ray diffraction beamline with high throughput and high resolution. The beamline uses a sagittally bent double‐Laue crystal monochromator to provide X‐rays over a large energy range (30–70 keV). In this paper the optical design and the calculated performance of the XPD beamline are presented. The damping wiggler source is simulated by the SRW code and a filter system is designed to optimize the photon flux as well as to reduce the heat load on the first optics. The final beamline performance under two operation modes is simulated using the SHADOW program. For the first time a multi‐lamellar model is introduced and implemented in the ray tracing of the bent Laue crystal monochromator. The optimization and the optical properties of the vertical focusing mirror are also discussed. Finally, the instrumental resolution function of the XPD beamline is described in an analytical method.     

Kirkpatrick–Baez mirrors to focus hard X‐rays in two dimensions as fabricated,tested and installed at the Advanced Photon Source

The micro‐focusing performance for hard X‐rays of a fixed‐geometry elliptical Kirkpatrick–Baez (K–B) mirrors assembly fabricated, tested and finally implemented at the micro‐probe beamline 8‐BM of the Advanced Photon Source is reported. Testing of the K–B mirror system was performed at the optics and detector test beamline 1‐BM. K–B mirrors of length 80 mm and 60 mm were fabricated by profile coating with Pt metal to produce focal lengths of 250 mm and 155 mm for 3 mrad incident angle. For the critical angle of Pt, a broad bandwidth of energies up to 20 keV applies. The classical K–B sequential mirror geometry was used, and mirrors were mounted on micro‐translation stages. The beam intensity profiles were measured by differentiating the curves of intensity data measured using a wire‐scanning method. A beam size of 1.3 µm (V) and 1.2 µm (H) was measured with monochromatic X‐rays of 18 keV at 1‐BM. After installation at 8‐BM the measured focus met the design requirements. In this paper the fabrication and metrology of the K–B mirrors are reported, as well as the focusing performances of the full mirrors‐plus‐mount set‐up at both beamlines.     

In situ removal of carbon contamination from optics in a vacuum ultraviolet and soft X‐ray undulator beamline using oxygen activated by zeroth‐order synchrotron radiation

Carbon contamination of optics is a serious issue in all soft X‐ray beamlines because it decreases the quality of experimental data, such as near‐edge X‐ray absorption fine structure, resonant photoemission and resonant soft X‐ray emission spectra in the carbon K‐edge region. Here an in situ method involving the use of oxygen activated by zeroth‐order synchrotron radiation was used to clean the optics in a vacuum ultraviolet and soft X‐ray undulator beamline, BL‐13A at the Photon Factory in Tsukuba, Japan. The carbon contamination of the optics was removed by exposing them to oxygen at a pressure of 10^?1–10^?4 Pa for 17–20 h and simultaneously irradiating them with zeroth‐order synchrotron radiation. After the cleaning, the decrease in the photon intensity in the carbon K‐edge region reduced to 2–5%. The base pressure of the beamline recovered to 10^?7–10^?8 Pa in one day without baking. The beamline can be used without additional commissioning.     

同步辐射中双压电片反射镜的研究现状

反射镜是同步辐射光束线中应用广泛的光学元件之一,双压电片反射镜由于具有结构简单、面形能动以及自适应可调等优点,逐渐引起同步辐射界的重视.本文综述了同步辐射中双压电片反射镜的研究现状.主要讨论了双压电片反射镜的工作原理和研究概况,包括在几个大型同步辐射装置中的结构特点、制备技术及面形校正结果等;简要介绍了双压电片反射镜面形校正时所采用的反射波前探测技术和反馈控制算法;最后总结了其发展中存在的关键问题,并展望了其未来的发展方向.     

Microfocusing options for the inelastic X‐ray scattering beamline at sector 3 of the Advanced Photon Source

Synchrotron radiation from third‐generation high‐brilliance storage rings is an ideal source for X‐ray microbeams. The aim of this paper is to describe a microfocusing scheme that combines both a toroidal mirror and Kirkpatrick–Baez (KB) mirrors for upgrading the existing optical system for inelastic X‐ray scattering experiments at sector 3 of the Advanced Photon Source. SHADOW ray‐tracing simulations without considering slope errors of both the toroidal mirror and KB mirrors show that this combination can provide a beam size of 4.5 µm (H) × 0.6 µm (V) (FWHM) at the end of the existing D‐station (66 m from the source) with use of full beam transmission of up to 59%, and a beam size of 3.7 µm (H) × 0.46 µm (V) (FWHM) at the front‐end of the proposed E‐station (68 m from the source) with a transmission of up to 52%. A beam size of about 5 µm (H) × 1 µm (V) can be obtained, which is close to the ideal case, by using high‐quality mirrors (with slope errors of less than 0.5 µrad r.m.s.). Considering the slope errors of the existing toroidal and KB mirrors (5 and 2.9 µrad r.m.s., respectively), the beam size grows to about 13.5 µm (H) × 6.3 µm (V) at the end of the D‐station and to 12.0 µm (H) × 6.0 µm (V) at the front‐end of the proposed E‐station. The simulations presented here are compared with the experimental measurements that are significantly larger than the theoretical values even when slope error is included in the simulations. This is because of the experimental set‐up that could not yet be optimized.     

开放的V型三能级系统中原子注入和退出速率对位相相关的无反转激光增益和强度空间演化的调制作用

利用数值计算结果, 研究了具有自发辐射诱导相干的开放V 型三能级原子系统中的传播效应. 研究表明: 改变探测场和驱动场之间的相对位相对无反转激光(LWI)增益和 强度随传播距离的变化即空间演化具有重要的影响; 而原子的注入速率比(S)和退出速率(r₀)的改变将对位相相关的LWI增益和强度的空间演化产生明显的调制作用. 在S(r₀)的一定取值范围内, S(r₀)的值越大, LWI增益和强度越大且强度达到极大值需要的传播距离越长; 相应封闭系统中LWI增益和强度的最大值及能产生增益的传播距离都小于开放系统. Doppler效应对LWI增益和强度的空间演化也具有明显的影响, 存在Doppler效应时得到的LWI增益和强度明显小于无Doppler效应时的值.     

Simultaneous measurement of X‐ray diffraction and ferroelectric polarization data as a function of applied electric field and frequency

The characteristics of a new ferroelectric measurement system at the European Synchrotron Radiation Facility are presented. The electric‐field‐induced phase transitions of Pb(Mg_1/3Nb_2/3)O₃–xPbTiO₃ are determined viain situ measurements of electric polarization within the synchrotron diffraction beamline. Real‐time data collection methods on single‐crystal samples are employed as a function of frequency to determine the microstructural origin of piezoelectric effects within these materials, probing the dynamic ferroelectric response.