Multilayer Laue Lenses Research Articles

Finite-difference propagation for the simulation of x-ray multilayer optics

Recent progress in nanofabrication, namely of multilayer optics, and the construction of coherent hard x-ray sources has enabled high resolution x-ray microscopy with large numerical aperture optics for small focal spot sizes. Sub-10 nm and even sub-5 nm focal spot sizes have already been achieved using multilayer optics such as multilayer Laue lenses and multilayer zone plates. However these optics can not be described by the kinematic theory given their extreme aspect-ratio between the depth (thickness) and the layer width. Moreover, the numerical simulation of these optics is challenging, and the absence of an accessible numerical framework inhibits further progress in their design and utilization. Here, we simulate the propagation of x-ray wavefields within and behind optical multilayer elements using a finite-difference propagation method. We show that the method offers high accuracy at reasonable computational cost. We investigate how small focal spot sizes and highest diffraction efficiency of multilayer optics can be achieved, considering volume diffraction effects such as waveguiding and Pendellösung. Finally, we show the simulation of a novel imaging scheme, allowing for a detailed study of image formation and the development of customized phase retrieval schemes.

Calculated performance of multilayer Laue lens based on actual layer thickness and coupled wave theory

The multilayer Laue lens (MLL) is a promising optical element with large numerical aperture and aspect ratio in synchrotron radiation facility to focus hard x-ray to 1 nm with ideal structure. We use a new method of combining actual film thickness and the coupled wave theory to calculate focusing performance. Here, a 17.2-μm-MLL with a focal spot size of 17 nm at 10 keV is designed and fabricated by dynamical diffraction theory and direct current magnetron sputtering technology. Based on a new rate calibration and symbol layer insertion method, we calculate d-spacing of multilayer instead of individual layer thickness and change the order of two layers as a symbol so as not to damage zone plate law. The scanning electron microscope image is smoothed and binary transformed to measure the actual thickness of each layer. The full-width at half-maximum of focus spot is 18 nm, which is close to the theoretical result of 17 nm.

High-resolution achromatic X-ray optical systems for broad-band imaging and for focusing attosecond pulses.

Achromatic focusing systems for hard X-rays are examined which consist of a refractive lens paired with a diffractive lens. Compared with previous analyses, we take into account the behaviour of thick refractive lenses, such as compound refractive lenses and waveguide gradient index refractive lenses, in which both the focal length and the position of the principal planes vary with wavelength. Achromatic systems formed by the combination of such a thick refractive lens with a multilayer Laue lens are found that can operate at a focusing resolution of about 3 nm, over a relative bandwidth of about 1%. With the appropriate distance between the refractive and diffractive lenses, apochromatic systems can also be found, which operate over relative bandwidth greater than 10%. These systems can be used to focus short pulses without distorting them in time by more than several attoseconds. Such systems are suitable for high-flux scanning microscopy and for creating high intensities from attosecond X-ray pulses.

Design of multilayer-based diagnostics for measurement of high energy x rays and gamma rays

We investigate several possible multilayer-based optic designs for future hard x-ray and gamma ray diagnostics, including the detection and measurement of the positron annihilation radiation at 511 keV. The focus is set on increasing the photon efficiency and signal-to-noise ratio, compared to a previous multilayer-based system that was successfully employed to measure spectra in the 55 keV-100 keV range. Several possible designs using multilayer coatings are discussed, including mirror-based optics and multilayer Laue lenses.

Analysis of X-ray multilayer Laue lenses made by masked deposition.

Multilayer Laue lenses are diffractive optics for hard X-rays. To achieve high numerical aperture and resolution, diffracting structures of nanometer periods are required in such lenses, and a thickness (in the direction of propagation) of several micrometers is needed for high diffracting efficiency. Such structures must be oriented to satisfy Bragg's law, which can only be achieved consistently over the entire lens if the layers vary in their tilt relative to the incident beam. The correct tilt, for a particular wavelength, can be achieved with a very simple technique of using a straight-edge mask to give the necessary gradient of the layers. An analysis of the properties of lenses cut from such a shaded profile is presented and it is shown how to design, prepare, and characterize matched pairs of lenses that operate at a particular wavelength and focal length. It is also shown how to manufacture lenses with ideal curved layers for optimal efficiency.

A ray-trace analysis of x-ray multilayer Laue lenses for nanometer focusing

Thick diffractive optical elements offer a promising way to achieve focusing or imaging at a resolution approaching 1 nm for x-ray wavelengths shorter than about 0.1 nm. Efficient focusing requires that these are fabricated with structures that vary in period and orientation so that rays obey Bragg’s law over the entire lens aperture and give rise to constructive interference at the focus. Here the analysis method of ray-tracing of thick diffractive optical elements is applied to such lenses to optimise their designs and to investigate their operating and manufacturing tolerances. Expressions are provided of the fourth-order series expansions of the wavefront aberrations and transmissions of both axi-symmetric lenses and pairs of crossed lenses that each focuses in only one dimension like a cylindrical lens. We find that aplanatic zone-plate designs, whereby aberrations are corrected over a large field of view, can be achieved by axi-symmetric lenses but not the crossed lenses. We investigate the performance of 1 nm-resolution lenses with focal lengths of about 1 mm and show their fields of view are mainly limited by the acceptance angle of Bragg diffraction, and that aberrations can limit the performance of lenses with longer focal lengths. We apply the ray-tracing formalism for a tolerancing analysis of imperfect lenses and examine some strategies for the correction of their aberrations.

Micromachined Silicon Platform for Precise Assembly of 2D Multilayer Laue Lenses for High-Resolution X-ray Microscopy.

We report on a developed micromachined silicon platform for the precise assembly of 2D multilayer Laue lenses (MLLs) for high-resolution X-ray microscopy. The platform is 10 × 10 mm2 and is fabricated on ~500 µm thick silicon wafers through multiple steps of photolithography and deep reactive-ion etching. The platform accommodates two linear MLLs in a pre-defined configuration with precise angular and lateral position control. In this work, we discuss the design and microfabrication of the platform, and characterization regarding MLLs assembly, position control, repeatability, and stability. The results demonstrate that a micromachined platform can be used for the assembly of a variety of MLLs with different dimensions and optical parameters. The angular misalignment of 2D MLLs is well controlled in the range of the designed accuracy, down to a few millidegrees. The separation distance between MLLs is adjustable from hundreds to more than one thousand micrometers. The use of the developed platform greatly simplifies the alignment procedure of the MLL optics and reduces the complexity of the X-ray microscope. It is a significant step forward for the development of monolithic 2D MLL nanofocusing optics for high-resolution X-ray microscopy.

Ptychographic X-ray speckle tracking with multi-layer Laue lens systems.

The ever-increasing brightness of synchrotron radiation sources demands improved X-ray optics to utilize their capability for imaging and probing biological cells, nano-devices and functional matter on the nanometre scale with chemical sensitivity. Hard X-rays are ideal for high-resolution imaging and spectroscopic applications owing to their short wavelength, high penetrating power and chemical sensitivity. The penetrating power that makes X-rays useful for imaging also makes focusing them technologically challenging. Recent developments in layer deposition techniques have enabled the fabrication of a series of highly focusing X-ray lenses, known as wedged multi-layer Laue lenses. Improvements to the lens design and fabrication technique demand an accurate, robust, in situ and at-wavelength characterization method. To this end, a modified form of the speckle tracking wavefront metrology method has been developed. The ptychographic X-ray speckle tracking method is capable of operating with highly divergent wavefields. A useful by-product of this method is that it also provides high-resolution and aberration-free projection images of extended specimens. Three separate experiments using this method are reported, where the ray path angles have been resolved to within 4 nrad with an imaging resolution of 45 nm (full period). This method does not require a high degree of coherence, making it suitable for laboratory-based X-ray sources. Likewise, it is robust to errors in the registered sample positions, making it suitable for X-ray free-electron laser facilities, where beam-pointing fluctuations can be problematic for wavefront metrology.

2D MEMS-based multilayer Laue lens nanofocusing optics for high-resolution hard x-ray microscopy.

We report on the development of 2D integrated multilayer Laue lens (MLL) nanofocusing optics used for high-resolution x-ray microscopy. A Micro-Electro-Mechanical-Systems (MEMS) - based template has been designed and fabricated to accommodate two linear MLL optics in pre-aligned configuration. The orthogonality requirement between two MLLs has been satisfied to a better than 6 millidegrees level, and the separation along the x-ray beam direction was controlled on a micrometer scale. Developed planar 2D MLL structure has demonstrated astigmatism free point focus of ∼14 nm by ∼13 nm in horizontal and vertical directions, respectively, at 13.6 keV photon energy. Approaching 10 nm resolution with integrated 2D MLL optic is a significant step forward in applications of multilayer Laue lenses for high-resolution hard x-ray microscopy and their adoption by the general x-ray microscopy community.

Effect of the Mismatch of Layer Thicknesses on the Focusing of X Rays by Multilayer Laue Lens

A numerical simulation has been performed to study the effect of the mismatch of layer thicknesses of multilayer Laue lenses (MLLs) on X-ray focusing. The spatial distributions of X-ray intensities in the bulk of a lens have been calculated with different gradients of the variation of the period of a MLL. It has been shown that the focal length, as well as the focal spot size, decreases with an increase in the mismatch of layer thicknesses of the MLL. The calculated focal spot size are significantly different from the values reported in other works. A physical nature of the focusing by the MLL has been revealed. It is determined by the Bragg diffraction and is not related to the configuration of the Fresnel zone plate.

О фокусировке рентгеновских лучей клиновыми многослойными Лауэ линзами

О фокусировке рентгеновских лучей клиновыми многослойными Лауэ линзами

Multilayer Laue lenses at high X-ray energies: performance and applications.

X-ray microscopy at photon energies above 15 keV is very attractive for the investigation of atomic and nanoscale properties of technologically relevant structural and bio materials. This method is limited by the quality of X-ray optics. Multilayer Laue lenses (MLLs) have the potential to make a major impact in this field because, as compared to other X-ray optics, they become more efficient and effective with increasing photon energy. In this work, MLLs were utilized with hard X-rays at photon energies up to 34.5 keV. The design, fabrication, and performance of these lenses are presented, and their application in several imaging configurations is described. In particular, two "full field" modes of imaging were explored, which provide various contrast modalities that are useful for materials characterisation. These include point projection imaging (or Gabor holography) for phase contrast imaging and direct imaging with both bright-field and dark-field illumination. With high-efficiency MLLs, such modes offer rapid data collection as compared with scanning methods as well as a large field of views.

Large Aperture and Wedged Multilayer Laue Lens for X-ray Nanofocusing.

Diffraction optics fabricated from multilayers offer an intriguing alternative to lithography-based zone plates due to their advantages of virtually limitless aspect ratio and extremely small feature size. However, other issues, intrinsic to thin-film deposition, such as film stress and deposition rate instability, for example, limit the total achievable aperture. Over the last decade, Multilayer Laue Lens (MLLs) have progressed from a mere curiosity with initial aperture sizes in the 3-10 μm range, to real beamline-deployed optics with apertures in the 40-50 μm range (X. Huang, et al., Scientific Reports 3, 3562 (2013); E. Nazaretski, et al., Rev. Sci. Instrum. 85, 033707 (2014); E. Nazaretski, et al., Journal of Synchrotron Radiation 24, 1113 (2017)). By optimizing deposition conditions and incorporating new materials, MLLs have now broken the 100 μm thickness milestone. A flat WSi₂/Al-Si MLL with a deposition thickness of 102 μm, the largest MLL to date, is reviewed. New large aperture wedged MLLs (wMLL), which were first fabricated by APS in 2006 using the WSi2/Si material system, are presented which demonstrate high focusing efficiency across a broad energy range. These results confirm findings by other groups who have also independently fabricated wMLL (A. J. Morgan, et al., Scientific Reports 5, 9892 (2015); S. Bajt, et al., Nature Light: Science and Applications 7, 17162 (2017)) based on a similar material system.

Multilayer Laue Lenses (MLL) with 45 mm Focal Length as Optics for In-situ Nanoindentation Experiments

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High-Resolution and High-Throughput Ptychography with Depth Sensitivity Using Multilayer Laue Lenses

High-Resolution and High-Throughput Ptychography with Depth Sensitivity Using Multilayer Laue Lenses

Characterization of High Numerical Aperture Multilayer Laue Lenses

Characterization of High Numerical Aperture Multilayer Laue Lenses

Multi-slice ptychography with large numerical aperture multilayer Laue lenses

The highly convergent x-ray beam focused by multilayer Laue lenses with large numerical apertures is used as a three-dimensional (3D) probe to image layered structures with an axial separation larger than the depth of focus. Instead of collecting weakly scattered high-spatial-frequency signals, the depth-resolving power is provided purely by the intense central cone diverged from the focused beam. Using the multi-slice ptychography method combined with the on-the-fly scan scheme, two layers of nanoparticles separated by 10 μm are successfully reconstructed with 8.1 nm lateral resolution and with a dwell time as low as 0.05 s per scan point. This approach obtains high-resolution images with extended depth of field, which paves the way for multi-slice ptychography as a high throughput technique for high-resolution 3D imaging of thick samples.

On the Properties of WC/SiC Multilayers

A study of the materials properties of WC/SiC multilayer coatings is presented. We investigated the dependence of interface and surface roughness, intrinsic stress, microstructure, chemical composition, and stoichiometry as a function of multilayer period and in some cases compared these to W/SiC multilayer systems. The WC/SiC material pair forms multilayers with extremely smooth and sharp interfaces and both materials remain amorphous over a wide range of thicknesses. These properties are desirable for multilayer-based high-resolution diffractive x-ray optics, such as multilayer Laue lenses (MLLs), which require very thick films in which the layer spacing varies considerably. Thermal and structural stability studies show that WC/SiC multilayers have exceptional thermal stability, making this an extremely robust and favorable material pair for MLLs and other multilayer-based X-ray optical elements.

Sub 25 nm focusing with a long working distance using multilayer Laue lenses

We report on recent results of focusing experiments with monolithic assembled multilayer Laue lenses (MLLs) at ESRF ID13 with a focal length of 9.5 mm at an X-ray photon energy of 12.7 keV. Using an aperture of approximately 40 \ extmu m we have achieved a size of the focal profiles of less than 25 nm in horizontal and vertical direction with a physical working distance of approximately 2.5 mm. The current MLL mounting approach is aiming for the reduction of the physical distance of the two crossed lenses. Assuming an identical focal length of both ideally the downstream surface to downstream surface distance of the lenses should be smaller than the depth of focus. This would avoid the otherwise necessary matching of the focal lengths and significantly reduce the alignment complexity of an MLL pair.

Multimodal hard x-ray imaging with resolution approaching 10 nm for studies in material science

We report multimodal scanning hard x-ray imaging with spatial resolution approaching 10 nm and its application to contemporary studies in the field of material science. The high spatial resolution is achieved by focusing hard x-rays with two crossed multilayer Laue lenses and raster-scanning a sample with respect to the nanofocusing optics. Various techniques are used to characterize and verify the achieved focus size and imaging resolution. The multimodal imaging is realized by utilizing simultaneously absorption-, phase-, and fluorescence-contrast mechanisms. The combination of high spatial resolution and multimodal imaging enables a comprehensive study of a sample on a very fine length scale. In this work, the unique multimodal imaging capability was used to investigate a mixed ionic-electronic conducting ceramic-based membrane material employed in solid oxide fuel cells and membrane separations (compound of Ce0.8Gd0.2O2−x and CoFe2O4) which revealed the existence of an emergent material phase and quantified the chemical complexity at the nanoscale.