Albert T. Macrander

Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens

We report improved results for hard x-ray focusing using a multilayer Laue lens MLL. We have measured a line focus of 16 nm width with an efficiency of 31% at a wavelength =0.064 nm 19.5 keV using a partial MLL structure with an outermost zone width of 5 nm. The results are in good agreement with the theoretically predicted performance.

Short focal length Kirkpatrick-Baez mirrors for a hard x-ray nanoprobe

We describe progress in the fabrication of short-focal-length total-external-reflection Kirkpatrick-Baez x-ray mirrors with ultralow figure errors. The short focal length optics produce nanoscale beams (<100nm) on conventional (∼64m long) beamlines at third generation synchrotron sources. The total-external reflection optics are inherently achromatic and efficiently focus a white (polychromatic) or a tunable monochromatic spectrum of x rays. The ability to focus independent of wavelength allows novel new experimental capabilities. Mirrors have been fabricated both by computer assisted profiling (differential polishing) and by profile coating (coating through a mask onto ultra-smooth surfaces). A doubly focused 85×95nm2 hard x-ray nanobeam has been obtained on the UNICAT beamline 34-ID at the Advanced Photon Source. The performance of the mirrors, techniques for characterizing the spot size, and factors limiting focusing performance are discussed.

Takagi-Taupin description of x-ray dynamical diffraction from diffractive optics with large numerical aperture

We present a formalism of x-ray dynamical diffraction from volume diffractive optics with large numerical aperture and high aspect ratio, in an analogy to the Takagi-Taupin equations [Acta Crystallogr. 15, 1311 (1962); Bull. Soc. Fr. Mineral. Crystallogr. 87, 469 (1964)] for strained single crystals. We derive a set of basic equations for dynamical diffraction from volume diffractive optics, which enable us to study the focusing property of these optics with various grating profiles. We study volume diffractive optics that satisfy the Bragg condition to various degrees, namely, flat, tilted, and wedged geometries, and derive the curved geometries required for ultimate focusing. We show that the curved geometries satisfy both the Bragg condition everywhere and phase requirement for point focusing and effectively focus hard x rays to a scale close to the wavelength. Our calculations were made for an x-ray wavelength of 0.064 nm (19.5 keV).

Two dimensional hard x-ray nanofocusing with crossed multilayer Laue lenses

Hard x-ray microscopy with nanometer resolution will open frontiers in the study of materials and devices, environmental sciences, and life sciences by utilizing the unique characterization capabilities of x-rays. Here we report two-dimensional nanofocusing by multilayer Laue lenses (MLLs), a type of diffractive optics that is in principle capable of focusing x-rays to 1 nm. We demonstrate focusing to a 25 × 27 nm(2) FWHM spot with an efficiency of 2% at a photon energy of 12 keV, and to a 25 × 40 nm(2) FWHM spot with an efficiency of 17% at a photon energy of 19.5 keV.

Reconstruction of an astigmatic hard X-ray beam and alignment of K-B mirrors from ptychographic coherent diffraction data.

We have used coherent X-ray diffraction experiments to characterize both the 1-D and 2-D foci produced by nanofocusing Kirkpatrick-Baez (K-B) mirrors, and we find agreement. Algorithms related to ptychography were used to obtain a 3-D reconstruction of a focused hard X-ray beam waist, using data measured when the mirrors were not optimally aligned. Considerable astigmatism was evident in the reconstructed complex wavefield. Comparing the reconstructed wavefield for a single mirror with a geometrical projection of the wavefront errors expected from optical metrology data allowed us to diagnose a 40 μrad misalignment in the incident angle of the first mirror, which had occurred during the experiment. Good agreement between the reconstructed wavefront obtained from the X-ray data and off-line metrology data obtained with visible light demonstrates the usefulness of the technique as a metrology and alignment tool for nanofocusing X-ray optics.

Multielement spectrometer for efficient measurement of the momentum transfer dependence of inelastic x-ray scattering

Nonresonant x-ray Raman scattering (XRS) is the inelastic scattering of hard x rays from the K shell of low-Z elements or the less tightly bound shells of heavier elements. In the limit of low momentum transfer q, XRS is determined by the same transition matrix element as is measured by x-ray absorption spectroscopies. However, XRS at higher q can often access higher order multipole transitions which help separate the symmetry of various contributions to the local density of states. The main drawback of XRS is its low cross section—a problem that is compounded for a q-dependent study. To address this issue, we have constructed a multielement spectrometer to simultaneously measure XRS at ten different values of q. By means of example, we report new measurements of the XRS from the L- and K-edges of Mg. This instrument is now available to general users at the Advanced Photon Source as the lower energy resolution inelastic x-ray scattering (LERIX) spectrometer.

Wedged multilayer Laue lens

A multilayer Laue lens (MLL) is an x-ray focusing optic fabricated from a multilayer structure consisting of thousands of layers of two different materials produced by thin-film deposition. The sequence of layer thicknesses is controlled to satisfy the Fresnel zone plate law and the multilayer is sectioned to form the optic. An improved MLL geometry can be created by growing each layer with an in-plane thickness gradient to form a wedge, so that every interface makes the correct angle with the incident beam for symmetric Bragg diffraction. The ultimate hard x-ray focusing performance of a wedged MLL has been predicted to be significantly better than that of a nonwedged MLL, giving subnanometer resolution with high efficiency. Here, we describe a method to deposit the multilayer structure needed for an ideal wedged MLL and report our initial deposition results to produce these structures.

Sectioning of multilayers to make a multilayer Laue lens

We report a process to fabricate multilayer Laue lenses (MLLs) by sectioning and thinning multilayer films. This method can produce a linear zone plate structure with a very large ratio of zone depth to width (e.g., >1000), orders of magnitude larger than can be attained with photolithography. Consequently, MLLs are advantageous for efficient nanofocusing of hard x rays. MLL structures prepared by the technique reported here have been tested at an x-ray energy of 19.5 keV, and a diffraction-limited performance was observed. The present article reports the fabrication techniques that were used to make the MLLs.

Multilayer Laue lenses as high-resolution x-ray optics

Using Fresnel zone plates, a spatial resolution between 20 nm for soft x-rays and 70 nm for hard x-rays has been achieved. Improvement of the spatial resolution without loss of efficiency is difficult and incremental due to the fabrication challenges posed by the combination of small outermost zone width and high aspect ratios. We describe a novel approach for high-resolution x-ray focusing, a multilayer Laue lens (MLL). The MLL concept is a system of two crossed linear zone plates, manufactured by deposition techniques. The approach involves deposition of a multilayer with a graded period, sectioning it to the appropriate thickness, assembling the sections at the optimum angle, and using it in Laue geometry for focusing. The approach is particularly well suited for high-resolution focusing optics for use at high photon energy. We present a theory of the MLL using dynamic diffraction theory and Fourier optics.

Depth-graded multilayers for application in transmission geometry as linear zone plates

Fresnel zone plates for x-ray focusing optics are typically made using lithographic techniques. To achieve optimum efficiency for hard x rays, a depth of several microns is required, which limits the minimum zone width and hence minimum focal spot size achievable using lithography. We are exploring the fabrication of zone plates by an alternative technique that surmounts these limitations: the growth of a multilayer film to be used in transmission (Laue) diffraction geometry, in which the thickness of consecutive layers gradually increases according to the Fresnel zone formula; the film is sectioned after growth to the required depth. For a planar multilayer, this produces a linear zone plate that can focus x rays in one dimension. Here we report the growth and characterization of a depth-graded multilayer suitable for use as a zone plate for hard x-ray focusing. The multilayer has a total of 470 alternating layers of WSi2 and Si with thicknesses increasing monotonically from 15 to 60 nm, for a total thic...