High numerical aperture multilayer Laue lenses

Hard X-rays are ideal for high-resolution imaging and spectroscopic applications due to their short wavelength, high penetrating power, and chemical sensitivity. Many imaging and micro-spectroscopy applications require a focusing optic to produce a small beam that can be rastered over an object or used to form a magnified image of the object. In these cases the spatial resolution, δ, of the image depends on the numerical aperture (NA) of the optic, following the same relationship for optical lenses, δ = 0.61 λ/NA (for incoherent imaging) where λ is the wavelength. The penetrating power that makes X-rays useful for imaging also makes focusing them technologically challenging. For high-energy X-rays the refractive index of suitable lens materials differs from unity by approximately 10−5, which means that a large number of refractive surfaces are required to deflect or focus a beam1. The state of the art in focusing hard X-rays has been achieved by reflection from a curved mirror at grazing incidence to produce a 7 nm spot size2. This required fabricating mirrors of large surface areas (over 8 cm long) with nanometre figure accuracy. Diffractive lenses based on Fresnel zone plates have been successfully used to obtain images with about 10 nm Rayleigh resolution3 with soft X-rays. These devices can be described as concentric circular transmission gratings in which the grating period (zone period) decreases with radius to diffract rays to a common axial focal point, a relationship referred to as the zone-plate condition. Again, the properties of materials limit their use at shorter wavelengths. For example, to achieve a π phase shift in alternating zones requires the X-rays to transmit through a thickness of about 105 half wavelengths, or about 5 μm thickness for 1 A wavelength. At the same time, the focussed spot size matches the outermost zone period, implying an aspect ratio of 500:1 for those zones if a 10 nm spot size is to be achieved. Not only are such structures difficult to fabricate using conventional lithographic methods, but their high-aspect ratio prevents a simple thin-mask description of X-ray diffraction. In particular, such structures are akin to planes in a crystal, in which X-rays only reflect when they are tilted at the Bragg angle θ (given by sin θ = λ/(2 d), where d is the zone period). This comparison is indeed very apt and provides the insight into constructing an efficient hard X-ray lens of high resolution which ideally consists of reflecting confocal parabolic layers (for an incident plane wave) spaced apart such that each period introduces an additional wavelength of path for the rays arriving at the focus4. That is, the lens is composed of layers that simultaneously follow the zone-plate condition and are oriented to obey Bragg’s law across the entire lens aperture. The lens performance is described by dynamical diffraction, and as such the optical thickness of the lens should be set at half a pendellosung period to direct most of the incident beam into the diffracted (focused) beam, giving much higher efficiency than could be achieved with a thin zone plate (which is limited by equally partitioning the beam into positive and negative orders). A method to fabricate volume zone plates of high aspect ratios was introduced a decade ago5,6,7. Called multilayer Laue lenses (MLLs)8, these structures are fabricated by layer deposition, using technologies developed for making multilayer mirrors9. Layer periods thinner than 1 nm are achievable by magnetron sputtering10. Lenses are made by alternately depositing two (or more) materials with layer periods that follow the Fresnel zone-plate condition and then slicing the structure approximately perpendicular to the layers to the desired optical thickness. Lenses fabricated to date have consisted of parallel layers in a one-dimensional (1D) stack deposited onto a flat substrate. Two-dimensional focusing can be achieved with crossed 1D stacks6,13 or by depositing a multilayer on a thin wire to create a circular multilayer zone plate11,12. In the former case each lens must be tilted relative to the incident X-ray beam to maximize the region of the lens that satisfies Bragg’s law. Even so, the NA of the lens will depend on the rocking-curve width of the Laue reflection (which unfortunately becomes narrower as the thickness of the lens and efficiency of the Laue reflection is increased or as the layer period is reduced). A tilted MLL consisting of parallel layers was used to focus 12 keV X-rays to a spot of 11.2 nm (FWHM) with 15% efficiency14. When the NA of the lens exceeds the Darwin width of the reflection at any part of the lens then the lens focus will be significantly apodised and the effective NA will be limited by the diffraction efficiency. Only by varying the tilt of the layers throughout the stack, so that Bragg’s law and the zone plate condition are simultaneously fulfilled for every layer, is it possible to construct a large enough NA to focus X-rays to nanometer spots. Such a structure is referred to as a wedged MLL, and is schematically illustrated in Fig. 1 (a). Figure 1 (a) A wedged multilayer Laue lens of focal length f is constructed from layers whose spacing follows the zone-plate condition. To achieve high efficiency the lens must be thick, in which case diffraction is a volume effect described by dynamical diffraction. ... Numerical modelling of MLLs has been carried out using methods such as coupled wave theory, the beam propagation method (equivalent to the multislice technique), and dynamical diffraction of distorted lattices. In the latter case, it was predicted that efficient wedged MLLs with NAs as high as 0.1 should be achievable; that is, focal spots smaller than 1 nm should be possible using wedged MLLs15. Until now, however, a wedged MLL has not been realized experimentally, due to difficulties in controlling material deposition to the necessary precision both in the direction of the film growth and transverse to this direction. Recently, we solved the manufacturing problem of wedged MLLs by depositing the layer materials by magnetron sputtering onto a substrate shadowed by a straight-edged mask16. The required layer period and layer angle was achieved in the penumbra of the mask where the deposition rate changes with distance in a direction perpendicular to the mask edge. Here we present the measured one-dimensional (1D) focusing performance of a high-NA wedged MLL made in this fashion, and compare this performance to calculations based on the beam propagation method (see Methods). We find that the diffraction efficiency is nearly uniform across the entire pupil of the lens, which had a NA of 0.006 at 22 keV photon energy. The depth of the lens (the thickness in the direction of the optical axis) was 6.5 μm, which gives a computed efficiency of 60 ± 1% for a perfect structure. We characterized the focused wavefield by pytchography17,18,19,20,21,22,23 using a 95 nm period transmission grating as a test structure. By carrying out ptychographic measurements (far-field diffraction patterns as a function of the transverse position of the object) with the grating placed at various defocus positions (Fig. 2) we recovered the focal properties along with the structure of the grating. We determined a focal spot size of 8.4 nm using the Rayleigh criterion, despite a phase defect in the pupil of the lens. Figure 2 Experimental arrangement of the X-ray measurements, indicating the orientation of the coordinate system and the tilt of the lens, α. Diffraction patterns were recorded on a Lambda detector located 3.4 m from the MLL. Ptychograms were measured ...