1. Introduction

Since its inception as a hard x-ray nanofocusing optic in 2004 [1], multilayer Laue lens (MLL) has undergone a long development path and has evolved from a novel concept to real optics for scientific applications [2,3]. The focus size has been reduced steadily from 30 nm [4] to 11 nm [5] and below [6], while the aperture size has increased from 12 μm [4] to over 100 μm [7]. Together with other appealing properties (e.g., high efficiency at high energy and the resistance to radiation damage), MLL has become an excellent candidate for focusing optic in many applications, particularly for high-spatial resolution imaging. However, MLLs are one-dimensional focusing optics and two of them must be aligned in a cross geometry to produce a point focus [8]. In order to achieve the best performance, a dedicated MLL manipulator is required [8–11]. The additional alignment degrees of freedom and associated mechanical complexity pose a technical difficulty in adapting them to many existing microscopy systems, limiting their usage.

An obvious solution to this problem is to bond two MLLs permanently to form a monolithic optic. Initial concept of MLL bonding was first introduced to achieve a larger numerical aperture by joining two partial MLLs into a full structure [12]. Subsequent attempts of MLL bonding have been reported to achieve a point focus. Niese et al. used a focused ion beam (FIB) to weld two MLLs together, and integrated it successfully into a full-field x-ray imaging microscope with a lab-source [13]. Because they can place two lenses very close to each other, two identical MLLs may be used without introducing strong astigmatism. The challenge in this method is to align two MLLs perfectly orthogonal to each other, which is crucial to achieve an aberration-free point focus [14]. An error less than 0.01 degree is required for a focus of 10 nm. We have reported gluing two MLLs manually with the aid of an optical alignment system, resulting in a misalignment error on orthogonality down to 0.03 degree [15]. However, for the lens to survive the bonding process, the supporting substrate needs to be sufficiently thick to avoid mechanical distortion. This thickness requirement leads inevitably to a large gap between two MLLs (in the range of several hundred microns); as a result, strong astigmatism arises if two identical MLLs are used, making it not very useful for general scientific applications. To address this issue, lenses with two different focal lengths are bonded with an accurate control of their gap.

Here we report a bonded monolithic lens consisting of two MLLs with different focal lengths. Pre-characterization of the individual MLLs and precise alignment during the bonding process allowed us to construct a monolithic lens for a designated energy. We show experimentally that a common focal plane was achieved at 9.317 keV, and demonstrate the usage of the lens for a conventional scanning transmission x-ray microscopy (STXM) measurement. An image resolution of 50 × 50 nm² was obtained. We also show that the combination with ptychographic reconstruction improved the image resolution to 13 × 13 nm². Because of the simplicity in its mechanical structure and alignment, we believe that the application of bonded MLLs will expand in both scanning and full-field imaging microscopies.

2. Bonded MLL fabrication

MLLs used in this work had aperture sizes of 53 μm and 43 μm, respectively, and the outermost zone width was 4 nm for both lenses; they should yield a diffraction-limited focal size of 10 nm (Rayleigh criterion) in absence of aberrations. We used the inserted marker layers to pre-characterize the optical parameters of the bonded MLL by high-resolution scanning electron microscopy (SEM) [16]. Each marker layer was a zone with triple nominal zone width, thereby increasing the visibility in SEM. They were designed to span the whole stack of the multilayer, and the separation distance between two neighboring markers increased progressively. The latter avoids potential confusion of marker positions when we stitch multiple high-resolution images together to cover the whole aperture. A SEM image depicting marker layers is shown in Fig. 1(a). According to the zone plate law, the position of a zone is linearly proportional to the square root of its corresponding zone index number, $n$,

 

Fig. 1 a) SEM image of the MLL. Marker layers are clearly visible. The inset is a magnified image in the thinner zone region. b) Linear fits of the marker layer positions vs. square root n (where n is the zone index) of two MLLs used in bonding. These MLLs have apertures of 43 and 53 μm. Insets show residual errors after fitting, which indicate the perfection of the lens.

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We used reactive ion etching (RIE) [18] and focused ion beam (FIB) to thin each MLL down to a thickness of about 4 μm and a transverse width of about 100 μm. The thickness was optimized for operation around 9 keV. Figure 2(a) shows a SEM image of the bonded MLLs. Based on the SEM measurement, a gap of 0.724 mm between the two MLLs was needed to ensure an astigmatism-free focus. By adding a spacer in between and using an optical alignment system, we were able to adjust the gap within an accuracy of ± 10 microns. After bonding, the measured gap was 0.715 mm, slightly off from the target value. This small difference could be compensated by changing the operation energy. Using a reference prism with perfect perpendicular surfaces, the two MLLs were aligned orthogonally to each other with a small deviation angle of 0.03 degree. Details of the alignment and gluing processes can be found elsewhere [15].

 

Fig. 2 a) A SEM image of the cross-bonded MLLs. Because of the viewing angle, the two MLLs appear as if they were not centered to each other. Significant glue residues are visible on the vertical MLL with 43 μm aperture. b) A schematic of the lens alignment. Three translational and two rotational degrees of freedoms are needed to fully align the bonded MLLs. An OSA is used to block the direct beam and high diffraction orders. c) Far-field diffraction recorded on a detector with 55 μm pixel size and with a distance 0.64 m to the optics.

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3. Performance characterization

The bonded pair was mounted in an apparatus designed for MLL characterization [19]. The MLL manipulator has five degrees of freedom, which includes three translations and two rotations [Fig. 2(a)]. Rotation is required to tilt an MLL to the Bragg angle for optimal performance [20]. Because the tilting angle is typically less than 1 degree and the two MLLs are orthogonal to each other, the two tilting angles are decoupled. As a result, rotation in one direction has no impact on the angle in the other direction. This makes the angular alignment straightforward and simple. Translational degrees of freedom allow us to position the bonded set into a rectangular beam shaped by an upstream beam-defining slit. The beam size is set to match the dimensions of the lens. A rectangular order sorting aperture (OSA) made of Au was used to block the direct transmitted beam and unwanted higher-order diffractions. Figure 2(c) is a far-field pattern recorded on a pixel-array detector (Timepix, 512 × 512, 55 μm pixels) placed 0.64 m downstream of the MLL optics. To characterize the resolution in both directions, we used an Au Siemens star resolution pattern fabricated by a lithography method. It has a thickness of 1 μm and variable feature sizes of 100-500 nm.

The focal length obtained from SEM could be slightly off from the true value, depending on the absolute calibration of the scale bar of the SEM image and the perfection of the optics. As a result, the optimal energy at which the astigmatism vanishes has to be determined experimentally. By checking the location of the focal plane in each direction, we found 9.317 keV was the energy at which line scans across the test pattern show a similar resolution. The focusing efficiency (after two MLLs) was measured to be 7.3%. Figure 3(a) is a STXM image of the test pattern with 50 × 50 pixels and a pixel size of 20 nm. Based on a power spectral density (PSD) analysis of the image [Fig. 3(b)] [21,22], the resolution was approximately 50 × 50 nm² if we ignore the slight resolution difference in horizontal and vertical directions. Observed image resolution was worse than the theoretically-estimated focus size of 13 x 20 nm², presumably due to multiple factors. One factor could be mechanical distortion of the MLL. We observed that the lens was bent considerably after bonding, which is known to cause focus degradation [2,23]. Another factor could be glue contamination. A close examination afterward revealed that part of the vertical MLL (43 μm) was contaminated by excessive glue with thickness of around 300 nm, which introduced phase aberration into the lens. This aberration led to a broadened focus with strong side lobes (confirmed by ptychography wavefront reconstruction), and deteriorated the image quality as a scanning probe. Glue residues were clearly observed in the SEM image [Fig. 2(a)].

 

Fig. 3 a) A scanning transmission x-ray microscopy (STXM) image of a star test pattern, 50 × 50 pixels with 20 nm step size. The two dark pixels correspond to two bad frames with missing data. The scale bar is 250 nm. b) A power spectral density (PSD) analysis of a) shows a slightly better resolution in x direction, as expected. If we ignore this small difference, the resolution is roughly 50 × 50 nm² (cut-off frequency of 0.01 nm⁻¹). c) Reconstructed complex object function from ptychography; its brightness and color represents the amplitude and phase, respectively (see the inset image in e). Note that some edges are not very sharp because of the imperfection of the test pattern and carbon deposition. Because of the small step size and high overlap ratio, the two locations with missing data were covered sufficiently by neighboring data points and successful reconstructions were still achieved. d) A PSD analysis of c) shows a resolution of 13 × 13 nm² (cut-off frequency of 0.04 nm⁻¹). e) The reconstructed complex probe in the sample plane; a point focus is evident, though there are side lobes due to imperfections of MLLs and the bonding process. The projected intensity profiles indicate a FWHM size of 17 nm in horizontal and 38 nm in vertical direction.

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Ptychography has been shown to improve image resolution by decoupling the probe and the complex object [24,25]. This is done by analyzing the variation of the far-field pattern at the single pixel level, unlike the STXM image shown in Fig. 3(a) that corresponds to the total intensity sum of all the pixels. With the same 50 x 50 grid scan data, we used the difference map ptychography reconstruction algorithm [26] to recover both the focused beam and the object transmission function. Figure 3(c) is the reconstructed star pattern with its brightness representing the amplitude and the color representing the phase of the complex object function. Not only was the image resolution improved significantly, but also the phase was measured. The reconstruction converged quickly within 100 iterations. We attribute this fast convergence to the structured profile of an imperfect probe. All the imperfections of the lenses and the glue contamination create a “dirty” probe characterized by complex structure [Fig. 3(c)] which had an adverse impact on the achievable resolution of the direct scanning image; however, it helped the solution convergence in ptychography because of the translational diversity of the probe [27]. A similar PSD analysis of the reconstructed object image yielded a resolution of 13 × 13 nm². The probe size at the sample plane, determined from the full-width-of-half-maximum (FWHM) of the projected intensity profile, was 17 (H) × 38 (V) nm². If we draw two lines across the focus instead, the number becomes 11 (H) × 17 (V) nm², which is within 1 pixel (6 nm) of the theoretical value. As aforementioned, the larger focus size in the vertical direction was due to the imperfect lens and glue contamination. We recognize there is still notable azimuthal misalignment between the two MLLs. Even though we aligned the top surfaces of the MLLs to each other, the crossed parts still possessed an azimuthal misalignment error due to the residual stress. To further improve respective alignment of two linear MLL optics one can consider fabrication of dedicated features on the MLL structures to minimize the amount of applied glue. Alternatively, a dedicated silicon template can be fabricated to mechanically clamp two individual MLL optics together avoiding distortions due to the glue curing process. The complex wavefront obtained from ptychography reconstruction allowed us to propagate the beam along the optical axis to find the focal plane. The best focusing in either direction was indeed achieved in the same plane, indicating an astigmatism-free 2D lens at this particular energy.

4. Summary

In summary, we report the first scanning-probe x-ray imaging experiment performed using a bonded MLL pair, which significantly reduced the alignment complexity and the number of motorized stages required for positioning. We show that with optics pre-characterization and accurate control of the orthogonal angle and separation distance between two MLLs, one can create a monolithic focusing optic with a common focal plane for a given energy. Although the not-yet-optimized bonding method introduced bending and glue contamination, a resolution of 50 × 50 nm² was still observed with a conventional STXM image of a test pattern. By applying a ptychography reconstruction algorithm on the same data set, we obtained a probe size with a projected FWHM of 17 × 38 nm² and a complex object image with a resolution of 13 × 13 nm². Fast convergence for ptychography reconstruction was observed, due to the translational diversity of the probe. Propagating the beam along the optical axis confirmed that an astigmatism-free 2D focus was indeed achieved at 9.317 keV. With continued improvement, bonded-MLLs can become a practical nanofocusing optic for many microscopy systems aimed at high spatial resolution in the hard x-ray energy range.