High‐Resolution Kinoform X‐Ray Optics Printed via 405 nm 3D Laser Lithography

Efficient focusing of X‐rays is essential for high‐resolution X‐ray microscopy. Diffractive X‐ray optics called kinoforms offer the highest focusing efficiencies in theory. However, they have long remained unavailable due to their challenging nanofabrication. Recently, various X‐ray optic geometries including kinoforms have been realized using 3D laser lithography at near‐infrared wavelengths. As the smallest features (period) of the kinoform determines the resolving power, there is a natural drive to find ways to fabricate kinoforms with ever smaller features. Here, a custom‐built 3D laser lithography setup with an excitation wavelength of 405 nm is used, which allows to half the smallest period of the kinoforms compared to previous work. A 40% improvement in scanning transmission X‐ray microscopy image resolution, that is, a cutoff resolution of 145 nm, and an efficiency of 7.6% at 700 eV is achieved. A reconstructed pixel size of 18.5 nm, reaching the limit imposed by the design of the microscopy set‐up, is demonstrated through ptychographic imaging of a magnetic sample which has a strongly reduced contrast mechanism. Moreover, X‐ray lenses manufactured by 405 nm 3D laser lithography have the potential to become much less expensive than X‐ray lenses made by other means.


Introduction
After his discovery of X-rays in 1985, Röntgen describes an image of a human hand and the shadows cast by the bones, thereby demonstrating a novel nondestructive technique to are extensively used. [11][12][13][14][15][16][17] The simplest version of FZPs, binary FZPs, consist of concentric annuli that alternate between fully transparent and opaque zones. A disadvantage of binary absoprtion FZPs lies in their limited focusing efficiencies of ~10% in theory.
Focusing efficiencies reaching 100% can be achieved in the theoretical lossless limit by correcting the intra-period optical path-length difference of a FZP for every zone [18] by introducing a surface relief profile. Such special FZPs, which are called kinoforms, have been known since decades. [19,20] The correction of the intra-period optical path-length differences requires distinctive parabolic profile of the kinoforms. Moreover, in diffractive X-ray optics one often uses a central stop that blocks the nondiffracted light. This stop slightly improves the resolution, but makes the light go in the side lobes of the Airy disc. In ideal kinoforms, a central stop is neither needed nor wanted. It would only increase the energy going into the side lobes. However, the practical realization of X-ray kinoforms with their complex 3D nanoscale profiles and high aspect ratios is exceptionally challenging, despite the rapid advancement of modern fabrication techniques. [21][22][23][24][25] Kinoforms are not only relevant for conventional X-ray microscopy: In the last decade, with the emergence of powerful X-ray CCD cameras, faster computing, and optimized reconstruction algorithms, various flavors of coherent imaging techniques such as ptychography have moved into the focus. [26,27] In a typical ptychography experiment, a sample is scanned with partly overlapping sample illumination while the diffraction patterns are recorded. An iterative reconstruction algorithm simultaneously reconstructs the complex object exit-wave and probe functions from these recorded intensities. In contrast to imaging using FZPs, ptychography provides a resolution much better than the focal spot size, theoretically limited by the wavelength of the incident X-rays. In practice, the resolution of the reconstructed image is limited by the largest detectable scattering angle, where the intensity drops sharply. As a consequence, the performance of ptychography depends on the brightness and the coherence of the illumination function. Hence, thanks to the decoupling of the achieved resolution and the resolving power of the optic, already an intermediate-resolution focusing optic with a sub-micron spot size with improved efficiency greatly benefits ptychography. [28] Consequently, kinoforms with sub-micrometer resolution and high diffraction efficiencies are not only attractive for medium-resolution scanning transmission X-ray microscopy (STXM) but also for high-performance X-ray ptychography.
Recently, the fabrication of high-quality kinoforms has been demonstrated using conventional 3D laser lithography at an excitation wavelength of 780 nm. [29] In this paper, we show the merit of a reduction of the excitation wavelength to 405 nm using a custom-built 3D laser lithography setup for the advanced fabrication of X-ray kinoforms. Using these kinoforms as the lens of a state-of-the-art STXM, we evaluate their performance in both STXM and ptychography experiments, demonstrating an improvement in focal spot size and resolution by a factor of about two as compared to the aforementioned previous results [29] and a 7.6% efficiency at 700 eV X-ray energy. Our work paves the way for a fast and cost-efficient fabrication of high-resolution 3D kinoforms and reinforces the trend toward shorter excitation wavelengths in 3D laser lithography.

3D Laser Lithography
The most commonly used version of 3D laser lithography employs a femtosecond-pulsed near-infrared laser which is tightly focused into a reservoir of liquid negative-tone photoresist. In a small volume of the laser focus, a so-called voxel, the resist is sufficiently crosslinked to withstand the subsequent development process. Scanning the laser focus using a galvanometer mirror system or moving the photoresist reservoir with respect to the laser focus allows for the fabrication of almost arbitrary 3D structures with sub-micrometer resolution.
The performance of kinoforms is directly linked to the resolution of the manufacturing process. While the resolution of 3D laser lithography is much higher than that of most other 3D printing techniques, [30] it is fundamentally limited by diffraction-provided that the photoresist is not limiting the spatial resolution. Under these conditions, the minimum distance between two neighboring point exposures is determined by the two-photon Sparrow criterion, which can be approximated by the two-photon modified Abbe criterion [31] where λ is the excitation wavelength in free space and NA is the numerical aperture of the objective lens. Using high-NA objective lenses, two possibilities of obtaining higher resolution remain. First, one can overcome the diffraction limit by, for example, adapting the idea of stimulated-emission-depletion (STED). [31] Using this approach, line gratings with periods below 200 nm were achieved. [32,33] However, STED requires complex setups and special resist systems. Second, and more obvious, following the decade-long trend of the semiconductor industry, one can decrease the wavelength used for excitation. Here, we employ a reduction of the excitation wavelength from the conventionally used region around 800 to 405 nm. This enabled us to roughly halve the outermost period of the kinoforms as compared to the aforementioned previous work, [29] which directly translates to a doubled cutoff resolution of the lens in theory.
This wavelength reduction requires a change of the photoresist composition. Typically, the photoresist consists of two main components: a monomer, which can crosslink via a radical polymerization reaction to form dense polymer networks, and a photoinitiator, which is nonlinearly excited by the laser in the visible or near-infrared regime and triggers the polymerization reaction. By reducing the wavelength to 405 nm, the radical polymerization reaction can be triggered by directly nonlinearly exciting the monomer itself without the need for a dedicated photoinitiator. [34] An example of a suitable resist is pure pentaerythritol triacrylate (PETA), an acrylatic monomer that is frequently used in 3D laser lithography.
Fabrication of the kinoforms was carried out using a homebuilt 3D laser lithography setup [35] which shares its basic design with many commercially available setups while offering additional flexibility (see Experimental Section for a detailed description). The setup comprises a piezoelectric stage for moving the sample with respect to the laser focus along almost any desired 3D trajectory. Silicon nitride membranes embedded in silicon frames were used as substrates, enabling the characterization of the kinoforms in X-ray microscopy experiments. The targeted high-resolution and the constraints imposed by the working distance of the objective lens led to the intricate writing configuration shown in Figure 1.
3D models of the kinoforms were generated according to the usual set of parametric equations [36] (see Experimental Section for details). An illustration of the geometry is shown in Figure 2a. The outermost period, Λ, determines the resolution of the lens, while its thickness, t, is chosen such that the optical path difference, ΔΦ, is equal to 2π. The 3D models were then converted to sets of coordinates forming the trajectories for the piezoelectric stage and the kinoforms were printed. The quality of the structures was optimized by systematically varying both the writing speed and the excitation power. Scanning electron micrographs of the 3D printed structures are shown in Figure 2b,c.

X-Ray Focusing Performance
The kinoforms presented in this paper were designed for an X-ray energy of 700 eV. Being diffractive optics, such as zone plates, the kinoforms achieve their peak efficiency at the design photon energy. However, it is known that the diffraction efficiency stays very high in a range of several hundreds of eV around the design energy. [29] From the fabricated kinoforms, one was selected randomly to be tested at a state-of-the-art scanning transmission X-ray microscope, MAXYMUS (magnetic X-ray microscope with UHV spectroscopy), at the UE46-PGMII beamline of BESSY II. The experimental setup is shown in Figure 3 (see ref. [37] for details).
The diffraction efficiency was tested by a pinhole scan method (see Figure 4a for an example and Experimental Section for a detailed explanation) in the photon energy range between 600 and 1100 eV (see Figure 4b). The kinoform demonstrated a reasonable diffraction efficiency throughout the tested energy range, achieving a peak diffraction efficiency of 7.6% at 700 eV  . a) Schematic representation of a kinoform illustrating its distinctive parabolic surface profile and geometry parameters. Ideally, the optical path difference, ΔΦ, at maximum thickness, t max , is equal to 2π. The resolution is determined by the outermost period, Λ, which is equivalent to two outermost zone widths (Δr) of an equivalent binary Fresnel zone plate. b,c) Scanning electron micrographs of a kinoform fabricated on a glass substrate, and its first few inner ridges in detail, respectively. as depicted in Figure 4b. The reason for lower than ideal efficiencies are attributed to the printing errors and surface roughnesses which are visible in the SEM images. The roughness is not expected to change the resolution of the optic. The current kinoform design has half the outermost zone width (200 nm instead of 400 nm) and a slightly larger diameter (40 μm instead of 38 μm), compared to our previous work. [29] Confluent with an increase in the number of zones, the current kinoform offers a five times greater focal plane intensity, in theory. The reason for this impressive improvement is the quadratic dependence of the focal plane intensity on the number of zones, given by the following equation, [18] ( ) where I(θ)/I(0) is the relative focal plane intensity, N is the number of zones in an equivalent zone plate, J 1 is the Bessel function of first kind and first order, k = 2π/λ, a is the kinoform radius, and the function inside the brackets is the Airy pattern. A comparison of the theoretical radial intensity distributions of the Airy patterns for the current and previous kinoform designs in 1D is shown in the Figure 4c. Besides the five times greater focal plane intensity, the two times smaller focal spot size, which is due to the two times smaller outermost zone width, is also evident in the graph. We assessed and cross-validated the STXM resolution and focal spot size of our kinoform using three independent methods. First, we performed STXM scans on a varying line space grating and determined the spatial frequencies at which the contrast disappears into the noise floor. An integrated intensity profile of the STXM image was used to determine the cutoff resolution. The half-pitch cutoff resolution was estimated to be 145 nm as depicted in Figure 5a. Second, a Siemens star test sample with 30 nm smallest features was imaged. The tips of the third inner ring, which correspond to a smallest feature-size of 120 nm, are barely not resolved (see Figure 5b), in general agreement with the linear test sample. The resolution of the linear and horizontal structures does not show a significant amount of astigmatism. Third, a Fourier ring correlation analysis with a 1/7 threshold was performed, which also reveals a 285 nm full-pitch cutoff resolution, Figure 3. a) Schematic illustration of the undulator-based X-ray source and beamline optics. The electrons from the storage ring pass through an Apple-II type helical undulator and create energy and polarization tunable X-rays. After passing through a set of toroidal mirrors and plane grating monochromator filters, the X-rays are incident onto a set of slits. The slits act as a secondary source and determine the coherence on the optic located 3 m downstream. b) Illustration of the experimental setup of the MAXYMUS scanning transmission X-ray microscope. The kinoform optic that is fully coherently illuminated focuses the X-rays into a set of foci on the optical axis. An order selecting aperture (OSA) filters the spurious diffraction orders. The sample is located at the focal plane. An interferometrically controlled piezo scanner is used for raster scanning with nanometer level accuracy. An avalanche photodiode (APD) and a CCD can be used as the detector for STXM and ptychography experiments, respectively. agreeing with the results mentioned above, as depicted in Figure 5c.
To evaluate the kinoform's zone quality, we imaged the kinoform as a sample at MAXYMUS in STXM using a second kinoform, with an identical design and fabrication para meters, as the focusing optic. The resulting image is shown in Figure 5d. Here, a nonconcentricity of the lens is visible, which is quantified by the distance between the center of the zones and the brightest pixel in the image corresponding to γ = 385 nm. This value is slightly larger than the tolerance values stated in the literature for our designed optic (γ < 1.2Δr = 240 nm). [38] The nonconcentricity is expected to cause a slight coma aberration. [38] Furthermore, we deduced a map of the relative optical thickness, Δx, of the parabolic zones from the STXM image. Assuming a uniform volumetric mass density distribution, ρ, and a uniform mass absorption coefficient, μ, throughout the  kinoform, the relative thickness of the zones can be estimated by the Beer-Lambert law. To do so, we first took the natural logarithm of each pixel of the image in Figure 5d and then inverted the image using the open-source image processing software ImageJ. [39] A 3D surface plot of the resulting relative X-ray optical thickness distribution is shown in Figure 5e. This method is superior in characterizing X-ray optics to surface imaging techniques such as scanning electron microscopy in the sense that the X-ray absorption map gives the volume profile of the kinoform, which is important for the X-ray optical performance. Structural roughness inside the kinoform, density variations or porosity inside the zones can be visualized. However, due to the fact that we used a second kinoform as the focusing optic, only the innermost zones are accurately represented. Figure 5e shows a slight tilt in the inner zones of the kinoform. The relative optical thickness distribution of the kinoform gives no indication of substantial inhomogeneity in the volume of the printed kinoform.
The relatively low diffraction efficiencies shown in Figure 4b are at least partly attributed to the measured nonconcentricity of the kinoform, which is likely caused by a drift of the sample with respect to the laser focus during the fabrication process. Such a drift could also explain the slight tilt in the inner zones that can be seen in Figure 5e. As the effects of drifts are typically less pronounced for shorter fabrication times, one promising avenue to obtain higher efficiencies in future studies is the use of a galvanometer mirror system instead of a piezoelectric stage in the printer set-up. Such a system could reduce the fabrication time from about 3 h down to several minutes or even less.
Because the performance of ptychography has been linked to the available dose incident on the sample, [28] we define the figure-of-merit of a kinoform as the dose in its focal spot. Using this figure-of-merit, we can estimate the ptychographical performance of our kinoform from the above analysis of the STXM results. As a reference, we use the results previously obtained using conventional 3D laser lithography at near-IR wavelengths. [29] Considering the effects of the increased number of zones, the smaller effective outermost zone width, the slightly larger diameter, and the reduced focusing efficiency, we obtain an improvement in the figure-of-merit by a factor of about 1.6.
As a next step, we examined the performance of the kinoform through a ptychographic analysis. The results of the ptychographic reconstruction of the phase and amplitude images of the Siemens star test sample exhibit all of its features down to the central 30 nm spokes (see Figure 6a,b). The reconstructed pixel size of about 18.5 nm was determined from the distance between sample and CCD, the illumination wavelength, and the detection NA. [40] A simultaneously reconstructed complex illumination function was used to calculate the 3D wavefield along the optical axis using a freespace Fourier beam propagation method to reveal the distribution of intensity in the vicinity of the focal plane, as shown in Figure 6c. The amplitude of the wavefield at the circle of least confusion was derived from this 3D wavefield and is shown in Figure 6d. The overall size of the reconstructed spot is in good agreement with the STXM results. However, there seems to be a slight astigmatism in the spot (see Figure 6d), which can be attributed to the above mentioned nonconcentricity of the kinoform (see Figure 5d). To further demonstrate the potential of the optics in a more realistic use case, the 3D printed kinoforms were used to image the magnetization distribution of an amorphous iron-gadolinium (FeGd) magnetic multi-layer thin film with out-of-plane (oop) magnetization using X-ray circular magnetic dichroism (XMCD) contrast. The absorption contrast of 0.06 at the Fe L 3 -edge is significantly smaller compared to the 180 nm thick gold lines of the Siemens star with a Michelson contrast of 0.91 at 709 eV. The reconstructed object can be seen in Figure 7a. From this multi-modal reconstruction, we also derived the mode decomposition in the illumination function. [41,42] The most intense top four modes are shown in Figure 7b-e. The purity of the fundamental mode was 94%. The slight decoherence can originate from source instabilities and higher modes or vibration of the sample or the optic. [44] However, considering that a purity of 95-100% would correspond to a fully coherent illumination, we can conclude that the kinoform performs well in filtering out the high harmonic contributions from the undulator, even in the absence of a beamstop.

Conclusions
In summary, 405 nm based 3D laser lithography was employed to 3D print kinoform X-ray holographic lenses with half the critical structure size compared to our previous work, [29] which used a wavelength of 780 nm. As a result, we have almost doubled the resolving power of the 3D printed lenses down to 145 nm half-pitch resolution as evidenced by STXM, Fourier ring correlation (FRC) analysis, and ptychographic reconstruction of the probe. A measured focusing efficiency of 7.6% at 700 eV photon energy was achieved, resulting in a 1.6-fold increase of the figure-of-merit for coherent imaging compared to the stateof-the-art. Furthermore, we demonstrated a realistic use case by imaging a low-contrast magnetic sample. The focusing efficiencies obtained here are larger than those previously obtained using gold kinoforms, [21] which were made by focused-ion-beam milling and operated at comparable photon energies.
The 3D printing manufacturing approach presented here can potentially be less expensive than other established approaches. Several future improvements are conceivable. For example, faster laser-focus scanning would reduce the effects of drifts during the printing process and enable finer discretization of the kinoforms, which is expected to reduce the surface roughness. Given the rapid progress in the field of 3D laser nanoprinting, [43] it can be expected that the efficiency as well as the resolving power of potentially inexpensive 3D printed kinoforms will improve further in the near future.

Experimental Section
Modeling of the Kinoforms: The kinoforms were modeled according to the usual set of parametric equations [36] cos( ) sin( ) mod(( / ) ,1) / where t max is the thickness, 0 ≤ r ≤ R the radius of the lens in μm, and 0 ≤ θ ≤ 2π the azimuthal angle. The quantities R and t are the radius and the thickness of the kinoform, respectively. The factor K defines the radius of curvature of the lens and depends on a constant A, the focal length f, and the design energy E. The free 3D computer graphics software Blender and its XYZ Math Surface add-on were used to create a 3D model of the kinoforms according to these equations. As design parameters, an outermost period of 400 nm 2 2 K Λ − Λ − = and a diameter of 2 40 m R = µ were chosen. The thickness was set to 2 m max t = µ resulting in an aspect ratio of 5 for the smallest features. The 3D model was then exported in the STL file format and converted to trajectories with the software DeScribe 2.5 (Nanoscribe GmbH) using a slicing and hatching distance of 100 nm. Finally, the trajectories were adapted to the MATLAB-based software of the 3D laser lithography setup.

Sample Preparation:
The silicon nitride membranes (500 m 500 m 100 nm µ × µ × ), which are embedded in silicon frames (5 mm 5 mm 100 m × × µ ), were purchased from Silson Ltd. (Warwickshire, U.K.). Prior to printing, the membranes were silanized for better adhesion of the structures: After activating the surface using an air plasma for 10 min, the substrates were placed in a solution of 3-(trimethoxysilyl)propyl methacrylate in toluene for 90 min and subsequently rinsed with deionized water.
3D Laser Lithography Setup: The home-built 3D laser lithography setup is based on a Ti:sapphire laser oscillator (Spectra Physics, MaiTai HP), which emited femtosecond laser pulses centered at a wavelength of 810 nm which are frequency-doubled in a SHG crystal resulting in a center wavelength of 405 nm. An acousto-optic modulator was used both as a high-frequency shutter and for gapless tuning of the excitation power. The pulses were tightly focused via a 100× oil-immersion objective (Leica HCX PL APO, NA = 1.4, 230 m µ working distance). In order to move the sample with respect to the laser focus, a piezoelectric stage (PI P-527.3CL) was used.
The point spread function of the laser focus was measured by scanning a 80 nm gold nanoparticle and subsequently measuring the intensity of the backscattered light with a photodiode. Using 405 nm excitation center wavelength, a full width half maximum of the laser focus of ≈175 nm in lateral direction and 620 nm in axial direction was achieved. While the lateral resolution was in good agreement with corresponding theoretical calculations of the vectorial field distribution of the laser focus in photoresist, the axial resolution could be improved.
Laser Printing of the Kinoforms: The 3D laser-printing configuration was shown and discussed in Figure 1. In this configuration, the X-ray lenses were printed on top of the silanized Si 3 N 4 membranes. Pentaerythritol triacrylate (PETA, Sigma Aldrich) was used as photoresist. The coverslips shown in Figure 1 have a thickness of 170 m µ . The immersion oil was purchased from Leica Microsystems GmbH (Type F, n = 1.5180). An optimization of the writing parameters led to best results for a writing speed of 25 m µ s −1 and a mean laser power of 1.5 mW as measured in the back focal plane of the objective lens. In the last step of the fabrication process, the samples were developed in mr-Dev 600 (micro resist technology GmbH) for 15 min, transferred to acetone, and dried using a supercritical drying process to avoid damage to the high aspect-ratio structures.
STXM Experiments: The soft X-rays with variable polarization in the energy range of 200-1800 eV were provided by an APPLE II type helical undulator. A grating monochromator was used to monochromatize the X-ray beam. A set of vertical and horizontal slits controlled the energy resolution and coherence. A kinoform located 3 m downstream the slits was used to focus the X-rays onto a sample, while an order selecting aperture filtered the undesired diffraction orders. The laser interferometrically controlled sample stage, that allows to move the sample in three axes with nanometer accuracy, was used for raster scanning the sample. An APD was used for STXM imaging.
The STXM imaging tests were performed using the third positive undulator harmonic. For imaging the linear test sample, a photon energy of 900 eV was used with exit slits set to 30 m 30 m µ × µ . The image acquisition time was 10 ms and a step size of 80 nm was used. For the Siemens star test sample a photon energy of 700 eV was used with exit slits set to 25 m 25 m µ × µ , 40 nm step size, and a 1.25 ms image acquisition time.
FRC was carried out using two subsequent images that were acquired with identical scanning parameters using the updated (July 2019) version of the FIJI FRC plug-in made by BIOPS. [45] The two images were aligned using the register plug-in of FIJI prior to FRC.
Efficiency Tests: For the diffraction efficiency estimations, a pinhole with a diameter of 4.4 m µ was raster scanned in the first-order focal plane while simultaneously recording the incident intensity, projected zeroth order, and the first-order focal spot using an APD. The resulting image consisted of a convolution of the focusing optic and the 4.4 m µ pinhole. An example is shown in Figure 8a. For calculating the diffraction efficiency, the dark count was measured and subtracted (see Figure 8b). Additionally, the absorption of the 100 nm thick SiN membrane was subtracted. Corresponding absorption data for each energy were obtained from the CXRO webpage. [46] Ptychography: A charge-coupled device (pnCCD) designed specifically for X-ray detection was used to detect the far field diffraction pattern. [47] The CCD had 264 pixels with a size of 48 m 48 m µ × µ . The experiments were carried out at 900 eV with 15 m 15 m µ × µ exit slits and 150 ms dwell time using the third undulator harmonic. The details of the upsampling method and mixed state analysis techniques used for the reconstructions shown in Figure 7 are explained in the literature. [48,49] In ptychographic imaging, the achievable image resolution can be ultimately limited by the available coherent dose, as discussed in the text. However, when the resolution is not dose-limited (like in the authors' case) the reconstructed pixel size defines the resolution. The reconstructed pixel size is a function of the X-ray wavelength, the sample CCD distance, the number of pixels on the CCD, and the physical size of the CCD pixels. Physical limitations resulting from the mechanical design of the ptychography set-up were explained elsewhere. [50] Fabrication of the FeGd Magnetic Sample: The ferromagnetic FeGd sample with out-of-plane (oop) magnetization under zero field was deposited using ion beam sputtering of 70 alternating layers of 3.6 Å thick Fe and Gd.