Scanning high-sensitive x-ray polarization microscopy

The development of x-ray polarimetry has considerably progressed during the last ten years [6–8]. Driven by the quest for the first observation of vacuum birefringence [9], x-ray quantum optics exploiting nuclear resonant scattering [10–12], and x-ray polarization-sensitive spectroscopy [4, 13], the degree of polarization purity has been improved to the level of 5.5 × 10⁻¹¹ [14]. High precision x-ray polarimeters are based on multiple reflections in channel-cut crystals at Bragg angles close to 45° [15]. For these angles, the polarization component parallel to the diffraction plane (π-component) is suppressed. The degree of suppression is determined by the divergence and energy bandwidth of the x-ray source as well as by presence of simultaneously excited Umweg reflections and the perfection of the crystal material [16, 17]. With present x-ray sources, polarization purities of 10⁻¹² are possible in principle, where the degree of polarization purity δ₀ is defined as the ratio of the transmission of the π-component T_π to the transmission of the σ-component T_σ of the polarimeter [18].

$$\begin{equation}{\delta }_{0}=\frac{{T}_{\pi }}{{T}_{\sigma }}.\end{equation} \tag{ 1 }$$

The transmission is a function of the reflectivity in the channel-cut crystals and the brilliance of the x-ray source.

As the degree of polarization purity depends on the divergence of the x-ray source, an x-ray polarization microscope requires close to perfect recollimation after focusing the x-ray beam. Both, focusing and recollimation, must take place between polarizer and analyzer crystal. Therefore, it is paramount that the focusing optical elements do not impair polarization.

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Several methods have been developed to focus x-rays. The most commonly used are based on grazing incidence reflection on curved surfaces (e.g. Kirkpatrick–Baez mirrors [19]), diffraction by Fresnel zone plates [20], and refraction by compound refractive lenses (CRLs) [21]. CRLs are based on the refraction of x-rays. The refractive index for x-rays in a material is less than one and is written as follows:

$$\begin{equation}n=1-\delta +\mathrm{i}\beta \end{equation} \tag{ 2 }$$

δ describes the refractive index decrement which is responsible for refraction and β is the absorption coefficient, describing the attenuation of x-rays. Due to the small and photon energy dependent refractive index decrement (δ ≈ 10⁻⁴...10⁻⁶), the deflection angles are small. To achieve a small focal length, x-ray lenses require small radii R of curvature and a large number N of single lens elements aligned in one row. Spherical aberration are avoided by a parabolic lens profile. Figure 1 shows a schematic sketch of a compound refractive lens.The focal length f for thin lenses is calculated as follows [22]:

$$\begin{equation}f=\frac{R}{2N\delta }.\end{equation} \tag{ 3 }$$

The achievable focal spot size (FWHM) of CRLs for an undulator source in vertical (B_ν ) and horizontal direction (B_h) is [22]:

$$\begin{equation}{B}_{\nu ,\mathrm{h}}=2.355\frac{{L}_{1}f}{{L}_{1}-f}\sqrt{\frac{{\sigma }_{\nu ,\mathrm{h}}^{2}}{{L}_{1}^{2}}+\frac{\mu NR+2N{k}^{2}{\delta }^{2}{\sigma }^{2}}{2{k}^{2}{R}^{2}}}.\end{equation} \tag{ 4 }$$

It thus depends on the source size σ_ν,h, the source-to-lens distance L₁, the selected focal length, the wavenumber k used, the linear coefficient of attenuation μ, as well as the surface roughness σ of the lenses. The focusing properties are also influenced by the form fidelity of the CRL and the homogeneity of the lens material. To achieve a μm-sized beam the surface roughness and deviations from the paraboloid shape should be less than 1 μm. Depending on the energy range, different lens materials are available. In our energy range of interest for precision polarimetry of 6–30 keV, beryllium lenses are most commonly used. Beryllium has the advantage of low absorption and the lens fabrication process is mature. Other lens materials include diamond, polymers and silicon. Diamond lenses have been developed for their excellent high thermal conductivity and low thermal expansion. However, the absorption compared to beryllium is higher and the processing is not yet as developed as for beryllium lenses. Polymer lenses are characterized by their excellent shape accuracy and low surface roughness. However, these materials have a lower transmission due to their chemical composition. Microstructured silicon lenses were developed for nanofocusing but suffer from a small effective aperture and therefore intensity losses at current x-ray sources [23].

In this work, CRLs made of different materials are evaluated for their suitability for polarization microscopy. The challenge is that the crystallinity of common lens materials can change the polarization purity of the beam due to accidental Bragg reflections inside the lens material [24]. Even angularly well separated reflections can lead to small polarization changes due to the long tails of their rocking curves. We compare four different lens materials for our CRLs: single crystalline diamond lenses [25], polycrystalline beryllium lenses [22], amorphous lenses made from SU-8 [26], and glassy carbon. Finally, the performance of the polarimeter is shown by studying polarization changes upon transmission through a beryllium foil.

The different lens materials were processed by various fabrication methods and, therefore, have different surface roughness which affect the achievable focal size of the beam. Four different lens materials were examined: beryllium lenses (RXOPTICS GmbH & Co KG), diamond lenses (S. Antipov, PALM Scientific), SU-8 lenses (A. Last, KIT) and glassy carbon lenses (I. Uschmann, processed by HEMA Formenbau + Kunstoffverarbeitung GmbH). Beryllium lenses are manufactured by a pressing technique and achieve a surface roughness of 0.1 μm [22]. SU-8 is a negative polymer photoresist. Lenses are fabricated by x-ray lithography allowing a surface roughness of 0.013 μm [27]. The glassy carbon lenses were manufactured by electrical discharge machining. The resulting surface roughness was 5 μm. The available diamond lenses were fabricated by ultrafast laser ablation and achieve a surface roughness of 1 μm [28]. Using the knife-edge method, we tested the focusing capabilities of the different lens materials when only the first CRL was placed in the beam. Two 2 mm tungsten blades were used for knife-edge scans of the beam size in the optimal focal distance, one blade for the horizontal and one for the vertical direction. For the determination of the focal size, the knife edge is moved through the focus in 3 μm steps. Assuming a Gaussian beam profile, the measured intensity behind the knife edge represents an error function. Its derivative was used to determine the size of the focus as characterized by its full width at half maximum (FWHM). Table 1 compares the results achieved for the four different CRLs.

The focal size is limited by the x-ray source size (367 μm (FWHM) in horizontal and 26 μm (FWHM) in vertical direction), the source-lens distance of 81.59 m and the focal lengths of the lenses. The obtained focal size is reasonably comparable with the expected size of 30 μm in horizontal direction and significantly higher than the expected size of 2.4 μm in the vertical direction. The last deviation is mainly due to the deterioration of the x-ray beam property in the vertical direction by the DCM. The smallest foci are achieved with the beryllium and the SU-8 lenses. The surface roughness of the diamond and the glassy carbon lenses resulting from the manufacturing process (respectively laser ablation and electric discharge machining, EDM) most likely is the reason for their larger foci. Laser ablation induces internal damage in the bulk of the diamond leading to random conversion of diamond into carbon. Therefore, the effective density profile of the lens deviates from the design values. In the case of glassy carbon lenses, errors in the form fidelity in the parabolic apex of the lenses lead to an additional broadening.

In order to determine the influence of the lenses on the polarization purity of the polarimeter, the purity of the polarimeter without lenses has to be determined first. The polarization purity of the polarimeter is determined by rotating the analyzer crystal around the diffraction plane of the polarizer crystal (η-circle). At each position the rocking curve of the analyzer crystal can be measured. The integrated intensity of the rocking curves (transmission as a function of Bragg angle θ_B of the crystal set) in each η-position of the analyzer crystal can be described by Malus' law:

$$\begin{equation}I={I}_{0}[{\mathrm{cos}}^{2}(\eta )+{\delta }_{0}\,{\mathrm{sin}}^{2}(\eta )].\end{equation} \tag{ 5 }$$

In the vicinity of the extinction position Malus' law can be approximated by a parabola,

$$\begin{equation}I\approx {I}_{0}\,{\left[\eta \frac{\pi }{180{}^{\circ}}-\frac{\pi }{2}\right]}^{2}+{I}_{0}{\delta }_{0},\end{equation} \tag{ 6 }$$

implying that the polarization purity can also be determined from the dependence of the peak intensity of the rocking curve on η [8]. Accordingly, the analyzer is adjusted to the peak of the Si(800) rocking curve and subsequently rotated on the η-circle close to the extinction position. The performance of the polarimeter strongly depends on the presence of excited Umweg reflections. The beamsize was restricted to 0.5 mm × 0.5 mm by a slit in front of the polarizer for the measurement. Thanks to the small divergence of the x-ray beam of the beamline and a precise azimuthal orientation of the analyzer as well as the polarizer crystal (better than 0.05°), a polarization purity of (1.4 ± 0.9) × 10⁻¹¹ is obtained, which actually sets a new record.

The next step in the characterization of the polarization microscope is to measure the influence of the lenses on the performance of the polarimeter. To this end both CRLs were inserted between polarizer and analyzer crystal in a focusing-recollimation setup. Table 2 and figure 3 display the achieved polarization purities for the different materials in comparison.

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The best result is achieved with the SU-8 lenses. No influence on the degree of polarization purity can be seen within the error margins; the slightly poorer numbers are in fact due to the lower count rate with the lenses in the beam. Beryllium leads to the largest change in the degree of polarization purity. Bragg reflections from small crystallites are the most obvious reason for the deterioration of δ₀ [24]. In contrast, the diamond lenses work very well in combination with the x-ray polarimeter. However, their effect on the polarization varies strongly with the orientation of the lenses. In the future, a careful alignment of the lenses in the stack may further improve their performance. The influence of the glassy carbon lenses on the polarization is presently determined by their focusing quality, which in turn is limited by shape fidelity and a large surface roughness. The recollimation of the beam did not work properly and so the degree of polarization purity is determined by the residual divergence of the beam and not by the material itself.

Finally, we present a first high-sensitivity polarization microscopy experiment with the SU-8 lenses. To this end, we scanned a PF-60 beryllium foil of 500 μm thickness through the focused and polarized beam (see figure 2). The step size was 20 μm and 5 μm in horizontal and vertical directions, respectively. Figure 4 shows the result of the measurement.

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The intensity behind the analyzer changes by more than 2.5 orders of magnitude across the scanned sample. The size of the areas with the largest polarization change varies over the scanned area and are unevenly distributed. This suggests that the polarization changes are related to the crystallite size in the material. Beryllium is available in different metallurgic grades. The fabrication process determines the crystallite size and the content of impurities. PF-60 stands for powder foil. It is processed via hot pressing and hot-rolling of Be powder [29]. PF-60 has a beryllium content of 99.0%. The grain size in PF-60 varies significantly. The average size is 25 μm ± 14 μm [29]. As can be seen in figure 4, the areas of polarization change show similar sizes. We therefore conclude that the polarization changes result most probably from small crystallites which are accidentally satisfying the Bragg condition. Compared to high-resolution x-ray polarimetry, scanning high-sensitivity polarization microscopy makes it possible to view the polarization changes with spatial resolution, making it easier to draw conclusions about their origin.