Laboratory-size three-dimensional x-ray microscope with Wolter type I mirror optics and an electron-impact water window x-ray source

Great demands exist in life science research fields for techniques that enable the observation of the three-dimensional (3D) inter-cellular structure of tissue samples and the mapping of the location of specific proteins within inner-cellular structure, for example. X-ray photons are suitable probes because they can penetrate thick samples and provide element-specific absorption contrasts. Especially within the so-called “water window” energy range from the carbon K absorption edge (284 eV) to the oxygen K absorption edge (543 eV), high contrast imaging is enabled between carbon containing substances like proteins and water.

Conventional projection-type high resolution computed micro-tomography (μ-CT) has been used in wide application fields because of its convenience. Its resolution has reduced to 1 μm,¹ and an apparatus has been developed that utilizes soft x-rays with a few keV energy² for light element material structural analysis. However, water window imaging with μ-CT remains unavailable. Another way to make 3D observations of sub-μm scale fine structure is combining wide-field transmission x-ray microscopy with tomographic reconstruction techniques. Since the 1980s, water window x-ray microscopy employing zone plate optics has been developed at synchrotron facilities,^3,4 and presently 3D tomographic imaging of cryogenic biological samples with resolution of around 50 nm is possible.^5,6

Even though the performance of synchrotron-based 3D x-ray microscopes is excellent, their accessibility is limited, and therefore laboratory-size 3D x-ray microscopes have been developed^7,8 to provide high resolution 3D x-ray imaging in the water window region at small individual laboratories. Those laboratory-size 3D x-ray microscopes are based on high resolution zone plate optics and provide cryogenic 3D imaging with a resolution of around 100 nm and utilize laser produced⁷ and gas discharge⁸ plasma sources to generate intense water window x-ray photons. Plasma x-ray sources, which are compact and easier to use than synchrotron-based x-ray sources, are still more complicated than conventional electron impact type x-ray sources. A solid target with such a high oxygen content material as metal oxides⁹ excited by electron impact emits oxygen Kα x-ray photons. An oxygen Kα line (525 eV) is located below the upper limit of the water window, and oxygen Kα photons are highly penetrative through wet samples. Thus an oxygen Kα x-ray source is suitable for a water window 3D x-ray microscope if a sufficient amount of x-ray photons is available on the image plane.

An electron-impact type oxygen Kα source with a water-jet anode was successfully demonstrated and the brightness of the Kα line of 3.0 × 10⁹ photons/s/sr/μm² at 7.8 W electron beam power was reported,¹⁰ which is, however, smaller than the brightness of the state-of-the-art nitrogen laser plasma source¹¹ of 7.4 × 10¹¹ photons/s/sr/μm² in a Lyα line at a laser power of 90 W. Thus high throughput illuminating and imaging optics are indispensable for utilizing an electron-impact type oxygen Kα source as a source of the 3D water window x-ray microscope. Using grazing incidence axisymmetric mirrors, such as an ellipsoidal mirror or a Wolter type I mirror,^12–14 is possible since they provide high reflectivity for x-rays with a grazing incidence angle below the critical angle. For example, the reflectivity of a SiO₂ surface with 2-nm rms roughness for oxygen Kα unpolarized x-ray photons with a grazing incidence angle of 1.5° is calculated^15,16 as high as 79%. Furthermore, an x-ray microscope with precisely fabricated Wolter type I mirror optics can magnify up to 300 times and resolve a 300-nm lines and spaces pattern.¹⁷ 

In this article we demonstrated a laboratory-size 3D x-ray microscope that exploits an electron-impact type water window x-ray source and a condenser and an objective Wolter type I mirror. In Secs. II and III, we first describe the details of our experimental apparatus and show images of an x-ray resolution chart and a micro glass capillary as a test sample. Then we present the initial results of the 3D imaging of biological samples.

The experimental apparatus for the 3D water window x-ray microscope is shown in Fig. 1. All components are enclosed in a vacuum chamber (not shown). The x-ray source is an electron-impact type with a Cr₂O₃ target on a stainless-steel anode. An electron beam of 10–15 keV energy from an electron gun impinges on the anode target. X-ray photons from the target are collected and focused on the sample by the condenser Wolter type I mirror, and the transmitted x-ray image is magnified by the objective Wolter type I mirror. Then the magnified image is detected by a back-illuminated CCD camera with 512 × 512 pixels at a physical pixel pitch of 24 μm. Since the distance from the x-ray source to the x-ray detector is only 3.4 m, the 3D x-ray microscope can be placed in a typical laboratory.

Optical design parameters and some characteristics of the condenser and objective Wolter type I mirrors are listed in Table I. These two mirrors are designed to enhance the throughput of the optics, from the target of the x-ray source to the image plane of the x-ray detector. The solid angle of the condenser mirror to collect the x-ray photons from the target is 5.4 × 10⁻⁴ sr, and the output angle's range of the condenser mirror (5.41°–6.01°) is almost fully covered by the input angle's range of the objective mirror (5.35°–5.99°). Thus efficient transfer of the x-ray photons between the condenser and objective mirrors is achieved. We evaluated the efficiency as 0.92 using ray tracing simulation. The mirrors were fabricated by a glass replication method. The shapes of the hyperboloid and the ellipsoid are replicated to the inner surface of a glass tube from an accurately figured mandrel. The inner surface is polished by a computer-controlled polishing machine to finish the mirror surface. The surface roughness and the profile of the replicated mirrors are measured using a contact-type profilometer (Form Talysurf Super S5K, Taylor Hobson Ltd., UK). The surface roughness and the figure error, which is evaluated by comparing the measured and designed profiles, are around 2 nm (rms) and less than ±0.1 μm, respectively, for both ellipsoid and hyperboloid sections. The total reflectivity of the condenser and objective mirrors is calculated as 37% on the oxygen Kα line (525 eV) using the SiO₂ surface's reflectivity with 2-nm roughness (rms). We also calculated the condenser mirror's reflectivity in the same way to be 8% at 1.0 keV, decreasing rapidly below 0.1% at 1.3 keV. High energy bremsstrahlung and K lines from Cr atoms (Kα₁: 5.415 keV and Kα₂: 5.405 keV) are filtered out through the condenser mirror. A photograph of the condenser and objective mirrors is shown in Fig. 2.

We selected Cr₂O₃ as a target material of the oxygen Kα x-ray source because it is electrically conductive. The charge-up effect is negligible for the x-ray source since the measured resistivity between the Cr₂O₃ target surface and the anode stem ranged from several hundred Ωs to several kΩs and no conspicuous degradation of the x-ray intensity was observed during overnight operations. The size of the x-ray source was determined to be 2 × 5 mm² from observation of a faint sign of the electron beam irradiation on the target surface, and the size of the x-ray illumination field on the sample plane was calculated based on the demagnification factor of the condenser mirror as 0.6 × 1.4 mm², which is larger than the field of view of the optics (0.11 × 0.11 mm²).

We mounted the condenser and objective mirrors on the motorized XYZ-stages with two-axis tilt control. The sample was placed on a manually adjustable XY-stage mounted on a motorized rotational stage, which was placed on a motorized XYZ-stage. The sample was first observed by an optical microscope placed beside the x-ray optics to locate the sample's region of interest (ROI) on the rotational axis before evacuating the vacuum chamber. Then the XYZ-stage was moved to place the sample's ROI on the focal point of the objective mirror. Both the mirror mounts and the sample stage are controlled outside of the vacuum chamber.

We hypothesized that the illumination x-ray spectrum was mainly the oxygen Kα line. To examine this hypothesis, we measured the x-ray attenuation through a Si₃N₄ membrane with a thickness of 0.1 μm placed at the sample position. The attenuation factor of the oxygen Kα x-ray through a 0.1-μm thick Si₃N₄ membrane was calculated¹⁶ as 0.66, and the measured attenuation ratio was 0.65. This is consistent with our hypothesis on the illumination x-ray spectrum.

To estimate the intensity of the x-ray source, we calibrated the CCD's response to oxygen Kα x-ray photons by operating it in the photon counting mode, in which each x-ray photon was detected as a bright single pixel with a pixel value larger than the CCD's noise level. Since the distribution of the pixel values for oxygen Kα x-ray photons peaked at a pixel value of 7, we determined the conversion factor for calculating the number of x-ray photons from the pixel value to be 7 per x-ray photon. Operating the x-ray tube at 15 kV and 185 μA tube current, the average pixel value of an image taken with no sample was 1700 with an exposure time of 480 s. Thus the detected x-ray intensity at the CCD was 0.5 photons/s pixel in this operating condition. Taking into account the collection solid angle of the condenser mirror, the total reflectivity of the condenser and objective mirrors, the efficiency of the x-ray photon transfer between the mirrors, the magnification factor of the optics, and the detection efficiency of the CCD (0.67), we estimated the brightness of the x-ray source to be 7 × 10³ photons/s/sr/μm². The x-ray intensity per unit solid angle was calculated as 7 × 10¹⁰ photons/s/sr by multiplying the brightness by the source size. This value is less than 1/20 of the prediction for a pure oxygen target at the same operating condition (1.7 × 10¹² photons/s/sr), according to an empirical formula given by Green and Cosslett.¹⁸ 

Although the objective mirror's magnification factor was designed to be 100, the actual magnification factor was determined to be 108 using a metal mesh sample. Since using ray tracing simulation confirmed that the discrepancy in the magnification factor had little effect on the imaging performance, no further adjustment of the optics was carried out. From the actual magnification factor, the pixel pitch on the sample plane and the Nyquist frequency of the imaging system were determined to be 0.22 μm and 2.25 line pairs per micrometer (lp/μm), respectively.

Figure 3(a) shows an image of a radial pattern of an x-ray resolution chart made of 500-nm thick tantalum (XRESO-50HC, NTT Advanced Technology Corp., Japan) that was observed by our 3D x-ray microscope with an exposure time of 30 min. The x-ray source was operated at 15 kV and 190-μA tube current. The spatial frequencies at the inner rim of the 1st, 2nd, and 3rd zones were 0.25, 0.5, and 1.0 lp/μm, respectively. The 3rd zone's pattern was almost resolved. The intensity profile at the 0.8-μm lines and spaces position along the white circle in Fig. 3(a) is plotted in Fig. 3(b). At this spatial frequency of 0.625 lp/μm, the image contrast is calculated as 21.9% ± 4.6% from the intensity values at the peaks and valleys of the intensity profile. The image contrasts at several other spatial frequencies were calculated from the radial pattern image and plotted in Fig. 3(c). Figures 3(a) and 3(c) show that a resolution limit of the 3D x-ray microscope at which the image contrast drops to 5% was achieved around 1.0 lp/μm.

The modulation transfer function (MTF) for an annular aperture (MTF_ap),¹⁹ whose numerical aperture and obscuration ratio are identical as those of the objective mirror, is plotted in Fig. 4. The wavelength is set to 2.36 nm (525 eV). At a spatial frequency of 0.86 lp/μm, MTF_ap is 89%. Considering the MTF for sampling by CCD (MTF_CCD), the total MTF for the imaging system (MTF_total = MTF_ap × MTF_CCD) remains 83%. However, the image contrast is 12% by 3D x-ray microscope at 0.86 lp/μm. This discrepancy was probably caused by such imperfections of the objective mirror as surface roughness and figure error.

As a test sample for 3D tomographic reconstruction, we used a micro glass capillary for cell manipulation (Femtotips, Eppendorf AG, Germany). Figure 5(a) shows an optical microscope image of a glass capillary. Its transmission x-ray image, obtained with eight-minute exposure time, is shown in Fig. 5(b). Transmission images were acquired for 180° rotation in 1.5° increments. The x-ray source was operated at 15 kV and 160–200 μA during the image collection. To improve the quality of the transmission images before 3D reconstruction, image restoration was performed using the Richardson-Lucy method,^20,21 which is a Bayesian-based iterative scheme for image restoration that deconvolves the point spread function (PSF) of the imaging system. The PSF can be obtained as a good approximation by rotating the line spread function (LSF) of the imaging system if the imaging system can be considered rotationally symmetric. We measured the LSF for both horizontal and vertical directions using a knife edge method with a 50-μm diameter platinum wire. Figure 6(a) shows the derivatives of the knife edge scans for both directions. These derivative data were fitted with a function consisting of two Gaussians with a common center to obtain LSFs for both directions, which are also shown in Fig. 6(a). Comparing the two normalized LSFs shown in Fig. 6(b), we assumed that the imaging system of the 3D x-ray microscope was rotationally symmetric since no clear difference could be seen between the LSFs. We used the PSF calculated by rotating the LSF for image restoration. Each restored image was divided by the illumination intensity image that was obtained with no sample on the imaging position. The negative logarithms of the transmissivity images were calculated for the 3D image reconstruction. Figure 5(c) shows the negative logarithm of the transmissivity image of Fig. 5(b). 3D tomographic reconstruction was performed using the convolution back-projection method. A reconstructed slice image parallel to the rotation axis is shown in Fig. 5(d). Images of slices perpendicular to the rotation axis, which correspond to the positions indicated by arrows in Fig. 5(d), are shown in Fig. 5(e) with profiles of the linear attenuation coefficient (LAC) along the white dashed line. All the scale bars are 10 μm. At positions B and C, the glass capillary's wall and hollow are clearly resolved, and a dip is visible in the LAC profile even at position A, 9.2 μm from the tip. The outer and inner diameters at position A were measured from Fig. 5(a) as 3.6 and 1.1 μm, respectively. As a result of the observation of the micro glass capillary, the 3D x-ray microscope can resolve 1-μm scale 3D structures.

To demonstrate the applicability of a water window 3D x-ray microscope to life science research fields, we observed some bio-medical samples including dehydrated mouse kidney slices. Figure 7(a) shows an optical microscope image of 5-μm thick dehydrated mouse kidney slice, which was fixed on a 0.1-μm thick Si₃N₄ membrane. This region of the slice was selected just based on structural interest rather than on bio-medical significance. We acquired transmission x-ray images in rotation angle ranges of 0°–45° and 127.5°–180° in increments of 1.5°. Each image was taken with eight-minute exposure time, and the x-ray source was operated at 15 kV and 180 μA. Figure 7(b) shows an x-ray transmission image at the 0° position after the image restoration. We observed different image contrast from that of the optical microscope image. In this case, the maximum likelihood expectation maximization algorithm was used for 3D tomographic reconstruction. Figures 7(c)–7(g) show the reconstructed slice images parallel to the rotation axis and perpendicular to the optical axis with 1.1-μm separation. Differences in the 2D structure between the reconstructed slices can be seen.

We constructed a laboratory-size water window 3D x-ray microscope using Wolter type I mirror optics and an electron impact type x-ray source to generate oxygen Kα line (525 eV) x-rays. We demonstrated a spatial resolution limit of around 1.0 lp/μm and the capability of resolving 1-μm scale 3D structures.

For practical applications, however, some improvements are necessary. The currently obtained spatial resolution limit and image contrast are insufficient for cellular level observation of bio-medical samples. Because the image qualities are degraded due to the imperfection of the mirror surfaces, we are making efforts to improve the replication and polishing accuracy to improve the resolution limit of the 3D x-ray microscope. A tomographic resolution limit of 0.5 μm could provide information equivalent to ten slices from a 5-μm thick sample. Increasing the x-ray intensity is also critical for practical use. The collection of transmission images for the reconstruction of Figs. 7(c)–7(g) took around 9 h. With high intensity, state-of-the-art electron gun technology and focusing electrons on the anode target with a diameter smaller than 1 mm, we can increase x-ray intensity more than 10 times. Since using the water window x-ray, which provides a natural absorption contrast between water and carbon containing such substances as proteins, is most useful for the observation of hydrated or frozen hydrated samples, incorporating a cryogenic stage into the 3D x-ray microscope increase its potential for bio-medical applications. Enough space exists between the condenser and objective mirrors for a cryogenic stage. With these improvements, the 3D x-ray microscope might become a complementary apparatus for synchrotron-based 3D x-ray microscopes to provide high accessibility and easy use.

This work was carried out under collaboration between the Research Center for Advanced Science and Technology of the University of Tokyo and Hamamatsu Photonics K.K. The authors gratefully acknowledge Professor Y. Nakano of the University of Tokyo and A. Hiruma and T. Hara of Hamamatsu Photonics K.K. who initiated this collaboration. The authors appreciate the support of Professor M. Naito of Niigata University for the sample preparation and thank Y. Inagaki, T. Suzuki, H. Suzuki, and K. Hara of Hamamatsu Photonics K.K for their technical support. One of the authors (S.O.) wishes to thank Professor K. Takahashi of the Graduate School for the Creation of New Photonics Industries for his encouragement throughout the development.