The achievable spatial resolution and the contrast transfer function (CTF) are key parameters characterizing an X-ray microscope. We measured the spatial resolution and the contrast transfer function of the transmission X-ray microscope (TXM) at the electron storage ring BESSY II. The TXM uses the radiation of an undulator source and operates under partially coherent illumination conditions. For spatial resolutions down to 25 nm, our measurements of the CTF’s are in good agreement with theoretical CTF data for partial coherence. With higher resolution zone plate objectives, we measured a spatial resolution (half-pitch) of 11 nm in 1st and 3rd order of diffraction. However, with these objectives the stray light level increases significantly.
©2012 Optical Society of America
X-ray microscopy has become a valuable research tool for numerous applications [1,2]. In particular, it permits nanoscale three-dimensional views of biological cells using only the natural contrast caused by the different absorption of organic matter and water [3–5]. An inherent element-specific contrast allows for element specific imaging and spectromicroscopic applications [6,7]. The short X-ray wavelengths permit high spatial resolution. However, in lens based X-ray microscopy the spatial resolution is limited by the numerical aperture (N.A.) of the optics. Today, the highest resolution in the soft X-ray photon energy range is achieved with zone plate objectives. The achievable spatial resolution of these diffractive optics is proportional to the outermost zone width drN and inversely proportional to the order of diffraction used for imaging.
The nano-fabrication challenges for zone plate structures with high aspect ratios set the limit of the achievable spatial resolution. A spatial resolution of features with 12 nm to 14 nm half-pitch was reported [8,9] for the TXM. For scanning X-ray microscopy a half pitch resolution of 9 nm was reported . However, the reported image contrast was extremely low. In general, an understanding of the contrast transfer function (CTF) of high resolution X-ray microscopes is essential for further developments. In particular, the radiation dose required to detect small object features is proportional to 1/η∙(Cobj x CTF)−2 where Cobj denotes the object contrast and η the diffraction efficiency of the zone plate objective . Therefore, microscopes providing a high contrast transfer are advantageous to minimize sample damage and exposure time. With this approach the measured absorption values are closer to the original object contrast for higher spatial frequencies. In this paper, we describe the fabrication of zone plates providing state-of-the-art resolution and the measurement of their resolving power. In addition, we characterize the CTF for different zone plate objectives under partially coherent illumination conditions in the TXM operated by the Helmholtz-Zentrum Berlin (HZB) at BESSY II.
2. Zone plate fabrication
The fabrication of the high resolution nickel or gold zone plates is similar to a previously described tri-layer process . To ensure sufficient transmission in the soft X-ray range, we employ commercially available 100 nm thick Si3N4-membranes (SILSON Ltd.) as support membranes for the zone plate objectives. Our state-of-the-art e-beam lithography system (model EBPG5000plusES from VISTEC) with 100 keV electron energy permits to expose thicker e-beam resist layers without significant loss of resolution by beam broadening due to electron scattering in the resist. Therefore, high resolution gold zone plates can also be manufactured with a single layer process. For this purpose, the Si3N4-membrane (coated with a plating base consisting of a 10 nm thick chromium layer and a 15 nm thick germanium layer) is spin coated with a 150 nm thick e-beam resist layer ZEP 7000 (Nippon Zeon) and baked 30 min at 170 °C. The zone plate patterns are exposed into the resist layer with the e-beam lithography system operating at 100 keV. The pattern is developed at room temperature in hexylacetate followed by an isopropanol rinse and dried in an air flow. The developed resist is used as a mold for gold electroplating. We used the gold electroplating bath AUTRONEX HSGL (ENTONE GmbH) to fill the 150 nm high resist structures with gold. Figure 1 shows SEM micrographs of the outermost part of the fabricated gold zone plates. A buttress pattern was introduced to increase the stability of the narrow structures during the development and electroplating process. We have fabricated four different types of zone plates (parameters listed in Table 1 ) applying the described nanostructuring process. The different zone plates have outermost zone widths drN = 25 nm, 20 nm, 17 nm and 15 nm, respectively. The zone thickness is about 80 nm, i.e. the mold was not completely filled. From diffraction theory, the 1st order diffraction efficiency of 80 nm thick gold zones is about 7% for photon energies between 500 eV and 700 eV and drops to 5% at 1200 eV photon energy. In the 3rd order of diffraction, the efficiency is about 0.8% in the photon energy range between 500 eV - 700 eV and only 0.5% at 1200 eV. The decreasing nanostructuring quality of the gold structures for the 15 nm wide zones (see Fig. 1) is due to problems in the plating process and is not limited by the e-beam exposure.
3. X-ray microscopy
The HZB full-field soft X-ray microscope is installed at the undulator U41 at the BESSY II electron storage ring in Berlin. It operates in the photon energy range between 0.25 - 1.5 keV. A spherical grating monochromator (SGM) provides a spectral resolution of 104. The divergent beam emerging from the exit slit of the SGM is collected by a single reflection ellipsoidal glass capillary condenser (Xradia Inc.). The condenser illuminates the object field with a measured focusing efficiency of 80% at 510 eV photon energy . The capillary condenser generates the required hollow cone illumination in combination with an opaque disk centered in the entrance aperture of the capillary. In addition, this central stop blocks the direct light (see Fig. 2 ). With this X-ray optical set-up, the image field is free of zero order radiation of the zone plate objective. The spot size formed by the capillary is about 1 µm x 1 µm and hence too small to illuminate the whole field of view . Therefore, the capillary condenser has to be helically scanned in a plane perpendicular to the optical axis to illuminate the usable object field. The sample is imaged with high magnification by the zone plate objective into the image plane and recorded by a two-dimensional, cooled back illuminated soft X-ray CCD camera (Roper Scientific, PI-SX 1300). The CCD detector has 1340 x 1300 pixel with a size of 20 µm x 20 µm. Mostly the 1st order of diffraction (m = 1) of the zone plate objective is used for imaging. To improve the spatial resolution, higher orders of diffraction of the zone plate objective can be employed . For life science applications, the microscope is equipped with a high-tilt object stage to perform cryo X-ray tomography . With the high spectral resolution from the SGM, the TXM also permits nanoscale spectromicroscopy .
In the X-ray optical set-up sketched in Fig. 2, the numerical aperture (N.A.) of the condenser and the zone plate objective are matched. The N.A. of the reflective condenser element is independent from the photon energy E. However, the N.A. of the zone plate objective decreases linearly with increasing photon energy. In all experiments described in this work the ratio of the apertures is N.A.condenser/N.A.objective < 1. Therefore, the TXM operates in partially coherent imaging mode. For the theoretical calculations of the CTF and the cut-off frequency, i.e. the spatial frequency at which the contrast transfer equals zero, the N.A. values of the condenser and the zone plate have to be taken into account.
The cut-off frequency fcut-off is given by the formula fcut-off = (N.A.objective + N.A.condenser)/λ , where λ denotes the X-ray wavelength. This relation is valid for N.A.condenser ≤ N.A.objective. The N.A. of a lens is defined as N.A. = n∙sin(α), where n is the index of refraction and α is one-half of the angular aperture of the lens . For X-rays the index of refraction is close to unity n ≈1. The low N.A. of the zone plate objective is in good approximation given by N.A. ≈m∙λ/(2∙drN) . The N.A. of the condenser is 0.0207. Under these conditions, we get for the cut-off frequency fcut-off = (N.A.objective + N.A.condenser)/λ ≈m/(2∙drN) + 0.0207/λ ≈m/(2∙drN) + 0.0207∙E/(h∙c) where h denotes Planck’s constant and c the speed of light.
3.1 Spatial resolution
The spatial resolution of the TXM is experimentally determined by imaging a sectioned multilayer test sample. The resolution test object consists of a Cr/B4C multilayer which was thinned to a lamella (about 100 nm thick). The multilayer has five different periods consisting of 10 Cr/B4C line pairs with 20.6 nm, 17.5 nm, 14.3 nm 11.0 nm and 7.8 nm half-pitch (see Fig. 3 ), respectively. The experiments were performed using in-house fabricated zone plate objectives with different outermost zone widths at different photon energies from 580 - 1200 eV in the 1st order of diffraction. To further increase the resolution, some zone plates were also used in the 3rd order of diffraction. The results of the resolving power test experiments for various objectives and photon energies are shown in Fig. 3 (the half-pitch values of the test sample structures are indicated on the right side). The outermost zone width drN of the used zone plate objective is specified on top of the X-ray images. The photon energy used for imaging, the image pixel size (which is given by the CCD pixel size of 20 µm divided by the magnification used for imaging) and the exposure time for taking the X-ray micrographs are given below the X-ray micrographs. In the 1st order of diffraction, the zone plate with drN = 25 nm outermost zone width resolves the 20.6 nm half-pitch structures at E = 580 eV photon energy. The zone plates with drN = 20 nm (E = 700 eV), 17 nm (E = 1200 eV) and 15 nm (E = 700 eV) resolve the 14.3 nm half-pitch structures. The zone plate with the smallest drN = 15 nm even resolves the 11.0 nm half-pitch structures at E = 1200 eV. In this case, the N.A.´s of the condenser and the zone plate objective are better matched than at lower photon energies because the cut-off frequency is a function of the photon energy as shown in the previous paragraph. This leads to an increased spatial frequency cut-off.
In general, we observe that zone plates operating in the 3rd order of diffraction provide a higher resolving power compared to zone plates used in 1st order of diffraction. In the 3rd order, the N.A. is 3-fold increased. Therefore, the effective drN_eff = drN/m is three times smaller for a zone plate used in 3rd order of diffraction. In the 3rd order of diffraction a zone plate with drN = 40 nm (effective drN_eff = 13.3 nm) resolves the 14.3 nm half-pitch structures at E = 580 eV. Zone plates with drN = 25 nm (drN_eff = 8.3 nm) and 20 nm (drN_eff = 6.7 nm) even resolve the 11.0 nm half-pitch structures at E = 580 eV and 700 eV, respectively.
Figure 3 includes a direct comparison of the resolving power of a zone plate with drN = 25 nm operating in different orders of diffraction at the same photon energy (E = 580 eV) and the same energy resolution (E/ΔE = 5400). The magnification used for imaging in the 3rd order of diffraction was 3-fold higher. It can clearly be seen that the resolution in the 3rd order of diffraction is significantly higher compared to the 1st order. In previous experiments, we resolved with a drN = 25 nm zone plate in the 3rd order of diffraction half-pitch structures of 14.3 nm but could not resolve the 11 nm lines and spaces . We assume that the better result shown in this paper is due to the better placement accuracy of the zone plate structures by using the new state-of-the-art e-beam lithography system. Furthermore, the zone plate pattern was corrected for 3rd order of diffraction imaging and the zone height of the gold zone plate was reduced to about 80 nm to avoid volume diffraction effects which potentially could lead to aberrations . In our resolution experiments (see Fig. 3), the best image quality for the 11.0 nm half-pitch structures was obtained with the zone plate with drN = 20 nm in 3rd order of diffraction (drN_eff = 6.7 nm).
The resolved half-pitch values of the multilayer structures are plotted as a function of drN_eff in Fig. 4 . In order to demonstrate how close the TXM operates to the theoretical limit, the corresponding theoretical cut-off values are also plotted for the different drN_eff values of the used zone plate objectives.
The circular dots in Fig. 3 represent the smallest visible feature size (half-pitch) of the multilayer structures as a function of drN_eff of the corresponding zone plate used for the measurements. In addition, the dots are labeled with the corresponding photon energy used for imaging. The black triangles show the next smaller half-pitch of the multilayer structures which are not resolved in the corresponding X-ray images of Fig. 3. Due to the discrete steps of the multilayer periods, it is not possible to find out whether structures with a half-pitch size in between the triangles and the circular dots would be visible. The gray squares show the theoretical feature size corresponding to the calculated cut-off frequency of the CTF. At this feature size (half-pitch) the contrast in X-ray images drops to zero. No structures below this limit (indicated by the gray shaded area in the plot) should be visible.
Figure 4 reflects the good performance of the zone plates. In almost all cases the smallest visible pitch of the multilayer sample in Fig. 3 (illustrated by the black dots in Fig. 4) is in good agreement with the minimum pitch of the multilayer sample expected to be resolved by theory (i.e. by the calculated cut-off value illustrated by the gray squares in Fig. 4). An exception is the measurement of the zone plate with drN = 20 nm in 3rd order of diffraction with an effective drN_eff of 6.7 nm. In this case, the multilayer structures with 7.8 nm half-pitch size should be visible, because the cut-off value of 5.8 nm is significantly lower than the 7.8 nm lines and spaces of the multilayer structures. We suspect that vibrations in the sample area or vibrations of the optical components may degrade the image quality of the X-ray microscope in this ultra-high resolution range below 10 nm.
3.2 Contrast transfer function
An in-house fabricated high quality Siemens-star pattern is used to measure the CTF of the X-ray microscope. The Siemens-star pattern consists of about 85 nm thick gold structures with 20 nm – 100 nm half-pitch. A TXM image recorded at 510 eV photon energy of the Siemens-star pattern is shown in Fig. 5 . For the CTF measurements, we generated circular profile plots at a certain half-pitch of the Siemens-star. The maxima and minima intensities of the profile plots are used to calculate the image contrast Cimage = (Imax-Imin/(Imax + Imin) as a function of the half-pitch (i.e. the spatial frequency f) of the structures. The CTF is obtained by CTF(f) = Cimage(f) / Cobject.
Figure 5 (right) shows an intensity plot with a periodicity of 110 nm along the semi-circle indicated in Fig. 5 (left). Note that the center of the plot where the periodicity is distorted due to the label “50 nm” in the Siemens-star pattern was excluded from the evaluation of the image contrast. In general, we excluded defect areas or labels in the Siemens-star pattern from the evaluation. Another effect which can be seen in the plot in Fig. 5 is the intensity variation along the evaluated path even in areas without obvious defects or artificial structures in the Siemens-star pattern. This is most likely caused by an inhomogeneous background signal in the image. Another explanation might be small local gold height variations in the Siemens-star. Therefore, we calculated an average contrast from the data which is shown in the CTF plots (see Fig. 6 ). The error bars indicate the corresponding maximum and minimum measured contrast values. The highest measured image contrast at low spatial frequencies is 77.3% (measurement of ZP1, 25 nm drN, 1st order of diffraction, average of the measured image contrast values at spatial frequencies ≤ 10 µm−1). This is assumed to be the object contrast. It corresponds to a calculated gold height of 86 nm which is in good agreement with the independently determined gold thickness of 85 nm given by process parameters of the Siemens-star pattern. This object contrast of 77.3% was used to normalize the image contrast Cimage(f) to obtain the CTF. Figure 6 shows the measured CTFs for different zone plate objectives at 510 eV photon energy. For comparison, theoretical CTFs calculated by a plane wave model are shown . These CTF calculations take into account the hollow cone illumination of the condenser as well as the N.A. values of the condenser and the zone plate objective. The diamond shaped dots (measurement with ZP1) in the diagram of Fig. 6 display the measured CTF using a zone plate objective with drN = 25 nm, 90 µm diameter, used in 1st order of diffraction with a focal length of 939 µm at 510 eV photon energy. The Siemens-star was imaged with a magnification of 3650. The black solid line in the plot of Fig. 6 shows the corresponding calculated CTF. For this calculation, a photon energy of 510 eV, a gold grating sample of 86 nm thickness with rectangular shaped profile, and the 1st order of diffraction was assumed. It can be seen that the measured CTF is in good agreement with the calculation taking the error of the measurement into account. Especially, the expected contrast drop in the calculated CTF at a spatial frequency of 11.25 µm−1 (44 nm feature size) fits with the measured data. However, the deviation between theory and experiment is significantly pronounced at spatial frequencies ≥16.7 µm−1 (corresponding to ≤ 30 nm feature size).
Additional measurements were performed using a second zone plate “ZP2” with 91 µm diameter and the same outermost zone width drN = 25 nm in 1st order and 3rd order of diffraction. Figure 6 displays the measured CTF for the zone plate “ZP2” in 1st (square dots) and 3rd (circular dots) order of diffraction. The focal length of this zone plate at 510 eV photon energy is 923 µm in 1st order of diffraction and 3-fold shorter in 3rd order of diffraction. The Siemens-star was imaged with a magnification M = 3700 in 1st order and M = 6160 in 3rd order of diffraction. Note that within the error of the measurement the 1st order diffraction measurement with “ZP2” is in agreement with the theoretical CTF (black solid line).
At low spatial frequencies the CTF should be equal one, i.e. the obtained image contrast of all measurements should be the same and express the object contrast given by the transmission of the object material and height. However, for 3rd order imaging the measured CTF is significantly lower than one (see circular dots in Fig. 6). A CTF < 1 for the measurements at low spatial frequencies can only be explained by a background signal in the recorded images which lowers the image contrast. The strong background in 3rd order of diffraction might be due to stray light from other diffraction orders of the zone plate and non-ideal optical components of the microscope due to fabrication difficulties. The image contrast is reduced by a background intensity I´B according to C´image = (I´max-I´min)/(I´max + I´min + 2I´B).
A constant background intensity I´B was added to the calculated theoretical intensities I´max and I´min in order to fit the CTF at spatial frequencies below 14.3 μm−1 to the measured CTF which has a value of 0.304 at these low frequencies. The black dotted line in Fig. 6 shows the calculated CTF (I´B = 1.64 a.u. was used for the fit, at low frequencies is I´max = 1.24 a.u., I´min = 0.14 a.u.). Within the displayed spatial frequency range the calculated CTF is constant. This is in agreement with the measurement taking the error of the measurement into account. Although the CTF is lowered by a strong background, the calculated contrast in 3rd order of diffraction (25 nm drN) is exceeding the contrast in 1st order of diffraction at spatial frequencies ≥25 µm−1 (corresponding to ≤ 20 nm feature size). At a spatial frequency of 28.8 µm−1 (17.3 nm feature size) the CTF for “ZP2” in 3rd order of diffraction is still constant whereas the CTF drops to zero in the 1st order of diffraction. Therefore, very small structures can only be resolved in 3rd order of diffraction as demonstrated in the previous chapter using the ML resolution test sample.
The gray triangular shaped dots in Fig. 6 show a CTF measurement using a zone plate objective in the 1st order of diffraction with drN = 17 nm, d = 61 µm and f = 428 µm at 510 eV photon energy. The magnification during imaging the Siemens-star pattern was 4440. The background signal lowering the image contrast is also quite strong in this 1st order of diffraction measurement. The gray solid line in the diagram shows the calculated CTF for the zone plate with drN = 17 nm. A constant background signal of I´B = 0.41 a.u. was used to fit the CTF to the measured value of 0.643 at spatial frequencies below 9.1 µm−1. Within the error bars the measured data are in good agreement with the calculated CTF data for spatial frequencies ≤ 14.3 µm−1 (corresponding to ≥ 35 nm feature size). For higher spatial frequencies ≥14.3 µm−1 the measured contrast transfer is significantly lower than calculated. The calculation predicts a constant CTF within the measured spatial frequency range. In general, the deviation of the measured CTF from the calculated CTF for higher spatial frequencies might be explained by the poorer nanostructure quality of sample structures below 30 nm in size. For the zone plate with drN = 17 nm the lower quality of the fabricated very narrow outer zones might cause a radial decrease of the zone plate efficiency. As a consequence, high spatial frequencies of the sample are transferred by the objective with lower contrast compared to zone plates with constant radial efficiency. This might also cause an additional drop in contrast for high spatial frequencies.
From our measurements, we conclude that the background signal in our TXM increases with shorter focal length and/or larger N.A. of the zone plate objectives. A possible explanation is stray light which is increasingly blocked by the zone plate aperture for larger focal length or smaller N.A. objectives. By ray-trace simulations, Bertilson et al.  showed that other orders than the diffraction order used for imaging, produce stray light in the image and reduce the image contrast. The −1st order makes the largest contribution to the stray light since the first order diffraction efficiencies are significantly larger than any high order diffraction efficiency. Bertilson et al. found that the stray light in the image field decreases with larger focal length and increases with the size of the illuminated area in the sample plane. Furthermore, in the 3rd order of diffraction the ratio of stray light caused by the efficient −1st order to the light of the inefficient + 3rd order of diffraction used for imaging is larger compared to + 1st order imaging. Therefore, more stray light and as a consequence a lower contrast is expected for 3rd order imaging. In our X-ray microscope, the size of the illuminated area in the sample plane is matched to the field of view (< 10 μm in our experiments) by adjusting the amplitude of the capillary condenser scanner (see section 3). The stray light dependency on the focal length and the lower contrast in 3rd order imaging is basically what we observe in the experiments. A very large illuminated area in the sample plane increases the stray light. Due to the figure error in the capillary condenser, it is likely that an area significantly larger than the imaged object field is illuminated. From measurements we know that ~80% of the light incident on the condenser is focused within 15 um diameter in the sample plane in the absence of scanning of the condenser compared to an expected diffraction limited focus significantly smaller than 1 um. For the smaller field of views imaged with the 17 nm zone plate in the first diffraction order and the 25 nm zone plate in the third diffraction order, we would expect to have a more significant portion of the light outside of the field of view. Light from this extended area is collected by the zone plate objective and yields an increased stray light level in the image plane. The presence of the observed high background level in the measurements of the zone plate with 17 nm drN and the zone plate with 25 nm drN used in 3rd order has to be investigated in future experiments in more detail to obtain quantitative data.
In summary, we have characterized the resolving power and CTF of the HZB TXM. For this purpose, we manufactured gold zone plates with smallest line width down to 15 nm and resolution test pattern to analyze the microscope contrast transfer. The measurements show that the TXM resolves 11 nm lines and spaces. Our measurement of the CTF is in good agreement with theory for the zone plate with 25 nm smallest zone width operating in 1st order of diffraction. In particular, the theoretical CTF curve for partially coherent illumination is experimentally confirmed. The high contrast under these imaging conditions is important to ensure that the radiation dose for the object is as low as possible.
Zone plate objectives with smaller zone widths below 20 nm provide the expected higher resolving power. However, their contrast transfer is significantly lower and exhibits a severe background level caused by unwanted stray light. In particular, imaging in high orders suffers so far from the high background. Future work will concentrate on reducing this background by manufacturing more efficient zone plate objectives and advanced X-ray optical set-ups reducing the stray light.
The authors gratefully acknowledge the VISTEC Electron Lithography Group as well as S. Braun, P. Gawlitza (IWS, Dresden, Germany), E. Zschech and Y. Ritz (Fraunhofer IZFP, Dresden, Germany) for their valuable support. We thank M. Feser (Xradia Inc.) for helpful discussions. This work was supported by the EU within the 7th framework program (Grant agreement 226716, WP23 NANOFOX) and the BMBF/VDI within the “L-TXM” project (Contract No. 13N8915).
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