2.1.1.

Experimental setup

We have designed a nanofocus x-ray setup for propagation-based x-ray phase-contrast tomography, as depicted in Fig. 2. Its central component is the NanoTube N1 60 kV (Excillum AB) x-ray source, with two-dimensional (2-D) spatial resolution down to 150 nm according to the manufacturer (lines-and-spaces, metal test objects in absorption contrast). The source is operated at 60 keV with a power between 0.2 and 1.2 W, depending on the spot size. The NanoTube system was calibrated for three different spot sizes $s$ [full width at half maximum, (FWHM)]: “big spot, high flux” at $\sim 1\mu \mathrm{m}$, “middle spot, middle flux” at $\sim 0.5\mu \mathrm{m}$, and “small spot, low flux” at $\sim 0.3\mu \mathrm{m}$ (FWHM). Figure 2(a) shows the schematic of the transmission-anode target, which consists of a $0.50\mu \mathrm{m}$ W-film providing a rather high ${\mathrm{e}}^{-}$ stopping power $S$ ($S=54.4\mathrm{MeV}/\mathrm{cm}$²⁷) on a $100\text{-}\mu \mathrm{m}$ layer of diamond, serving as carrier layer and for heat mitigation at fewer ${\mathrm{e}}^{-}$ interactions ($S=18.1\mathrm{MeV}/\mathrm{cm}$). As shown in the zoomed-in optical micrograph in Fig. 2(c), samples can be positioned in direct proximity to the target, since it also serves as a vacuum exit window. The cone-shaped front end of the NanoTube allows to position the sample tower underneath the x-ray target and to achieve small source-to-sample distances down to $z_{01}\ge 100\mu \mathrm{m}$. Owing to the small submicron spot size $s$, high geometrical magnification $M=z_{02}/z_{01}\gg 1$ can be realized without source blurring, making it possible to use direct (photon-counting) pixel detectors, which are available only with relatively large pixel size $px$. Accordingly, the effective pixel size in the sample plane is reduced to²⁸

Fig. 2

Illustration of the nanotube setup: (a) schematic of the transmission target x-ray source; (b) recording geometry: the cone-shaped front end of the nanotube allows for small distances $z_{01}$ between source $s$ and the sample. The detector is aligned at $z_{02}$ from the source. The axis camera allows for visual inspection of the setup in general, while the Manta camera gives a microscopic control of the tight $z_{01}$ environment; see exemplary view in (c).

At the same time, phase contrast is still feasible, since small $s$ also assures the spatial coherence length $\zeta$²⁹ to be of the same order of magnitude as $p{x}_{\mathrm{eff}}$

2.1.2.

Data recording settings

For tomographic acquisition, 2-D x-ray projections were recorded at 1201 rotation angles, equally distributed over 192 deg (due to the cone-beam angle of 12 deg, an increased angular sampling range was required), with sets of 25 flat-field images before and after each scan. The $z_{02}\approx 20\mathrm{cm}$ was kept fixed, varying $z_{01}$ and $s$. The detector was operated with a lower-limit cut-off energy of 4 keV. The acquisition time was adjusted depending on the spot size $s$ to avoid overexposure, which is at maximum counts of 11810 ph. Most scans were split into four consecutive tomographic scans with $1/4$ exposure time each, and then recombined via cross correlation in Fourier space.³⁰ Thus, for these cases, four different exposures were recorded and averaged for each projection. All scan parameters are tabulated in Tables 1Table 2–3. This acquisition scheme was found to reduce ring artifacts arising from a statistically varying response of the modules.

Table 1

Parameters and quality measured for the tomographic scans at fixed F. Exposure times also indicate whether the scan was performed as a single or multiple ones. FSC is based on volumes of 4003  voxels, with a Kaiser–Bessel window of 7 pixels.31 The SNR was calculated as (μft−μbg)/σbg on five GC nuclei, four PC bodies, and their nuclei, respectively. Scan time refers to the full scan, including readout and motor positioning.

Table 2

Analysis of image quality as a function of s and F. Exposure times also indicate whether the scan was performed as a single or multiple ones. FSC evaluation is based on volumes of K3 voxels, with a Kaiser–Bessel window of 7 pixels.31 SNR was calculated as (μft−μbg)/σbg on five GC nuclei, four PC bodies, and their nuclei, respectively.

Table 3

Analysis of the tomographic scans for nanofocus setup with pxeff≈1.07  μm, in comparison to a rotating-anode scan with the same pxeff. Exposure times also indicate whether the scan was performed as a single or multiple ones. FSC analysis is based on volumes of 4003   voxels, with a Kaiser–Bessel window of 7 pixels.31 SNR was calculated as (μft−μbg)/σbg on five GC nuclei, four PC bodies, and their nuclei, respectively.

2.1.3.

Phase retrieval

The data are recorded in the “direct contrast” or “edge enhancement regime” at Fresnel numbers:

In practice, the relevance of using the BAC is to choose the two regularization parameters $\alpha$ and $\gamma$ such that the resulting somewhat hypothetical intensity distribution contains contributions from intensity and phase contrast, even though expressed only in terms of transmitted intensity. As for reconstructions assuming a homogeneous object, the two contributions cannot be separated. For high-resolution laboratory $\mu$- and nano-CTs, this scheme yields unparalleled image quality. Afterward, the phase-retrieved 2-D projection data are processed for ring artifact mitigation according to Ref. 36 and then recombined to a 3-D volume using the ASTRA-toolbox.^37,38 Visualization was done with Avizo (Thermo Fisher Scientific, Waltham, Massachusetts).

3.2.1.

Variation of $\mathrm{s}/\mathrm{\zeta }$ at constant $\mathrm{F}$

We have first investigated the influence of the lateral coherence length $\zeta$ on the tomographic image quality by setting two different spot sizes (I) $s=0.95\mu \mathrm{m}$ and (II) $s=0.51\mu \mathrm{m}$, respectively, while keeping $F\approx 2.0$ constant, and the dose also approximately at the same level. Hence the larger source size resulted in a significantly reduced total scan time. All experimental and phase reconstruction parameters are listed in Table 1. In this work, the radiation dose was calculated combining the photon counts from the projection data with the spectra in Fig. 3. Figure 4 illustrates the data reconstruction steps from projection to orthoslices through the reconstructed volume. The projections in Fig. 4(a) reveal slight edge enhancement in both cases, especially for the polyimide–air interface, as plotted in Fig. 4(b). As expected, the higher coherence for the $0.501-\mu \mathrm{m}$ source spot yields a more pronounced edge enhancement compared to $0.934\mu \mathrm{m}$. In the same plot, the blue curves show the profiles after phase retrieval, and the respective 2-D images are given in Fig. 4(c). Virtual slices through the same position in the $xz$ plane and $xy$ plane are shown in Figs. 4(d) and 4(f), respectively, with a corresponding zoom in shown in Fig. 4(e). Data for (I) were recorded as a single tomographic scan, acquisition for (II) was split into four as described in Sec. 2.1. By fractionating the dose over four scans, ring artifacts were found to be reduced. Based on visual inspection, both data sets appear to be of very similar quality. Different cerebellum-specific regions, as outlined in Fig. 1, are clearly identifiable: as for the zoom ins (I.e) and (II.e), the cell-dense GL on the right and the ML on the left are separated by the sparsely distributed, bold PCL cells (red arrows). The resolution was quantified exploiting Fourier Shell Correlation (FSC).^40,41 In this analysis scheme, two independently recorded Kaiser–Bessel-filtered data are evaluated for their consistency, defined via the intersection of the cross correlation in Fourier space with a threshold criteria of 1/2-bit in this case.⁴² Therefore, FSC values are not only governed by spatial resolution but also by the overall noise level. In this work, two independent data sets are reached performing the tomographic reconstruction twice, using half of the angular projections each. Hence, FSC-based resolution evaluation serves as an upper limit estimate. For both scans inspected here, the analysis results in similar values of around $\sim 1.8\mu \mathrm{m}$. However, case (I) for $s=0.51\mu \mathrm{m}$ has superior feature contrast (see Table 1).

Fig. 4

Data from tomography scans at fixed Fresnel number of 2.0, at (I) $s=0.95\mu \mathrm{m}$ ($\zeta =0.501\mu \mathrm{m}$) and (II) $0.51\mu \mathrm{m}$ ($\zeta =0.934\mu \mathrm{m}$). (a) Respective flat-field-corrected projections and (c) BAC-reconstructed projections. Colored bars indicate the position of the profiles shown in (b). The same virtual slice (d) in the $xz$ plane with a zoom-in in (e) and (f) in the $xy$ plane. Red arrows mark PCs. Data from quantitative analysis are summarized in Table 1. Scale bars: $100\mu \mathrm{m}$.

3.2.2.

Variations of $\mathrm{F}$ at constant source spot size $\mathrm{s}$

Next, we investigate the influence of $F$ on tomographic image quality, as controlled by the source-to-sample distance $z_{01}$, while keeping $z_{02}$ fixed. Hence $p{x}_{\mathrm{eff}}$ [Eq. (3)] and $\zeta$ [Eq. (2)] vary accordingly. Most scans were recorded at $s=0.51\mu \mathrm{m}=\mathrm{const}$. In addition, we include a scan at the minimally achievable $s=0.30\mu \mathrm{m}$, as well as at $s=0.95\mu \mathrm{m}$. For the latter, the $0.95\mu \mathrm{m}$ scan from Table 1 was repeated four times to reach an equal overall scan time of $\zeta$. All parameters are detailed in Table 2. Figure 5 shows the virtual slices along the $xy$ plane through the reconstruction volume in similar positions. By repeating the $2\mathrm{h}\text{-}0.95\mu \mathrm{m}$-scan from Table 1 four times, and increasing the dose accordingly, the 3-D resolution (FSC) is increased to $1.00\mu \mathrm{m}$, i.e., close to the voxel size. The signal-to-noise ratio (SNR) also increased for GCs and PC nuclei, but only marginally for PC bodies. To increase the SNR of PC bodies substantially, it was necessary to double $\zeta$ (via reduction of $s$) at constant $F$ (constant $z_{01}$). Despite the significantly lower dose, which compromised the resolution, the contrast for the rather large cell bodies is higher. As an overall trend, reducing $F$ (via $z_{01}$) results in increased resolution, which is expected based on higher dose (smaller $p{x}_{\mathrm{eff}}$). At the same time, despite the rise in dose, the SNRs are lower, indicating that the increase in $\zeta$ is more important, in particular for intrinsically low-contrasted features such as PC bodies. This conclusion is also confirmed by comparing the results in Table 2 for $s=0.95\mu \mathrm{m}$ and $s=0.30\mu \mathrm{m}$. In these scans, a roughly similar coherence length $\zeta \approx 0.5$ to $0.7\mu \mathrm{m}$ results in a constant $\mathrm{SNR}\approx 0.83$ to 0.86 for PC bodies, even though the radiation dose deviates by more than a factor of 4.

Fig. 5

Virtual $xy$ slices through the tomographic reconstruction at similar positions in the biopsy punch for spot sizes of (a) $0.95\mu \mathrm{m}$, (b)–(d) $0.51\mu \mathrm{m}$, and (e) $0.30\mu \mathrm{m}$ and Fresnel numbers of (a) 1.97, (b) 1.96, (c) 1.40, (d) 0.83, and (e) 0.60. Note the rise in geometrical magnification from (a) and (b) to (e). The respective analysis parameters are given in Table 2. Scale bars: $50\mu \mathrm{m}$.

3.2.3.

Comparison with data from microfocus laboratory setup

To put the nanotube results into perspective with earlier implementations of 3-D histology with laboratory x-ray phase-contrast tomography, Fig. 6 and Table 3 present a comparison to a reconstruction obtained at the microfocus rotating-anode x-ray source with instrumentation described in Sec. 2.2. For the comparison, we selected the nanotube data set recorded for $s=0.51\mu \mathrm{m}$ and $F=1.96$ in order to achieve similar effective pixel size $p{x}_{\mathrm{eff}}\approx 1.07\mu \mathrm{m}$ and coherence length $\zeta \approx 0.93$ to $1.09\mu \mathrm{m}$. The nanotube setup achieves slightly higher resolution (FSC-based) and increased SNRs (for the features considered), but requires only half of the scan time. However, as is directly apparent from Fig. 6(a), this comes at the cost of reduced FOV, reflecting the different detector technologies. For sufficiently narrow samples, this could be compensated by consecutively scanning two volumes and stacking them, which would result in similar overall scan time for both setups. The plots in Fig. 6(b) show profiles across the capillary edges indicated in Fig. 6(a). The two setups give very similar intensity profiles; absorption and edge enhancement are slightly more pronounced for the microfocus rotating-anode data. Finally, Figs. 6(c) and 6(d) show virtual slices through the $xz$ and $xy$ planes to judge image quality by visual inspection.

Fig. 6

Comparison of (I) nanotube tomography with (II) microfocus rotating-anode results. Settings were chosen such that $p{x}_{\mathrm{eff}}\approx 1.07\mu \mathrm{m}$ same for both data sets. (a) Flat-field-corrected projections. The colored bars show the position of the intensity profile plots in (b). Note the identical ranges of the $y$ axis. Virtual slices through the same position in the reconstructed sample volume are shown in (c) for the $xz$ plane and (d) the $xy$ plane. Scale bars: $100\mu \mathrm{m}$.