1. Introduction

X-ray Coherent Diffractive Imaging (CDI) takes advantage of the penetration depth and specific interaction of X-rays with matter to reveal intracellular features within biological specimens [1–7]. Spatial resolution beyond the limits imposed by image-forming optics can be obtained by applying iterative algorithms to reconstruct the sample distribution from oversampled diffraction patterns [8], while removal of optics between the sample and detector results in an increase in dose efficiency [9]. However, since it is desirable to image biological samples in as close to their native state as possible, recent research into CDI of biological samples has focused on applying the technique to hydrated samples [10], and at X-ray energies in the water-window [11]. Within this region the incident X-ray energy is below the oxygen K edge (530 eV) but above the carbon K edge (280 eV) hence the largely carbon based biological structure of a hydrated specimen can be easily distinguished from the surrounding water [12, 13].

Ptychography is a CDI method that combines multiple coherent diffraction measurements from overlapping regions of a sample [14]. It has been widely adopted in recent years because it allows high quality imaging of objects that extend beyond the illuminating probe [14]. Ptychography benefits from the additional information obtained in the overlapping probe areas that are distributed over a plane transverse to the beam [11, 14, 15].

Ptychography has also been demonstrated using a curved illumination in a technique called Fresnel CDI (FCDI) that generally requires fewer overlapping probes [16]. Phase-diverse FCDI includes greater diversity in the illumination by combining coherent diffraction data obtained by translating the curved illumination both transversely and longitudinally (i.e. parallel to the beam direction) [17]. This has been shown to deliver further improvements in the image quality even for considerably lower X-ray fluence [17–19]. These images have been shown to provide information that is complementary to that obtained by other whole cell imaging methods [19] that generally require more elaborate sample preparation such as sectioning or labelling with specific flurophores [20].

In this work we present a demonstration of phase-diverse FCDI in the water window. In order to characterise and provide validation of this technique we start by imaging an optically dense fabricated ‘test sample’ of known composition. We then show the results of applying the method to a high-resolution imaging of a malaria infected red blood cell, demonstrating phase-diverse FCDI of a biological sample in the water-window. The results confirm improved phase contrast for the intracellular architecture in the reconstructed complex transmission function of the sample in comparison to previously reported results from similar samples at higher X-ray energies [7, 19, 21]. We show correlative images of the same sample from scanning electron microscopy (SEM) and optical microscopy to highlight the complementary nature of the information obtained across the three different imaging modalities.

2. Method

2.1 Sample preparation

The test sample was prepared from a film of sputtered gold approximately 200 nm thick on a 100 nm Si₃N₄ membrane using a focused ion beam (FIB). Additional features were formed at a thickness of approximately 200 nm using FIB induced deposition of platinum from a precursor gas of (methylcyclopentadienyl)trimethyl platinum.

Red blood cells (RBCs) infected with the malaria parasite Plasmodium falciparum at the trophozoite life-cycle stage were cultured in vitro and fixed in 2.5% gluteraldehyde and 1% vanadatomolybdate (3(NH₄)₂O.2V₂O₅.4MoO₃) [22] to stabilise the lipid components during drying and under vacuum conditions. The cells were then deposited onto Si₃N₄ windows and air-dried prior to imaging. It has previously been established in the literature that heavy metal staining to this level does not have a noticeable effect on the soft X-ray FCDI results [3].

2.2 X-ray data collection and analysis

X-ray data were collected using a 520 eV X-ray beam at the TwinMic beamline at the Elettra Synchrotron [23, 24] focused with a 320 μm diameter Fresnel zone plate (FZP) with an outer zone width of 50 nm placed approximately 2 m downstream of a 25 μm aperture that defines a secondary source. A 150 μm aperture was placed off-axis immediately upstream of the zone plate (Fig. 1(a) and 1(b)), to improve the quality of the incident beam. A cooled charge-coupled device (CCD) detector (Princeton MT-MTE) with 1300 × 1340 square pixels each with a 20 μm side length was placed 73 cm downstream of the FZP. The incident illumination and diffraction data (Fig. 1(c) and 1(d)) were padded to 4096 × 4096 pixels centred on the full beam without the upstream aperture to allow numerical propagation through the focus. Under this experimental arrangement, the theoretical resolution limit due to the numerical aperture (NA) of the detector is equal to 69 nm. However, according to Abbe theory [25], the limit of resolution, $\Gamma$, for coherent illumination is $\Gamma =0.82\lambda /NA\simeq 110$nm. Due to the fixed experimental geometry, the maximum achievable resolution with diffractive imaging in this particular instance is less than the resolution that would have been achievable through scanning transmission X-ray microscopy using the same FZP. The resolution in FCDI is a function of the experimental geometry, namely the distance from the focal point of the FZP to the detector and the physical size of the detector rather than the optics. Although in the present proof-of-principle work practical constraints to the position of both the FZP and detector limit the resolution, in general the spatial resolution of FCDI can be higher than that of the FZP used to form the incident curved beam [26, 27].

 

Fig. 1 Experimental arrangement from above (A; not to scale), shows an aperture (illustrated relative to the FZP in B) placed directly upstream of the zone plate to ensure sampling requirements were met and to improve the incident beam quality. The sample was initially placed 220 μm downstream of the focus, with the CCD detector placed in the farfield of the illuminated region. The transverse and longitudinal directions of sample translation are indicated. Example illumination (C) and intensity of diffraction from the test sample (D) measured at the detector under this experimental arrangement are shown on a logarithmic colour scale.

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Phase-diverse FCDI data collection involved carrying out two-dimensional transverse scans at several different longitudinal distances [17], defined here as the distance from the focal point of the FZP to the sample, z_fs [as shown in Fig. 1(a)]. A single exposure of 6 s for the test pattern [Fig. 1(c)] and 2 s for the cellular samples was taken at each data collection point [19]. The minimum lateral overlap fraction (O_F) [17] for each two-dimensional grid was equal to 66%, while the Fresnel number (F_N) [28] over the sample ranged from 29 to 56. A summary of all of the measurements carried out is given in Table 1.Single lateral probe positions at a particular z_fs, were also included to increase the overall longitudinal phase-diversity. Measurements of the illumination (with the sample moved out of the beam) and detector dark-field were taken with a single exposure at each longitudinal position. We calculate the total dose received as less than 1.8 × 10⁷, 1.2 × 10⁷, and 1.0 × 10⁷ Gy respectively for the test sample (Fig. 2, comprised of gold and platinum) and two cellular samples (Fig. 3, taking their average composition as close to model protein [29, 30]). The data were treated according to the method described in Ref [28], before being reconstructed using the phase-diverse CDI reconstruction functions [17] in the NADIA software library [31]. As the cellular samples are composed of a mixture of proteins, a the ratio of the phase and magnitude were constrained to within 15% of expected for an empirical protein (C₃₀H₅₀N₉O₁₀S, density 1.35 g/cm²) [30, 32]. Fluctuations in the intensity distribution of the illumination over time resulted in an incomplete illumination subtraction. Errors in the illumination subtraction led to the propagation of residual errors whose influence resulted in a worsening error metric for large numbers of iterations. It was found that the minimum error metric was achieved after only 5 iterations of the phase-diverse algorithm.

Table 1. Summary of the key geometrical parameters for the data acquired from each sample. N_Pt, O_F, and F_N are the number of ptychography frames, probe lateral overlap fraction, and Fresnel number at the each sample defocus distance, z_fs.

View Table

 

Fig. 2 Phase (A) and magnitude (B) of the reconstructed transmission function of the test pattern. An SEM micrograph of the test pattern at 52° tilt angle is shown in panel C, with the area imaged using X-rays outlined in red. The scale bar in panels A and C are equal to 1 and 2 μm respectively. Line profiles of the thickness of two features made from gold (1) and platinum (2) are shown in D, calculated from the phase (dashed line) and magnitude (solid line) images respectively at the positions indicated in A.

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Fig. 3 Phase (A, E) and magnitude (B, F) of the reconstructed transmission function of two red blood cells infected with the malaria parasite P. falciparum. The scale bar in (B) is equal to 1 μm. Optical images taken before X-ray imaging (C, G), and Scanning Electron Micrographs (D, H) following X-ray imaging are shown for comparison. The host red blood cell (RBC) and parasite (p) are marked. A flattened area (f) of the red blood cell can be observed and an exomembrane (em) extension into the host red blood cell is evident.

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2.3 SEM and optical imaging

Optical microscopy was carried out before and after the X-ray imaging using an Olympus CX41 visible light microscope equipped with a 100x objective in order to map the cells. Higher resolution scanning electron microscopy (SEM) images of the cells were obtained using a secondary electron detector in low vacuum on a Philips XL30 scanning electron microscope.

3. Results

The reconstructed phase and magnitude of the complex transmission function of the test pattern is shown in Figs. 2(A) and 2(B). An SEM micrograph of the sample at 52° tilt angle is shown in Fig. 2(C) with the imaged area indicated by the red box. Figures 2(A) and 2(B) show a high level of correlation to the SEM image of the sample in panel C, with feature sizes approaching the theoretical resolution limit. In particular, surface roughness of the background seen in Fig. 2(C) can be seen in both Figs. 2(A) and 2(B). The spatial resolution of the X-ray images was estimated from the power spectrum density (PSD) giving a value of 125 nm, which is close to the anticipated maximum achievable resolution of 110 nm calculated in Section 2.2.

Line profiles across the ‘l’ made from sputtered gold and the ‘X’ made from platinum precursor (as described in Section 2.1) were taken at positions indicated in Fig. 2(A) and are presented in Fig. 2(D) (1 and 2) respectively. The self-consistency of the reconstruction can be clearly seen in the correlation of the object thickness in Fig. 2(D) derived from the phase (dashed line) and magnitude images (solid line). The interaction strength of X-rays with matter is dependent on the object’s composition and density [33]. It is well established that the density of a deposited material is highly dependent on the deposition method and conditions [34–37]. In this case, from the quantitative phase and magnitude values obtained by the phase-diverse FCDI reconstruction we can calculate the density of the gold to be 6.5 g/m³, and the platinum density to be 7.9 g/m³. As expected, these values are significantly less than the bulk density values of 19.3 g/m³ and 21.4 g/m³ for gold and platinum respectively. The analysis of the results presented in Fig. 2 demonstrates that the FCDI method can be reliably applied in the water window at close to expected maximum resolution achievable for this experimental geometry.

X-ray images of cellular samples C1 and C2, represented by the phase and magnitude of the reconstructed complex transmission functions are shown in Figs. 3(A), 3(B) and Figs. 3(E), 3(F), respectively. Optical and SEM micrographs of the samples are also shown in Figs. 3(C), 3(G) and Figs. 3(D), 3(H) respectively for comparison. The outlines of the host red blood cells are readily evident in all three imaging modalities. SEM, which is predominantly sensitive to surface topography of the infected red blood cells, reveals a region of flattening (f) of the host RBC above the region occupied by the parasite in cell sample (C2). This region of flattening also manifests in the optical and X-ray images as a region of reduced optical thickness. The X-ray and optical images also contain some information related to internal features. The regions of high X-ray absorption (dark blue region (p) in panels B and F) in each of the infected red blood cells likely correspond to the regions occupied by the parasite. A region of higher X-ray absorption and phase retardation extending from the parasite in cell sample (C2) indicates the presence of an exomembrane (em) extension from the parasite, which has previously been identified with FCDI at higher X-ray energies [7]. The resolution of the X-ray images was estimated from the PSD as 190 and 180 nm for samples C1 and C2 respectively.

Discussion

This study demonstrates the application of phase-diverse FCDI on both a fabricated test sample and cellular specimens in the water-window. Previous studies using this technique with a similar cellular sample at the higher X-ray energy of 2.5 keV observed a maximum phase retardation of approximately 1.3 radians [19], approximately one half the variation in the phase decrement over the area of the cell observed in the present study, indicating the potential for high phase contrast imaging. This result is largely expected as the phase retardation is dependent on the decrement from unity of the real part of the refractive index (δ), which for protein (C₃₀H₅₀N₉O₁₀S), the main constituent of the biological specimens [29], has an increasing trend as the X-ray energy decreases, from $4.8\times {10}^{-5}$ at 2.5 keV, to $9.7\times {10}^{-4}$ at 520 eV [33].

The general shape of the host red blood cells and parasite can easily be recognised from the X-ray images and correlate well with the information provided by the other imaging modalities. Because of the ability to acquire the X-ray images with relatively low dose, the method can be used as a correlative microscopy tool to inform the interpretation of images obtained using electron and optical methods. In particular, internal features of the whole cell such as the exomembrane system of the parasite, which cannot be resolved at high resolution using light microscopy and which are inaccessible to scanning electron microscopy, can be distinguished in the X-ray images. Following this proof-of-principle work on dehydrated samples, future work will apply water window phase diverse FCDI to hydrated unstained samples under more ideal experimental geometry and illumination, and will compare the method to conventional scanning transmission X-ray microscopy.