1 Introduction

Ptychography is a scanning coherent imaging technique which allows to image samples at resolutions beyond the optical limits of the imaging system [1]. A standard ptychographic acquisition consists of moving the sample across a coherent beam at overlapping steps, while recording the diffraction patterns, typically in the far field. The diffraction patterns are subsequently inverted using an iterative algorithm [2,3,4,5] to form the image of the sample. When combined with the penetration power of X-rays, ptychography has enabled scientific breakthroughs in a range of fields, from magnetism [6] to nanoelectronics [7]. Ptychography has proven to be very suitable also to image weakly absorbing samples, such as biological soft tissues, as it is sensitive to small changes of electron density [8].

X-ray ptychography requires long acquisition times when compared to other nano-scale techniques (e.g. transmission X-ray microscope). This is due to large overheads when scanning sample precisely to thousands of positions for a single projection. These long acquisition times have prevented the deployment of X-ray ptychography for imaging large sample volumes or for dynamic/multidimensional studies such as X-ray near edge spectroscopy imaging. To overcome this limitation, in the latest years the ptychography community has strived to reduce the acquisition time by developing new scanning strategies [9], including multibeam ptychography [10] and fly-scanning methods [11,12,13,14,15,16,17,18,19]. The multibeam approach consists of using a coded aperture to generate multiple beamlets spatially separated at the sample and overlapping in the detector at the far field, to reduce the number of steps required for an acquisition. The fly-scanning approach consists of recording diffraction patterns while moving the sample along a continuous trajectory to reduce the motors’ stop-start overhead at each position. Thanks to these advances, fast X-ray ptychography now has the potential to image large samples (100’s of \(\upmu \mathrm{{m}}^2\)), of soft biological tissues, such as from lung, heart or brain.

The study of the human brain is indeed a phenomenal challenge due to the complexity of the tissue and its multiscale nature: from nanoscale molecular features to centimetres long structural connections. Understanding the interplay between its structure and function is key to diagnose, prevent and possibly treat diseases such as dementia. International projects are bringing together scientists around the world to tackle the problem [20, 21]. There is the need for a transformative tool to image the whole human brain in vivo at high (sub-micron) resolution. Diffusion magnetic resonance imaging (dMRI) is a promising MRI technique for this purpose. In dMRI the brain structure at cellular (microscopic) scale can be inferred via biophysical modelling of the diffusion of water molecules during in vivo measurements [22]. One of the main challenges is the validation of the model-based estimates of the microstructural features of the investigated tissue. The ideal benchmarking dataset is a large volume of brain sample of the order of \(1 \textrm{mm}^3\), that is approximately the size of a complete cortical microcircuit [23], imaged with nanoscale resolution.

So far this has been achieved with expansion microscopy [24] and multibeam scanning electron microscopy [25]. In the first, the sample gets infused with hydrogel and doing so expanded and made more transparent to be inspected with optical light [26]. In the second, tens of simultaneous electron beams illuminate the sample, which is prepared in thin slices, due to the low penetration power of electrons. Both approaches are destructive: hard X-ray fast ptychography could be a valuable non-destructive alternative to the above methods thanks to the higher penetration properties of hard X-rays with respect to electrons or soft X-rays, and the increased resolution with respect to visible light due to the shorter wavelength. Here we investigate its potential.

As a first step toward using ptychography for this purpose, we apply a high-speed ptychography setup at the I13-1 beamline of Diamond Light Source [19] to image \(10^6 \upmu \mathrm{{m}}^3\) volume of polymer phantom, which mimics the tissue structure within the brain, in 7 h. We also present the latest results where we performed fast ptychographic imaging of a 2D test resolution target at 110 kHz acquisition rate by combining fly-scanning and a prototype detector from DECTRIS Ltd. Based on the latest results we discuss the future prospectives in terms of scanning speed and resolution.

2 Results

2.1 Large volume imaging

We imaged a biomimetic phantom based on polymer microcylinders [27] made of polycaprolacton (PCL) [28] intended to mimic the axons found in the white matter of the brain. This type of phantom has comparable density to brain tissue, it has been extensively characterised [28] and proven to be representative of the brain white matter tissue, and it is used as validation tool for new approaches [29]. It is often considered as a superior alternative to software phantoms and histological samples. Indeed physical phantoms, similarly to virtual samples [30], are more controllable in structure than histological samples. Moreover, unlike the virtual samples, they offer the advantage of being scanned using identical procedures as for real samples. This allows realistic signal-to-noise ratios and image artefacts to be taken into account.

The sample was cut down with a scalpel in a quasi-cylindrical shape of \(100 \upmu \mathrm{{m}}\) diameter and imaged at the I13-1 beamline at Diamond Light Source [31] using a fly-scanning method based on the approach described in detail in ref [19]. In this method, the maximum acquisition rate is set by the maximum acquisition rate of the detector. For each detector acquisition a sample position is stored. In the eventuality the readout of the sample position is slower than the detector acquisition, extra positions get generated during the reconstruction by interpolating in-between the recorded positions. To improve the throughput of ptychographic tomography, the framework was upgraded with respect to ref [19] with a faster position capture device, the PandA trigger box, capable of up to 10 kHz acquisition rate [32], and the system was adapted such that all files where streamed continuously to disk.

The experimental setup is sketched in Fig. 1. The sample was illuminated with an 11 keV monochromatic X-ray beam of \(3.5 \upmu \mathrm{{m}}\) in diameter generated using a \(400 \upmu \mathrm{{m}}\) diameter blazed Fresnel zone plate [33] (FZP) with a 200nm outermost zone width. The sample was placed a few millimetres downstream of the FZP focal plane. For each 2D projection, the sample was scanned in a \(1000\times 100\) grid with a snake-like motion by continuously moving the horizontal motor back and forth (fast axis) and stepping in the vertical axis downwards (slow axis), see Fig. 1. The EIGER 500K photon counting detector (\(1030 \times 514\) pixels, \(75\upmu \mathrm{{m}}\) pixel size) was placed at 5.1 m downstream of the sample. Diffraction frames were acquired during the horizontal motion every \(0.15 \upmu \mathrm{{m}}\), the vertical step was \(0.5 \upmu \mathrm{{m}}\), corresponding to a field of view \(150 \times 50 \upmu \mathrm{{m}}^{2}\). Frames were recorded at 2874 Hz with an exposure time of \(340 \upmu \textrm{s}\), corresponding to \(220 \upmu \mathrm{{m}}^2/s\). All the sample positions were captured using a PandA trigger box without need for interpolation.

Fig. 1
figure 1

Experimental setup. The monochromated X-ray beam is focused down to the sample using Fresnel zone plate optics. The sample is scanned in a snake like motion in a continuous fashion the horizontal axis (fast axis, black arrow) and stepped vertically (slow axis, red line). A detector in the far field records the diffraction patterns

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We acquired 501 projections over a angular range of 180\(^{\circ }\) allowing us to image \(10^6\upmu \mathrm{{m}}^3\) in 7 h, which corresponds to 39 \(\upmu \mathrm{{m}}^3/s\)

Each projection was reconstructed, from \(128\times 128\) pixels cropped data, with 50 iterations of the ePIE algorithm [2] as implemented in the PtyREX software [34] with a reconstructed pixel size of 60 nm, using 4 spatial modes.

The projections were then aligned using the approach by Gursoy [35] and reconstructed using the gridrec algorithm implemented in tomopy [36]. The results are shown in Fig. 2. The spatial resolution was estimated to be 270 nm on the xz slice Fig. 2b, using an implementation of the Fourier ring correlation [37] provided as part of the BIOP ImageJ plugin [38] (see Fig. 2a inset). Two independent images were generated by splitting the original in even and odd indexes.

Fig. 2
figure 2

3D image of a brain-like phantom mimicking a bundle of axons in the white matter [28]. a rendered 3D volume. Inset: Fourier ring correlation on orthoslice b, representative also for orthoslice c and d. b–d Orthoslices through the volume in the xz, xy and zy plane, respectively. e SEM image of a similar sample of the phantom materials showing its cross-sectional morphology. The white scale bars in all the plots correspond to \(10 \upmu\)m

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2.2 110 kHz ptychography

The ultimate speed of the fast ptychography scanning method applied in this study [19] is determined by the detector acquisition rate. In the experiment presented in Sect. 2.1, this is 3 kHz, the maximum acquisition rate for the EIGER 500 K in continuous read/write mode. Recently a new photon counting prototype detector has been developed by DECTRIS Ltd capable of 120 kHz acquisition rate.

2.2.1 120 kHz photon counting detector

The hybrid photon counting detector is a prototype of the SELUN detector being developed by DECTRIS Ltd. The detector has a pixel array of \(192 \times 192\) pixels at \(100\times 100 \upmu \mathrm{{m}}^2\) pixel size, comprising an active area of \(19.2 \times 19.2\) mm\(^2\). Each pixel consists of two 12 Bit counters for continuous readout at 20 kHz. Effectively, the ASIC can be operated in an 8-Bit Floating Point compression scheme which enables framerates of up to 30 kHz. Additionally, by on chip binning of \(2\times 2\) pixels, the framerate can be further increased to 120 kHz with an effective pixel size of \(200 \times 200\upmu \mathrm{{m}}^2\). Based on preliminary measurements and simulations of the performance of the ASIC of the SELUN, the detector development aims to reach a count rate of 50 Mphotons/pixel/s unbinned, and 4 times higher, that is 200 Mphotons/pixel/s, with a 2\(\times\)2 binning [39, 40].

2.2.2 2D imaging at 110 kHz

We have performed a ptychography acquisition at 110 kHz to image a Siemens star test pattern using the prototype detector presented in Sect. 2.2.1 in a 2\(\times\)2 binning mode. The experiment was performed with similar experimental conditions as described in 2.1. The detector was placed 5.1 m downstream the sample and the X-ray energy was set to 11.1 keV. The sample positions were recorded with the PandA trigger box at 10 kHz. The missing intermediate positions were generated during the reconstruction by interpolation. A typical diffractogram obtained with an exposure of 7 \(\upmu \mathrm{{s}}\) is shown in Fig. 3c. The maximum number of counts recorded is 22 photons per pixel due to the very short exposure time, which corresponds to \(2\times 10^{6}\) photons/pixel/s and a total coherent flux at the sample of \(2\times 10^{8}\) photons/s. To preserve the total photon statistics per resolution element, we imaged a \(20 \times 20 \upmu \mathrm{{m}}^2\) area of the sample by acquiring over a \(2800 \times 20\) grid, that is a horizontal step size of 7nm, which corresponds to \(800 \upmu \mathrm{{m}}^2\,s^{-1}\). Because there were no photons counted beyond 32 pixels from the centre of the diffracted beam, the SELUN data were cropped to \(64\times 64\) pixels. The image was reconstructed from the cropped data with 50 iterations of the PtyREX ePIE module, by upsampling of a factor 2 [41] to compensate for the larger pixel size (\(200 \times 200\upmu \mathrm{{m}}^2\)), by including two spatial modes and the annealing approach to correct for position errors due to the interpolation process [42]. The reconstructed phase image is shown in Fig. 3. The reconstructed image pixel size is 88 nm (set by the cropping) and the measure resolution is 285 nm as shown with the line profile in Fig. 3b.

Fig. 3
figure 3

110 kHz ptychography: a Phase image of a Siemens star test patter scanned at 110 kHz. b Line profile extracted from the a (red line) showing a resolution of 285 nm. c A typical diffractogram captured during the 110 kHz scan. The maximum photons count is 22 photons per pixel

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3 Discussion and conclusion

In Sect. 2.1 we have shown 3D imaging of a brain-like sample obtained with a \(39\upmu \mathrm{{m}}^3 s^{-1}\) X-ray ptychographic tomography. In the experiment the scanning rate was limited to 3 kHz by the maximum continuous acquisition rate of the EIGER 500 k photon counting detector.

In Sect. 2.2 we have demonstrated the feasibility of ptychographic imaging at 110 kHz by coupling the fast ptychography method of ref [19] with a new DECTRIS Ltd prototype detector. The summary of the two experimental parameters is reported in Table 1. During the 110 kHz scan, to compensate for the low photon statistics of each frame, we reduced the step size in the fast axis (horizontal movement) with respect to the experiment in Sect. 2.1. In terms of \(\upmu \mathrm{{m}}^2 s^{-1}\), this means we scanned the sample 4 times faster than with the EIGER 500k detector. However, the scheme would allow a 36 times faster acquisition. To exploit this potential in full, a higher coherent flux is needed.

Table 1 Experimental parameters
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With the advent of 4th generation light sources (diffraction limited storage rings), the coherent flux increases up to a factor 100 with respect to 3rd generation light sources. This is already available at synchrotron facilities around the world (e.g. ESRF, MAX-IV, etc) and soon coming at others (Advanced Photon Source, Paul Scherrer Institute and Diamond Light Source). This extra two orders of magnitude flux increase would correspond, in a geometry similar to that described in this manuscript, up to \(200\times 10^{6}\) photons/pixel/s in the central disk, which is within the expected performance of the SELUN detector.

Regarding achievable resolution and future scaling, it is worthwhile noting that the active area of the current design of the SELUN detector is at the best half of the EIGER 500k active area (see Table 1). In ptychography the maximum resolution achievable depends on the angular coverage of the detector area. That is:

$$\begin{aligned} dx=\frac{\lambda z}{D} \end{aligned}$$
(1)

where dx is the reconstructed pixel size/maximum resolution, \(\lambda\) is the beam wavelength, z is the sample-detector distance and D is the width of the detector active area. To achieve with the SELUN the same nominal resolution as with the EIGER 500k, the detector would need to be closer to the sample (half of the distance). In the experiment reported, the sample-detector distance was the same for the EIGER and the SELUN, so the maximum resolution achievable was different for the two setups and, respectively, equal to 15 nm for the EIGER and 30 nm for the SELUN. However, we decided not to move the SELUN detector closer to the sample to achieve the same nominal resolution, because the resolution was dominated by the low photon statistics: already at 5.1 m at 110 kHz acquisition there were no photon counts beyond 32 pixels from the centre of the beam. Indeed, the reconstructed dataset of Fig. 3 is obtained from a \(64\times 64\) pixel cropped area of the SELUN detector, corresponding to a reconstructed pixel size of 88 nm.

Taking the above into account, we can extrapolate the results for the brain phantom obtained with the EIGER at 3 kHz (Fig. 2), toward 110 kHz scanning of brain tissue. Since the brain phantoms have similar electron density and structural properties as brain tissue [28], that is comparable scattering properties, we can expect to achieve a similar resolution of 270 nm in 3D on brain tissue at 110 kHz with a factor 50 increase in flux. The factor 50 corresponds to the ratio between the exposure time for the 3 kHz and the 110 kHz, respectively (see Table 1). Combining the factor 100 increase in coherent flux due to storage rings upgrade to higher efficiency pre-focussing optics such as KB mirrors instead of Fresnel zone plates, an additional increase in flux at the sample of more than a factor 5 can be foreseen. Therefore, in total we expect a flux over an order of magnitude higher than required for matching Fig. 2. A study by Deng et al. [43] shows that an increase of one order of magnitude in average flux on the sample corresponds to an increase of a factor 2 in resolution. Based on this scaling, it is therefore reasonable to expect 100 nm resolution to be achievable for brain-like samples at 110 kHz ptychographic acquisition in the near future. To be noted that to remain within 200 Mphotons/pixel/s in the central disk, the higher future flux would need to be distributed across the whole detector active area, for example by using a larger numerical aperture pre-focussing optics or a diffuser.

As described in Sect. 2.2.2, during the 110 kHz acquisition we compensated for the low photon statistics by reducing the scanning step size. This will not be any longer required with the estimated increase of coherent flux at diffraction limited storage rings and, in this scenario with the 110 kHz fast ptychography setup, we expect to be possible to scan samples up to \(6000 \upmu \mathrm{{m}}^2 \textrm{s}^{-1}\). Acquiring a single 1 mm\(^2\) projection will take 170 s and to image a 3D \(1 \textrm{mm}^3\) at 100 nm resolution, the acquisition would last 19 days (based on \(10^4\) projections collected over 180\(^{\circ }\), see Appendix A for further details) .

Further reduction of the acquisition time can be achieved by combining the fly-scanning to the multibeam approach. For example, using 9 probes as in ref [10], the acquisition time for 1 mm\(^3\) of brain would become as short as 2 days. Moreover, the overlap constraint can be relaxed with the combined ptycho-tomography reconstruction approach by Gursoy [44]. This is expected to provide at least a further factor 3 in the reduction of the scan duration. Combining all these developments together, the acquisition time for 1 mm\(^3\) of brain would become as short as 1 day.

To image a large volume of brain at the nanoscale, there are other outstanding challenges that need to be solved. These include but are not limited to:

  • Radiation damage: ptychography is considered a dose effective technique since it does not require imaging lenses [45]. The expected total dose delivered to a brain-like phantom sample during a ptychography acquisition to achieve 100 nm resolution, is of the order of the MGy (see Appendix B for the calculations). A dedicated study is required to understand the radiation damage and the effects of the dose fractionation implied by the scanning. Beside this, different strategies can be explored to prevent the deterioration of the sample during the acquisition, such as performing the experiment in a cryo-environment [46] and/or using higher photon energy to reduce the absorption.

  • Sample preparation: while the best preparation strategy specifically for ptychography needs to be identified, this can be based upon existing studies present in literature on sample preparation for microtomography [47,48,49,50].

  • Standard ptychographic reconstruction algorithms are based on the assumption that multiple scattering does not occur. This condition is violated when thick samples are imaged and a multislice approach [51] is required to take the multiple scattering into account. This method has been proven successful in modelling a few slices (less than ten) of samples of various thickness, from 100 s \(\upmu \mathrm{{m}}\) [52] to 1 mm [53]. This still needs to be proven to deal effectively with tens of slices.

  • Data processing: 1 day acquisition at 110 kHz would produce about 40TB of data. There is need for faster converging, highly parallelisable ptychographic reconstruction algorithms. The community is exploring several routes including deep learning approaches [54, 55].

The study presented here it is not the end of the story but a significant step toward imaging 1 mm\(^3\) at the nanoscale, which would represent a terrific tool to unravel the complexity of the human brain.