Friday, June 2, 2023

Comparing x-ray phase-contrast imaging using a Talbot array illuminator to propagation-based imaging for non-homogeneous biomedical samples – Scientific Reports

Sample preparation

The samples investigated during this work were a piece of human lung tissue and a mouse kidney. The human lung tissue was obtained as an exhibit of a forensics investigation after a COVID-19 fatality by the institute of forensic medicine of the Ludwig-Maximilians university, Munich, Germany. The Ethics Committee of the Ludwig-Maximilians university, medical faculty, waived the need for ethical approval and the need for informed consent (internal reference number 22-0572 KB). All investigations were in accordance with relevant guidelines and regulations.

For the mouse kidney, the animal housing and organ removal was carried out at the Klinikum rechts der Isar, Technical University of Munich following the European Union guidelines 2010/63 and with approval from an internal animal protection committee of the Center for Preclinical Research of Klinikum rechts der Isar, Munich, Germany (internal reference number 4-005-09). After removal, the sample was fixated in a formaldehyde solution and stained with a bismuth-oxo-cluster22. After a dehydration series, the stained sample was embedded in paraffin wax and mounted for scanning. All procedures were in accordance with relevant guidelines and regulations, and in accordance with the ARRIVE guidelines23.

Scan parameters

The setup was implemented at the micro-tomography end-station of the imaging beamline P05 operated by the Helmholtz-Zentrum Hereon at PETRA III, DESY24,25,26. An undulator source, in combination with a double crystal monochromator, was used to provide a high coherent monochromatic beam with a photon energy of 20 keV. As the camera, a Ximea CB500MG with a CMOSIS CMV50000 sensor and 7920×6004 pix was used, with a physical pixel size of 4.6 \({\upmu {\hbox {m}}}\). The field of view with a five-fold magnification objective is limited by the beam height to approx. 3 mm, the maximum width at this magnification is 7.29 mm. The spatial resolution of the detector system was determined during the focusing to approx. 1.9 \({\upmu {\hbox {m}}}\). To reach the microscope design limit of approx. 1 \({\upmu {\hbox {m}}}\), the system would have to be adjusted, which includes the usage of thin scintillator screens and closing camera apertures, resulting in a lower light efficiency. This was not done for the scans in this work. A similar setup is available at the High-energy material science beamline P07 at PETRA III for higher photon energies.

Typically used wavefront markers for SBI are sandpaper or steel wool. In order to avoid absorbing elements, phase-shifting grating structures can be used to imprint a pattern onto the wavefront27,28. We adapted our wavefront marker to use a 2D phase-shifting grating, a Talbot Array Illuminator (TAI)15,29. The grating had a period of 10 \({\upmu {\hbox {m}}}\), a duty cycle of \(DC=1/3\), and a phase shift of \(\phi =\frac{2\pi }{3}\), with a hexagonal lattice structure. The gratings were manufactured on 200 \({\upmu {\hbox {m}}}\) thick silicon wafers, using deep reactive ion etching to produce round holes with a suited depth. The duty cycle marks the ratio of hole distance to hole radius. At fractional Talbot distances of \(\frac{1}{6}d_T\) these TAIs show a focusing effect with a theoretical compression ratio of 1:3 in each direction, thus a high visibility can be achieved. By using TAIs as wavefront markers, absorptive elements were avoided and an efficient two-dimensional stepping could be applied. The periodic nature of such gratings implies an ideal, regular stepping scheme, using a square number of wavefront marker positions. Stepping was performed using a 2D piezo stepper which was directly connected to the detector granite structure for stability. By exchanging the grating and using different etching depths, the setup was already successfully tested at P05 and P07 in an energy range between 15 and 75 keV.

The samples were mounted on an air-bearing rotation stage in between the wavefront marker and the detector. The gratings were mounted 155 mm in front of the sample, the distance from sample to detector was 180 mm for the lung sample and 160 mm for the kidney sample. The total distance varies from the fractional Talbot distance of 538 mm and represents a trade-off between pattern visibility, setup sensitivity, and scan artifact due to edge effects. As edge-enhancement is not included in the UMPA speckle tracking model, too strong fringes cause artifacts at edges and therefore the distance from the sample to the detector is shortened. The distance from the grating to the sample was maximized within the limitations of the setup. The visibility of the wavefront marker was at approximately 0.5. For the given detector resolution, the distance from the samples to the detector is below the critical distance for PBI30.

Compared to previous work15, the scans were now recorded using a continuous rotation mode. Multiple wavefront marker steps are realized by recording multiple scans, with changing the wavefront marker position in between the scans. A set of 50–100 flat-field images are taken at the beginning and the end of each scan. This improves the scan time and the setup stability, as fewer motors need to be driven.

The scans were performed at a beam energy of 20 keV using 180 degrees rotation. For the lung tissue 4001 projections were taken with an exposure time of 110 ms each while continuously rotating the sample. A total of 16 wavefront marker positions were scanned. The mouse kidney was measured with 2001 projections at 80 ms per image, also with 16 wavefront marker positions. The detector used a 100 \({\upmu {\hbox {m}}}\) CdWO\(_4\) scintillator screen and a five-fold magnification objective, resulting in an effective pixel size of 0.92 \({\upmu {\hbox {m}}}\).

Data processing

The acquired images were corrected for camera dark-current and intensity fluctuations of the beam. As SBI requires reference images to be taken at precisely the same wavefront marker position as the sample projections, a correction for wavefront marker inaccuracies and drifts was required. For this, a principal component analysis (PCA) was performed on the flat-field images of each grating position \(f_j\)19. This yields several so-called Eigenflat-field images \(u_k\) and their corresponding Eigenvalues. By using a scree plot, the most important M components, in this case 15, were chosen and the remaining components were discarded.

In order to generate a best-fitting reference image at an unknown position of the wavefront marker, a new reference image \(f_n\) can be expressed by the averaged reference image \(\bar{f_j}\) a weighted sum over the relevant components:

$$\begin{aligned} f_n= \bar{f_j}+\sum _{k=1}^M w_k \cdot u_k. \end{aligned}$$


The optimal weights \(w_k\) were calculated, by defining a cost function in a background region of the projection \(p_{BG}\). Using a least-squares minimization of the difference between the projection and the flat-field image, the set of weights are determined:

$$\begin{aligned} w_k=\textrm{arg}\min _{w_k}\left( p_{BG}-f_{n,BG}\right) ^2. \end{aligned}$$


The resulting weights were used to generate the reference image according to Eq. 1. A comparison of the effect of the Eigenflat correction compared to using mean flat-field images can be seen in in Fig. 1b and c.

The projection images and the calculated reference images were then phase-retrieved by using the Unified Modulated Pattern Analysis (UMPA)14. The scan was evaluated for varying UMPA window sizes between \(1\times 1\) and \(17\times 17\) pix. The angular sensitivity \(\sigma _{x/y}\), corresponding to the smallest resolvable refraction angle, can be calculated from the noise in a background region, using the standard deviation (STD), of the refraction angle signal:

$$\begin{aligned} \sigma _{x/y}=STD(u_{x/y, BG})\cdot \frac{p_{eff}}{d_{prop}}, \end{aligned}$$


where \(u_{x/y, BG}\) denotes the calculated pixel shift signal, \(p_{eff}\) the effective pixel size and \(d_{prop}\) the propagation distance from the sample to the detector.

The resulting differential phase images were corrected for ramps and outliers, anti-symmetrically mirrored31, and integrated, using a Fourier approach32. After integration, the phase was filtered for ring artifacts and reconstructed via filtered back-projection and a Ram-Lak filter using the software X-Aid (Mitos GmbH, Garching, Germany).

The images for PBI were calculated by taking the mean over all phase steps. Thus the grating pattern is no longer visible, and a regularized approach, based on the Transport of Intensity Equation8,33, was used to retrieve the phase. The regularization strength for the slice shown was chosen from visual impression, where no more edge-enhancement was visible inside the sample and blurring was not yet dominant. The projections were reconstructed with the same settings as for the TAI images.

Resolution analysis

Determining the spatial resolution of the images is not trivial, as multiple effects are present in the images. The raw data contain edge enhancement, whereas the phase retrieved data are blurred to some extend. Therefore we compared multiple methods to for measuring the spatial resolution.

The first method is measuring the edge sharpness. Multiple edges in the reconstructed slices were chosen and an error function (ERF) was fitted. As a resolution criterion, the FWHM of the associated Gaussian of the ERF can be used, which corresponds to approx. \(\textrm{FWHM}\approx 2.35\,\sigma\). This method is able to identify blurring efficiently, however the values might be corrupted if edges are enhanced. At the same time, this method is dependent on the sample itself, as is requires sharp edges to be present in the scan.

As second resolution analysis, a Fourier Ring Correlation (FRC) was calculated20,21. For this, the image was subdivided in four sub set, by taking every second pixel horizontally and vertically. The FRC was calculated for each of the two diagonal subsets and averaged. The resolution was determined by identifying the intersection of a filtered FRC with a full-Bit and a half-Bit criterion, equivalent to each pixel containing an information content of 1 bit or 1/2 bit respectively. The advantage of this method lies in its independence of the sample. On the other hand, if correlated noise is introduced, the results are corrupted. As phase-retrieval requires processing the raw detector images, the results of the FRC might only be seen approximate for either small UMPA window sizes or small regularization strength.

Other common methods, as e.g. analyzing the Fourier power spectrum34 are not suited for determining the resolution of a phase-retrieved image, as they are insensitive to possible blurring introduced in the processing.

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