Optimal Image Denoising for In Situ X-ray Tomographic Microscopy of Liquid Water in Gas Diffusion Layers of Polymer Electrolyte Fuel Cells

PEFC & materials

An imaging PEFC with an active area of 0.16 cm² (4.5 mm × 3.6 mm), designed by Eller et al.,²⁶ was used for the XTM imaging experiments (see Fig. 1a). The flow field plates were made of graphitic material (BMA5, SGL Technologies) and have two channels for both anode and cathode with a width of 0.8 mm and a depth of 0.3 mm. The cell temperature was monitored and regulated during the XTM imaging experiments by PT100 temperature sensors and heating foils inserted in the cell assembly. A catalyst coated membrane (CCM) from W. L. Gore & Associates (Gore® Primea® A510.1/M815.15/C510.4 with a 15 μm thick reinforced Gore-Select® membrane and anode/cathode Pt loadings of 0.1/0.4 mg cm⁻²)³² together with plain Toray TGPH-060 carbon fiber (Toray Industries Inc.; 0% hydrophobic coating; no microporous layer; through-plane and in-plane average pore diameter of 29 μm and 49 μm⁷ respectively) as anode and cathode gas diffusion layers were used.

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Ex situ experiment

In situ experiment

Synchrotron based X-ray tomographic microscopy (XTM) experiments were implemented at the TOMCAT (X02DA) beamline of the Swiss Light Source (SLS) at the Paul Scherrer Institut (PSI) in Switzerland. A Ru/C multilayer monochromator (ΔE/E ∼2%–3%) was used to select monochromatic X-ray radiation at several different energies (11 keV, 13.5 keV, 16 keV, 18.5 keV). The radiography images were collected by the GigaFRoST camera system,³³ coupled with a 2–4× microscope (Elya Solutions, Czech Republic) equipped with a 100 μm thick LuAG:Ce scintillator. The magnification was set to 3.48 resulting in 3 μm voxel edge length. The XTM scan time is calculated by the multiplication of the exposure time per radiography (0.5 ms to 16 ms) and the number of projections (25 to 1600) per scan over 180° resulting in a scan time range of 0.05 s–25.6 s where the shortest achievable scan times were limited by the stage maximum rotation speed of 10 Hz. The camera readout was cropped to 2016 px (horizontal) × 700 px (vertical) to avoid camera readout time limitations for all exposure times. 3D XTM absorption contrast reconstructions were obtained from the collected radiographic projections through Gridrec reconstruction algorithm.³⁴

In order to quantify the influence of the imaging conditions and beam energies on the image quality, the contrast-to-noise ratio (CNR) was evaluated comparing gray scale values of bulk water in the liquid filled cathode flow field channels and an empty anode flow field channel (void domain) as an indicator of how well water and void domains can be distinguished in the GDL:

$$\begin{eqnarray}&&CNR\left({H}_{2}O/Void\right)=\displaystyle \frac{mean\left({H}_{2}O\right)-mean\left(Void\right)}{\sqrt{\left[Std{\left({H}_{2}O\right)}^{2}+Std{\left(Void\right)}^{2}\right]/2}}\end{eqnarray} \tag{ 1 }$$

The mean and standard deviation (Std) of the gray scale value (GSV) of the water filled and void channel domains were calculated for a total of 4.7 × 10⁷ voxels, by concatenating 5 different cuboid subvolumes (174 × 54 × 100 voxels) that were extracted from the tomographic dataset at different positions along the channel direction.

The 3D gray scale value (GSV) voxel data is obtained after reconstruction from the radiographies. The water signal provides higher GSVs than void but similar to the GDL fibers' GSVs, which causes difficulties in histogram-based segmentation. Thus a reference scan of the cell in dry state was obtained at the end of the experiments to subtract all the static dry structures from the scans of the operating cells to isolate the water signal. Careful alignment of wet scans to a reference dry scan is necessary to get precise segmentation of the correct water signal. The general denoising and segmentation pipeline is given in Fig. 2b. Both dry and wet scans were filtered with a 3D median filter (kernel radius size in pixel, denoted as M[1] for kernel radius of 1 px) to reduce image noise before subtraction. The resulting difference images were further filtered with an anisotropic diffusion filter (AD, denoted as AD[1] for iteration of 1),³⁵ known as edge-preserving filter, to enhance the water signal and prevent edge shifting due to intensive median filtering. There exist also alternative image denoising filters that are not discussed in this work, i.e. Garcia-Salaberri et al.³⁶ used 3D bilateral filter, Heenan et al.³⁷ applied a non-local means filter and Kaestner et al.³⁸ applied a regularized inverse scale space filter. A threshold value was then chosen and applied to obtain binary segmented water mask to which an additional 3D hole closing for filling small voids in the bulk water structure and a cluster cleaning for background noise removal were applied. In parallel, the dry scan was segmented to obtain the GDL fiber structure only. The pore structures in GDLs were obtained by inverting the binary segmented GDL fiber structure. The water mask and the solid fiber mask were merged in the end to obtain the final three phase segmented images for further quantification.

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The precise quantification of the water detection capabilities for the different XTM scan settings requires a reference state of the water distribution in the sample, called ground truth (GT). Considering the fact that the liquid water in the GDLs does not remain static over a long term observation period during an operando XTM experiment,³⁹ referencing operando liquid water by an operando ground truth seems impossible. Therefore, two alternative approaches were employed to obtain a water ground truth based on artificial and in situ water structures, respectively.

The artificial water structures approach in this work is similar to the work presented by Kaestner et al. on XTM of 3D root networks.⁴⁰ In this work, XTM data is simulated by adding background noise from XTM scans acquired with different imaging conditions to ground truth structures, instead of adding artificial noise to the ground truth structures as done in.⁴⁰ The water feature ground truth mask contains 3D structures simulating water accumulations in individual pores as spheres with diameter sizes in pixels of (60, 40, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1) and water accumulations in the throats connecting different pores to larger clusters as columns with diameter sizes in pixels of (13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1) as shown in the 3D rendering in Fig. 2a. The ground truth binary structures are then multiplied with a value that represents mean GSV difference between water and void domain based on CNR analysis. Finally the ground truth structures are added to the empty channel positions in ex situ XTM scans to simulate the water structures in real scans as shown in Fig. 2b.

For the in situ water structures, the electrochemically generated water was immobilized by freezing throughout the in situ XTM imaging period. The ground truth image was obtained by following the same filtering and segmentation workflow as detailed in Fig. 2b on a high quality XTM scan with 25.6 s scan time and only very mild image denoising by anisotropic diffusion filter (AD[1]).

The filtering processes applied during image denoising and the threshold selection during segmentation may influence the shape and the surface of the segmented water structures and therefore alter the overall detected total water volume. A shell-wise analysis of the near surface voxel layers within and outside the artificial water structures is used to investigate the accuracy of the surface identification. The quantification approach by surface identification uses a layer by layer (step of 1 voxel) decomposed shell structure of the ground truth as reference. For instance, for one of the ground truth water droplets (e.g. diameter of 20 voxels), the voxels belonging to the shell between the surface [0] and the inside [−1] position were defined as ground truth for the surface [0] position. The range of shells was selected from inside the object [−5] to the outside [+5]. Hence, for each scan the voxels belonging to a shell layer in a segmented image are counted and then divided by the number of voxels in the same shell of the ground truth to obtain the surface identification value in percentage. The analysis was applied at three independent positions in each XTM scan for same artificial water structures and the individual surface identification values were averaged to reduce statistical errors.

To characterize the image denoising and the segmentation workflow, the water detectability (WD) has been defined as a selection criteria for exploring suitable image filtering parameters. Through the denoising and segmentation workflow in Fig. 2b, a binary segmented image can be obtained and compared voxel by voxel with the pre-defined ground truth—a 3D water feature mask in case of the ex situ water experiment and a segmented high quality 3D mask in case of the in situ water experiment. The percentage of correctly water labeled voxels is defined as the 3D water detectability value. The percentage of incorrectly water labeled voxels in a shell of 10 voxels extending from the surface of the ex situ ground truth water is defined as the false water in the surrounding background. The evaluation was applied at five independent positions in each XTM scan and the calculated water detectability values were averaged to avoid fluctuations due to random sampling errors. For the artificial water case, it is possible to breakdown the water detectability assessment for each different sphere and column sizes to obtain feature based water detectabilities. For the segmented high-quality mask, the water detectability is defined and calculated considering the complete ground truth structures. The analyzed subdomain cuboid used for the evaluation of the in situ data was located under the channel in the cathode GDL with a dimension of 720 μm × 720 μm × 30 μm.

A summary of abbreviations used in this paper is listed in Table I.

Short tomographic scan times in the subsecond regime, which are necessary for studying water dynamics in GDLs will have inherently low image quality. In order to obtain best results at a given scan time, it is vital to understand the influence of the imaging conditions on the image quality. At first the influence of the beam energy, the radiography exposure time and the number of projections on the image quality is studied for the pure, bulk domains of the different phases in the cell's flow field channel domains (ex situ data). In a second step the sensitivity of the water surface location on threshold selection and image filtering is analyzed for artificial water structures. Finally the gained knowhow is applied to "real," in situ electrochemically produced water structures. These in situ measurements were performed at −20 °C to perfectly conserve the same water structure for all imaging conditions.

The CNR between liquid water and void domains as defined in Eq. 1 was studied for 4 monochromatic beam energies (11, 13.5, 16, and 18.5 keV) with tomographic scan times ranging from 0.05 to 25.6 s. For the chosen image dimensions, bounded by the sample size, the 0.05 s scan time was the fastest achievable acquisition speed supported by the hardware of the TOMCAT beamline. The effect of the scan time variation on image quality at 13.5 keV is shown in Fig. 3 for the full combination of exposure times (0.5–16 ms) and number of projections (25–800). While the empty flow field channels remain visible down to a scan time of 0.05 s in the through-plane slices, the GDL structure can be only seen until 0.8 s scan time, suffering though from significant detail losses. The general trend of the image quality losses with shorter scan times can be expected^41–43 and is quantitatively described by the CNR values stated for each tomographic slice in Fig. 3 by yellow numbers.

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The CNR values at the same scan times are similar, with slightly lower values for shorter exposure times, especially for exposure times below 2 ms, where also more ring artefacts are observed. Scans settings with 100 projections or less show well visible under-sampling artifacts in the form of stripes especially at the edge of the XTM through-plane slices. Therefore, all analysis steps beyond noise and CNR analysis are limited to scan conditions with ≥200 projections and ≥2 ms exposure times.

The influence of the beam energy on image contrast is shown in Fig. 4a. At an energy of 13.5 keV the CNR values are the highest for all scan times, though 16 keV shows very similar values. At the lowest energy of 11 keV, the X-ray flux at the beamline is the lowest and therefore the CNR values are the lowest. The reduction of the CNR values for 18 keV is due to the decrease of the attenuation coefficient of water at higher energies. It is important to note, that the energy dependency of the CNR value remains beamline specific when referencing to scan time, as the spectral distribution of the X-ray photon flux and the energy dependency of the detection system are beamline specific. A detailed analysis of the contributions of mean and standard deviation levels to the CNR at 13.5 keV is shown in Fig. 4b. The mean GSV of both H₂O and void domains remain stable with varying scan time, as the beam energy related attenuation coefficients are not affected by the scan time. The standard deviations increase with decreasing scan time as expected,^41–43 especially for subsecond scan times, reaching similar values for the water and void domains. When the scan time is reduced to 0.4 s or lower, the standard deviations of the background noise are almost the same as the mean GSV level of the H₂O domain, and with the noise level reaching the signal level, the CNR drops to 1 and below. In Fig. 4c, the square of the CNR value is plotted vs scan time to enable a linear fitting as the shot noise is proportional to the square root of the number of photons on the detector.⁴⁴ A coefficient α is introduced to fit the linear relationship for different XTM exposure times (see Fig. 4c). The coefficients of α for 0.5 ms and 16 ms exposure time define a lower and upper boundary conditions for the CNR values for different scan times. This enables the prediction of image quality in terms of CNR for untested combinations of scanning conditions. The CNR value range is given by the following Eq. 2:

$$\begin{eqnarray}&&\sqrt{1.52\,* \,ScanT\left(s\right)}\,\leqslant \,CNR\left({H}_{2}O/Void\right)\,\leqslant \,\sqrt{3.37\,* \,ScanT\left(s\right)}\end{eqnarray} \tag{ 2 }$$

These values correspond to the yellow domain in Fig. 4c.

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Threshold based segmentation is the simplest image processing approach to extract quantitative information from XTM scans. To evaluate the influence of denoising filter combinations on water detectability, a choice of the segmentation threshold needs to be made beforehand. Based on the detailed CNR analysis shown above, a threshold value at 50% of the difference between the GSVs of water and the background in the difference image was selected as the water threshold value.

The surface identification method was applied exemplarily to the artificial water sphere with a diameter of 20 px to show the sensitivity of the threshold selection on the segmentation result. In Fig. 5, the influence of threshold variations between 42.5% and 57.5%, where the mean GSV of the water signal corresponds to 100% and background signal to 0%, on identification of the water surface is presented. The selection of a too high threshold value (over-thresholding: >50%) reduces the false water detected beyond the spheres surface but results also in a loss of water volume detected within two or more layers underneath the sphere's surface, hence lowering the overall water detectability. On the other hand, a too small threshold value (under-thresholding: <50%) provides a higher amount of water closer to the shape edge profile of the ground truth, but the falsely identified water outside the original spherical domains increased as well. For the underlying noisy background of the 1.6 s scan time dataset used in this example, some errors in water detection will always remain, even after denoising.

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XTM scans with low CNR require appropriate image denoising prior to segmentation in order to increase the detection level of correctly labeled water domains and to minimize the amount of falsely assigned water domains. Median and anisotropic diffusion (AD) filters were chosen to reduce the noise in the data while preserving the edges of the water boundaries. In Fig. 6, the surface identification of all tested combinations of the median and AD filters are presented to demonstrate the influence of image denoising on the surface of selected features (artificial spheres with diameter of 5, 10, and 20 px; denoted as AS5, AS10, and AS20) for segmented images of the 1.6 s scan time dataset.

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In the unfiltered raw reconstruction, the background noise level is higher than 20% and the signal level is below 80%. Median and AD filters are both able to reduce the background noise down to below 5% and improve the water detection level of the inner bulk layers [−4, −5] up to 100%, when being applied individually with a radius of 3 (Median) or 5 iterations (AD). However, strong median filtering (e.g. M[3]) deteriorates the surface [0] and the inner layers [−1, −2] and decreases water detection levels compared to higher iterations of the AD filtering (e.g. AD[5]) for the larger spheres AS10 and AS20. The small sphere AS5 disappears almost completely by the median filtering with radius 3, but is better preserved, though not 100%, by the AD filtering with 5 iterations. Thus there is a limitation for employing strong median filtering for the denoising of datasets where small features need to be identified. Combinations of mild median and AD denoising are therefore beneficial to ensure a correct surface representation and the detection of small features, as i.e. for M[1]+AD[3] in this example.

The influence of the denoising filter combination was studied not just for the 1.6 s scan time but for a broad range of scan times. Figure 7 presents the quantification of the feature based water detectability (WD) of artificial spheres (AS5, AS10, AS20) and columns (AC5, AC10, AC20) for selected scan times. The WD values for all selected feature sizes decrease from nearly 100% at a scan time of 12.8 s to below 70% at 0.4 s and the background false detection rates increase accordingly from below 5% at 12.8 s up to nearly 40% at 0.4 s for the unfiltered raw data (see Fig. 7a). In general, the column structures were found less sensitive towards filtering in terms of WD than sphere structures, due to their higher connectivity. For realistic operando scans it means that the connected water clusters spanning over several pores will be better preserved than isolated droplets of a similar diameter.

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The influence of the filter combination on the WD values are presented for the selected scan times of 0.4 s, 1.6 s and 6.4 s. For a fast 0.4 s scan a strong filtering combination (M[3]+AD[5]) is required to obtain a clean background at the cost of losing any small features below 5 px (see Fig. 7b). By doing so the overall WD values for all sphere and column features are approximately 70%. Whereas, for a 1.6 s scan (see Fig. 7c), a less aggressive filter combination (M[2]+AD[3]) is appropriate to suppress background noise while keeping the detectability ratio high even for small sphere (AS5) and column(AC5) features. At the scan time of 6.4 s already mild filtering of AD[1] is sufficient to get rid of the minor background noise. The water structures are not significantly affected by the mild filtering itself, reaching a high overall WD level of around 90% (see Fig. 7d).

The influence of the image filtering quantified for surface identification and water detectability discussed above for the artificial water structures, remains to be verified for in situ water structures with electrochemically produced water. To maintain the in situ water structure stable for all combinations of scan settings, the water was immobilized by freezing the cell to −20 °C. Water detectability (WD) results for representative scan times of 0.4 s, 1.6 s, 6.4 s and selected filtering combinations are presented in Fig. 8.

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For the unfiltered, raw reconstructed XTM data, similar water detection levels as for the artificial datasets were found with correctly detected true water levels ranging from 78% to 96%, for 0.4 s to 6.4 s scan time, respectively. For a fast scan of 0.4 s, a strong filtering combination (M[3]+AD[5]) is required to reduce the background noise from 29% to only 8% and thereby increasing the true water detection level to almost 90%. Similarly, also for the scan time of 1.6 s, substantial image denoising is needed to reduce false water detection rates to 4%–5%, whereas the selected filter combinations have only minor influence on the true water detection rates at 93%. For a scan of 6.4 s, filtering of AD[5] is sufficient to suppress the background noise, while strong filtering does even slightly decrease the water detection level from 96% to 94% as contours are blurred and fine details are lost. Similar high water detection levels were reported recently by Xu et al.⁴⁵ for subsecond scans using a high magnification microscope (0.4 μm voxel edge length) and high intensity polychromatic beam conditions at the TOMCAT beamline. Since the density of ice is about 8.3% lower than that of liquid water at 0 °C,⁴⁶ the reported water detectability values can be considered as conservative, slightly underestimating the water detectability levels for GDLs containing liquid water.

A summary of the achievable water detectability levels for both the artificial and in situ water structures applying scan time specific image denoising is shown in Fig. 9. The selected filtering combinations are able to maximize the water detectability for various scan times. For a raw reconstructed scan with a CNR value of 1, a water detectability of nearly 90% is achieved after filtering, with false detection rate remaining below 10%. In case of the unfiltered raw conditions, the artificial water detectability is found underestimated for fast scans and overestimated for longer scans when compared to the in situ data. When image denoising filters are applied, the artificial and in situ water detectability analysis show similar trends with a maximum deviation of the true water detection levels at about 10%. The underestimation of the ex situ water detectability at short scan times is probably due to edge enhancement effects of the coherent X-ray beam in the absorption contrast in situ data. The edge enhancement, supposedly reducing edge blurring, especially with anisotropic diffusion filtering, is not included in the artificial water structures. Whereas the reduced in situ detectability at a long scan time of 12.8 s is probably caused by minor registration errors between the wet scans and the dry reference scan that are not present in the artificial data, since no image registration is needed for the artificial data.

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Since the water detection levels are presented relative to the CNR values of the corresponding scan times in Fig. 9, it could be possible to compare and transfer findings of this work to other fuel cell XTM imaging setups, independent if in situ frozen water detectability experiments are possible or not. Therefore, it provides guidelines for the selection of the imaging conditions, depending on the required precision of XTM quantitative analysis.