# A Novel Method for Hydrogen Permeation Detection Using Reflective Microscopy and Machine Learning

Aleksei Makogon, Frédéric Kanoufi, Varvara Helbert, Flavien Vucko, Viacheslav Shkirskiy

► To cite this version:

Aleksei Makogon, Frédéric Kanoufi, Varvara Helbert, Flavien Vucko, Viacheslav Shkirskiy. A Novel Method for Hydrogen Permeation Detection Using Reflective Microscopy and Machine Learning. Analytical Chemistry, 2026, 98 (5), pp.3899-3909. 10.1021/acs.analchem.5c06160. hal-05519211

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# A Novel Method for Hydrogen Permeation Detection Using Reflective Microscopy and Machine Learning

Aleksei Makogon,*,† Frédéric Kanoufi,† Varvara Helbert,‡ Flavien Vucko,‡ and Viacheslav Shkirskiy*,†

†Université Paris Cité, ITODYS, CNRS, 15 Rue Jean Antoine de Baïf, 75013 Paris, France

‡French Corrosion Institute, RISE (Research Institutes of Sweden), 220 rue Pierre Rivoalon, 29200 Brest, France

E-mail: aleksei.makogon@cnrs.fr; viacheslav.shkirskiy@cnrs.fr

## Abstract

Localized detection of hydrogen permeation in steel membranes is crucial for practical applications but remains challenging. We present a reflective microscopy (RM) approach combined with machine learning (ML)-driven image analysis to address this issue. Hydrogen permeation in press-hardened steel alters the Fe(II)/Fe(III) ratio in the surface layer, affecting reflected light intensity due to changes in the refractive index. Although initially near the optical detection limit, this subtle contrast was enhanced using time-series analysis with UMAP and K-means clustering. The detected regions corresponded to hydrogen-affected zones confirmed by Scanning Kelvin Probe measurements. This work establishes a novel RM-ML framework for detecting and quantifying hydrogen permeation, offering a promising and accessible alternative to conventional methods for localized analysis of metallic membranes.
Introduction

Detection of hydrogen permeation in metals has gained significant attention due to its in-
creasing relevance in the development of a renewable hydrogen-based economy. ¹⁻⁴ Key con-
siderations include hydrogen-controlled storage and release, as well as its safe transporta-
tion—all of which require fast, cost-effective, and efficient methods for monitoring hydrogen
in metals. ¹,⁴⁻⁶ To date, the electrochemical Devanathan–Stachurski method is considered
the standard and is widely recognized as the most reliable and precise technique for detect-
ing hydrogen permeation. ⁶,⁷ This method employs an electrochemical double-cell setup, in
which both sides of a metal membrane serve as electrodes in separate cells. On the entry
side, hydrogen is electrochemically introduced, while on the exit (or detection) side, anodic
polarization oxidizes the permeating hydrogen, with the resulting current directly indicating
the permeation rate. ⁸ Despite its proven robustness, the method is limited by its lack of
spatial resolution—a critical drawback, as local trap sites (such as lattice defects, vacancies,
foreign atoms, dislocations, and grain boundaries) can play a decisive role in the overall
hydrogen permeation rate. ⁵,⁷

To address this issue, local Scanning Kelvin Probe (SKP) and related Scanning Kelvin
Probe Force Microscopy (SKPFM) techniques have been proposed. ⁹⁻¹³ As vibrating capac-
itor methods for localized work function measurements, Kelvin probes have demonstrated
sensitivity to diffusible hydrogen on the detection side, achieving spatial resolutions down to
the nanometer scale and exceptionally high sensitivity to surface hydrogen concentrations at
sub-ppm levels. ⁹,¹¹,¹⁴ Initial quantification strategies involved depositing a nanometer-thick
Pd layer on the detection side, forming a Pd/H electrode. ⁷,¹¹,¹⁵ More recent approaches,
particularly those developed for ferrous substrates, rely on the sensitivity of the measured
SKP potential to the Fe(II)/Fe(III) ratio in the naturally formed oxide film. ¹⁴,¹⁶,¹⁷

In this approach, hydrogen is introduced on the entry side via the hydrogen evolution
reaction (HER), following a methodology analogous to the Devanathan–Stachurski tech-
nique, while the detection side is exposed to air, allowing the formation of surface oxides
predominantly containing Fe(III).<sup>9,16</sup> Upon diffusion through the ferrous membrane, hydrogen partially reduces Fe(III) to Fe(II),<sup>9,18</sup> thereby altering the SKP potential measured by SKP.<sup>9,16</sup> Identical experiments using the Devanathan-Stachurski setup enable a direct correlation between the SKP potential and surface hydrogen concentration, forming the basis for hydrogen quantification.<sup>9,13</sup>

It is worth noting that quantification of the Fe(II)/Fe(III) ratio in surface films can also be performed using optical microscopy techniques.<sup>19–24</sup> For example, reflective microscopy (RM) has been shown to detect the transition between maghemite (γ-Fe<sub>2</sub>O<sub>3</sub>) and magnetite (Fe<sub>3</sub>O<sub>4</sub>) due to changes in the intensity of reflected light at the metal/oxide interface, arising from differences in the refractive indices of Fe(II) and Fe(III) species.<sup>25</sup> In this work, we propose to adapt a similar RM setup to monitor, with spatial and temporal resolution, hydrogen permeation through ferrous membranes by tracking, on the exit side, the *in situ* evolution of the Fe(II)/Fe(III) ratio in the surface film. This readout then serves as a quantitative indicator for H<sub>2</sub> permeation mapping. However, caution is warranted regarding the sensitivity of RM,<sup>26,27</sup> as naturally formed surface films on industrially relevant ferrous alloys are typically in the nanometer thickness range<sup>28–30</sup> and are most often detected and analyzed using highly sensitive X-ray-based techniques.<sup>9,31,32</sup> In our recent work,<sup>26</sup> we demonstrated that a comparable level of sensitivity in RM setups can be achieved through noise analysis of optical signals, enhanced by the development of machine learning (ML)-based numerical procedures. The underlying concept—already validated by our group through passive layer identification on 316L stainless steel using RM<sup>26</sup>—is that optical signals below the instrument’s noise level can still be extracted by ML algorithms from sufficiently long time series data, enabling the algorithm to distinguish noise from meaningful information.<sup>26,33–36</sup>

Hydrogen uptake can occur under atmospheric corrosion, where deposited salts, humidity, and wet-dry cycles promote localized cathodic reactions. Hydrogen embrittlement, defined as the degradation of a metal's mechanical properties due to the ingress and accumulation of hydrogen, often leading to premature cracking or failure, can occur even when absorbed
hydrogen amounts are very low at the early stages (on the order of sub-ppm levels). Such con-
centrations are critical for initiating hydrogen-assisted cracking in high-strength steels.¹⁴,³⁷
To accelerate hydrogen ingress and enable sensitive permeation detection under laboratory
conditions, we employed 1.6 M NaCl as the charging electrolyte. This high chloride con-
centration not only promotes surface film breakdown and hydrogen entry but also provides
a relevant reference environment, since atmospheric exposure often involves chloride-rich
deposits.

With a primary focus on demonstrating the proof of concept of our novel optical approach for detecting hydrogen permeation, we selected press-hardened steel (PHS) as a model ferrous system, known for its ultra-high mechanical performance but severe susceptibility to hydrogen embrittlement and environmentally assisted cracking in industrial settings.³⁸⁻⁴⁰ The results from the combined ML-RM approach were successfully validated against independent SKP mapping and OCP measurements in Devanathan-Stachurski setup performed on a similar substrate.

**Experimental**

Materials

The Al–Si-coated PHS plates used in this study were supplied by ArcelorMittal (Maizières, France). Since only the steel substrate was investigated, the Al–Si coating was completely removed from both the hydrogen entry and detection sides by sequential grinding with P60, 320, 600, and 1200-grit SiC paper under a continuous stream of tap water. The detection side of the sample was further polished using a 1 µm diamond suspension on a Presi™ cloth to achieve a mirror-like finish, facilitating optical detection of reflected light, as surface roughness contributes to light scattering.

The composition and microstructure of the steel substrate were identical to those re-
ported in reference³⁸. In brief, the material exhibited a typical martensitic microstructure,
with martensitic laths ca. 5–7 µm in length and 1–2 µm in width. The average size of prior austenite grains was 8–9 µm, and no precipitates were observed on the surface. The PHS membrane was cut to fit into the optical setup and measured 2 cm × 4 cm with a thickness of 0.5 mm. To ensure a reproducible layer of Fe oxides on the detection side, the sample was oxidized in an air atmosphere at 100°C after polishing for 1–2 h, following a procedure previously reported and validated in SKP studies.⁹,¹⁴ The oxide layer thickness on the detection side was estimated to be ca. 3–4 nm using ellipsometry and was identified as Fe₂O₃ based on complementary X-ray photoelectron spectroscopy (XPS) analysis. As this finding aligns with previously reported results,⁹,¹⁴,³⁸ these complementary analyses are provided in Supplementary Information (SI)-1.

All electrochemical experiments were conducted in an aqueous solution of 1.6 M NaCl (analytical grade, Alfa Aesar), prepared using deionized water purified to a resistivity of 18 MΩ cm (Millipore™ system).

## RM setup for hydrogen permeation tests

A schematic of the experimental setup is shown in Fig. 1. The hydrogen detection setup resembles that used for SKP measurements⁹,¹⁴ and is inspired by the electrochemical Devanathan-Stachurski method.⁸ It consists of two compartments separated by the PHS membrane. The first compartment, referred to as the entry side, is a rectangular chamber measuring ca. 4 cm × 3 cm × 4.5 cm (height × width × length). It contains a three-electrode electrochemical cell, with the PHS membrane serving as the working electrode (WE), a circular counter electrode (CE) made from carbon fiber, and a leakless 3.4 M KCl Ag/AgCl electrode as the reference electrode (RE). The WE is fixed at the side wall and sealed with an O-ring, exposing a circular area of ca. 0.5 cm² to the 1.6 M NaCl electrolyte. The RE and CE are inserted through the top opening of the cell, which remains uncovered to allow free removal of hydrogen bubbles during hydrogen chronopotentiometric charging.

The second compartment, referred to as the detection side, is located on the side of the
<figure><img src="image_2.png" /><figcaption>Figure 1: (a) Schematic (not to scale) of the custom-built in-situ Reflective Microscopy (RM) setup used during galvanostatic hydrogen charging at a constant current density of -10 mA/cm² (vs. 3.4 M KCl Ag/AgCl) in 1.6 M NaCl solution. The configuration is based on the Devanathan-Stachurski principle and consists of two compartments separated by the PHS membrane: the entry side, where hydrogen is generated electrochemically, and the detection side, which is optically monitored. The entry compartment includes a three-electrode electrochemical cell with a carbon fiber counter electrode (CE), a leakless 3.4 M KCl Ag/AgCl reference electrode (RE), and the press-hardened steel (PHS) membrane as the working electrode (WE). (b) Front-facing view of the detection side. The hydrogen-charging region is defined by an 8 mm diameter O-ring (indicated by the red dashed circle), which confines the electrolyte contact area on the entry side. The black square represents the field of view captured by the optical microscope on the detection side. This area includes both the region directly affected by hydrogen charging and adjacent regions outside the O-ring, sufficiently far to neglect radial hydrogen diffusion and considered unaffected by hydrogen.</figcaption></figure>

rectangular chamber where the WE is positioned. It consists of a plate screwed onto the exterior of the rectangle to secure the WE in place. This plate includes a circular empty window of ca. 1 cm² to allow optical access for observations. The detection-side window was intentionally made larger than the 0.5 cm² hydrogen charging area on the entry side to facilitate optical monitoring of regions beyond the direct hydrogen exposure zone, including radial hydrogen diffusion. The entire setup is custom-made and was fabricated using a Formlabs Form 3B 3D printer with Clear V4 resin. Its design, along with all related code and original data, is available in the Zenodo repository: https://zenodo.org/uploads/16363585.

Optical imaging was performed using a commercially available Keyence VHX-7000 microscope equipped with a motorized XYZ stage. The most critical parameter in this context
is the pixel depth of the camera, as it determines the sensitivity of the setup to light in-
tensity variations. In this work, an 8-bit camera—the most accessible and cost-effective
type available on the market—was employed for the proof-of-concept investigations. This
approach distinguishes the present study from our previous works, in which 12-bit cameras
were utilized.²⁵,²⁶ White light illumination and image collection were carried out through
the objective lens. An electrochemical cell was positioned on the microscope stage, and the
objective was tilted 90° to enable optical observation of the sample from the detection side.

The electrochemical experiments were carried out using a CHI 760E potentiostat. After mounting the electrochemical cell on the Keyence stage, the planarity of the detection-side surface was adjusted by tilting the stage until a uniform focus across the entire observed area was achieved using the Keyence autofocus function. Then, 20 mL of NaCl solution was introduced into the cell on the entry side, and image acquisition from the surface on the detection side began simultaneously. Acquired images cover an area of 3.5 × 3.5 mm at a resolution of 2000 × 2000 px (1 px = 1.75 µm) with a time interval of 20 s throughout the experiment. After ca. 1 min at open circuit potential (OCP), a galvanostatic polarization of −10 mA/cm² was applied for a total duration of 9000 s to drive hydrogen generation at the steel-electrolyte interface on the entry side. The control experiment, conducted without polarization and without electrolyte, was used to estimate the drift in the optical signal (SI-2). Over the duration of the experiment, this drift did not exceed 0.1% in light intensity.

Numerical analysis of optical images

Mechanistic aspects of image analysis

The central concept underlying the interpretation of optical images is that the light reflec-
tivity values (R) are proportional to both the thickness (δ) and the composition (via the
refractive index n) of surface films on metal substrates. This results from light interference
at Metal/Oxide/Electrolyte (MOE) interfaces.¹⁹,²⁴,²⁵,⁴¹,⁴² This principle is analogous to el-
lipsometry.²⁷,⁴³ It is quantitatively described by the Fresnel equation in the case of normal
incidence:

$$R_{\text{MOE}} = \left| \frac{r_{\text{MO}} + r_{\text{OE}} e^{2i\pi/\lambda n_{\text{O}}\delta}}{1 + r_{\text{MO}}r_{\text{OE}} e^{2i\pi/\lambda n_{\text{O}}\delta}} \right|^2, \quad (1)$$

where $\lambda$ is the wavelength of the incident light, $i = \sqrt{-1}$, and $r_{\text{MO}}$ and $r_{\text{OE}}$ are the reflection coefficients at the metal/oxide and oxide/electrolyte interfaces, respectively. $r_{\text{MO}}$ (and analogously $r_{\text{OE}}$) is expressed as

$$|r_{\text{MO}}|^2 = \left| \frac{n_{\text{M}} - n_{\text{O}}}{n_{\text{M}} + n_{\text{O}}} \right|^2 \quad (2)$$

The experimentally measured intensity of the reflected light as a function of time ($I(t)$), normalized by the light intensity at $t = 0$ ($I(0)$), is then related to the relative variation of the reflectivity as

$$\frac{I(t)}{I(0)} = 1 + \frac{\Delta R_{\text{MOE}}}{R_{\text{MOE}}} \quad (3)$$

In this work, image normalization was performed pixelwise by dividing $I(t)$ at each pixel at a given $t$ by its initial intensity at $t = 0$, recorded at the onset of OCP measurements 40 s before the start of electrochemical polarization.

Equation 1 was solved numerically in this work using Python scripts available on Zenodo (https://zenodo.org/uploads/16363585). For $Fe_2O_3$ oxide growth, Eq. 1 was used directly. In contrast, for the partial transformation of $Fe_2O_3$ to FeO, a layered film structure—previously reported in the literature⁹—was employed. Accordingly, the transfer matrix method (TMM) was applied to model this system. For clarity and conciseness, technical details regarding the implementation of TMM in this work are provided in SI-3.

The optical constants used in this study are as follows: the complex refractive index of Fe metal is $n = 2.5845 + 2.7670i$, $^{44}$ $Fe_2O_3$ is represented by $n = 2.8090 + 0.873i$, reported for hematite, $^{45}$ and FeO is represented by $n = 2.291 + 0.8i$, reported for wüstite. $^{46}$ All optical constants correspond to a wavelength $\lambda = 450$ nm, which matches the blue channel of the
RGB camera used in the experiments. Similar trends were observed for the red and green channels, and these results are detailed in SI-4.

## Machine learning strategies to enhance optical detection

Traditional image analysis often relies on identifying prominent visual features within individual frames, a technique referred to as *static image analysis*. This approach evaluates spatial information without accounting for temporal evolution and is well-suited for systems with strong signal contrast. However, in the present study, such methods are inadequate due to the low signal-to-noise ratio of reflectivity changes caused by nanometer-thick oxide films.²⁶

To address this limitation, we implemented *dynamic image analysis*, which evaluates sequences of images to extract temporally evolving patterns. This methodology, originally developed for tracking particles or dynamic systems, helps suppress random fluctuations and isolate meaningful signal evolution over time.⁴⁷

As demonstrated in our earlier work²⁶ and extended here, we first decompose the image sequence into pixelwise time series of normalized reflectivity changes. Each pixel is thus represented by a high-dimensional vector encoding its temporal behavior. To reveal hidden structures in this data, we apply unsupervised dimensionality reduction to embed these time series into a 2D space, which are then further separated into clusters using the K-means algorithm. Among the dimensionality reduction methods tested—Principal Component Analysis (PCA), t-SNE, and others—Uniform Manifold Approximation and Projection (UMAP) proved to be the most effective, owing to its capacity to preserve nonlinear relationships.²⁶,⁴⁸⁻⁵⁰

The performance of the dimensionality reduction algorithms in distinguishing optical signals was evaluated using the Silhouette Score metric, defined as
$$s(i) = \frac{b(i) - a(i)}{\max\{a(i), b(i)\}}, \qquad (4)$$

where $a(i)$ is the average distance between data point $i$ and all other points in the same cluster (intra-cluster distance), and $b(i)$ is the minimum average distance to points in the nearest other cluster (inter-cluster distance) in the 2D space. The Silhouette Score evaluates two aspects for each point $i$: its closeness to points within its own cluster (cohesion) and its distance from points in the nearest other cluster (separation). The score ranges from -1 to 1, with higher values indicating better-separated clusters.

To interpret the reasons behind the differing performance of dimensionality reduction algorithms, we trained XGBoost regression models⁵¹ to map the original high-dimensional time series onto their corresponding 2D coordinates. Our goal was to identify which time points contributed most significantly to the separation of optical signal behaviors. We then performed permutation importance analysis.⁵²,⁵³ This method quantifies the importance of each time step by randomly permuting its values and observing the impact on model performance. Time points that cause the greatest drop in model accuracy when permuted are considered the most influential in determining the UMAP embedding.

## Scanning Kelvin Probe setup

To validate the optical observations, independent SKP measurements were performed in separate experiments under nearly identical conditions. The metal membrane had the same chemical composition and structure, was mirror-polished, and pre-oxidized in air at 100°C. It was mounted in a homemade Plexiglas cell resembling the custom 3D-printed optical cell.¹³ The entry side was exposed to 1.6 M NaCl and charged for 9000 s at -10 mA/cm². After charging, the membrane was transferred to the SKP chamber for a surface scan on the detection side.
A height-controlled SKP instrument (Wicinski GbR) was used. The Ni-Cr alloy probe had a 100 µm tip diameter. To maintain a constant probe-specimen distance during mapping, topography was measured simultaneously with potential. The topography accuracy was 1–2 µm. The electrode gap was set to 50 µm, with a vibration amplitude of 20 µm at ca. 1 kHz. The AC backing potential frequency was 10 Hz. Prior to measurements, the probe potential was calibrated with a saturated Cu/CuSO₄ electrode, and all potentials are reported versus the 3.4 M KCl Ag/AgCl reference electrode for consistency with the optical experiments. Measurements were conducted in ambient air at 55 ± 5% RH and 22 ± 1 °C. Probe stability was verified before and after each experiment. Further details are reported elsewhere.¹³,⁵⁴

## Devanathan-Stachurski measurements

To assess the sensitivity of RM for hydrogen detection, independent electrochemical measurements were performed using a standard Devanathan-Stachurski double-cell geometry. The PHS membrane was prepared with surface finishing and thermal pre-oxidation procedures identical to those used in the optical experiments. Note that no Pd layer was deposited on the detection side, consistent with the RM measurement setup. The entry side was subjected to identical hydrogen charging conditions: galvanostatic polarization at -10 mA/cm² in 1.6 M NaCl. On the detection side, the chamber was filled with 0.1 M NaOH. Instead of applying an anodic potential to oxidize bursting hydrogen (as in standard permeation current measurements), the OCP of the detection surface was monitored continuously versus a Hg/HgO reference electrode. All potentials are reported versus the 3.4 M KCl Ag/AgCl reference electrode for consistency with the optical experiments. This configuration allowed for the tracking of the spontaneous evolution of the surface potential—acting as an indicator for the chemical state of the oxide film—during the hydrogen permeation process.
# Results and discussion

## Galvanostatic hydrogen charging monitored optically

Optical microscopy based on the analysis of reflected light (referred to here as RM) on the detection side of iron-based substrates in the electrochemical hydrogen charging cell is a promising approach for detecting hydrogen permeation, due to changes in reflectivity associated with the reduction of $Fe_2O_3$ surface oxides by diffused hydrogen (Fig. 1a). To test this method, we used a mirror-polished PHS charged with hydrogen at a relatively high current density of $-10 \text{ mA cm}^{-2}$ for 9000 s to ensure a significant hydrogen presence at the detection side (Fig. 2). The optical observation area on the detection side was positioned directly opposite the edge of the circular charging area, providing contrast between hydrogen-affected and unaffected regions (Fig. 3). This section focuses on the analysis of raw normalized optical images to demonstrate proof of concept for hydrogen permeation detection, while the following section enhances the observed optical contrast using dynamic ML-based image analysis.

Fig. 2 shows the evolution of the electrode potential during potentiometric hydrogen charging. Initially (for $t > 5$ s), the potential is ca. $-2.4 \text{ V}$ vs. $3.4 \text{ M KCl Ag/AgCl}$, then rises sharply to around $-1.5 \text{ V}$, where it remains nearly constant until the end of the experiment, with intermittent potential spikes most pronounced at ca. 2800 s and 3100 s. The potential quickly reaches a constant value, which is consistent with what has been reported in the literature.⁵⁵ The initially prominent negative potentials observed on the charging electrode are attributed to slow interfacial and transport processes, including surface oxide reduction and progressive electrode activation, the formation and saturation of adsorbed hydrogen layers with subsequent subsurface uptake and trapping, and local electrolyte changes such as concentration polarization and pH shifts.⁵⁶,⁵⁷ After this transient phase, the electrode reaches a steady state, characterized by continuous hydrogen evolution and bubble detachment (visible to the naked eye), which likely cause the observed spikes
<figure><img src="image_3.png" /><figcaption>Figure 2: Potential-time curve recorded during galvanostatic hydrogen charging at −10 mA cm⁻² on the entry side.</figcaption></figure>

and apparent noise in the potential trace. Overall, these observations indicate successful hydrogen generation at the charging side.

Fig. 3a and b show optical images of the detection side at the start (t = 0 s) and at the end (t = 9000 s) of polarization. The images were first pixel-wise normalized to the initial frame recorded at OCP, taken immediately after the electrolyte was added to the charging compartment of the electrochemical cell. Normalization enhances subtle contrast changes that are otherwise hidden in the raw images (data available on Zenodo). Pixels darker than the reference frame correspond to normalized values below 100%, while brighter pixels exceed 100%.

The initial normalized frame (t = 0 s) exhibited no distinct pattern and showed random intensity fluctuations of 100.0 ± 0.5%, consistent with the expected quantization and sensor noise in the 8-bit camera. In normalized units, the standard deviation of this initial frame was std = 0.03, corresponding to roughly 3% variation relative to the mean. Because the expected intensity difference between hydrogen-affected and unaffected regions is below 1%, improving the signal-to-noise ratio was essential. To achieve this, we first applied Gaussian blurring with a kernel size of (11, 11), which reduced the standard deviation to 0.01 by suppressing high-frequency noise while preserving low-frequency features. A subsequent averaging with a 10 × 10 kernel further decreased the standard deviation to 0.006. For reference, in 8-bit intensity levels, this residual noise corresponds to only 1–2 counts above
<figure><img src="image_4.png" /><figcaption>Figure 3: (a) Initial normalized reflectivity image on the detection side, recorded at the beginning of polarization (blue channel only; full RGB images are available on Zenodo). The granular intensity variation around 100% is attributed to random noise. The red line indicates the position of the O-ring on the entry side, delineating regions affected and unaffected by hydrogen. (b) Final normalized reflectivity image of the surface following galvanostatic polarization at −10 mA cm⁻². (c) Histogram of normalized pixel intensities from image (b), segmented into two clusters using K-means clustering. The gray dashed line represents the clustering threshold at ca. 100%, identified for binarization by K-means. Pixels with intensities below 100% are assigned to 'Cluster 0' (blue), and those above 100% to 'Cluster 1' (yellow). (d) Binarized spatial map corresponding to the clustering result shown in (c), illustrating pixel-wise segmentation into two groups based on intensity distribution.</figcaption></figure>

the quantization floor, so additional filtering would risk losing meaningful spatial contrast.

The processed images in Fig. 3 therefore represent the best compromise between noise suppression and preservation of spatial information. After filtering, the final frame at *t* = 9000 s shows two regions of normalized intensity: a brighter zone (~101%) opposite the charging compartment and a darker zone (~99%) on the side opposite the reference compartment. These variations exceed those in the control experiment without hydrogen (SI-2), indicating a contribution from diffused hydrogen. However, because the residual noise after filtering remains comparable to the expected signal amplitude, the contrast in Fig. 3
is still at the very limit of detection. More advanced denoising or temporal averaging would
be required to fully resolve the boundaries of the hydrogen-affected regions.

To further improve sensitivity, we extended the filtering approach by temporal averaging,
i.e., calculating pixel-wise mean values across multiple consecutive frames before applying
Gaussian blurring and spatial binning. Two representative cases are shown in Fig. 4: av-
eraging the last four frames [panel (a)] and the last sixteen frames [panel (b)], followed by
K-means binarization. This averaging procedure reduces the impact of stochastic noise and
improves the separation between hydrogen-affected and unaffected regions.

To quantify the effectiveness of this separation, we evaluated the silhouette score of the
K-means clustering. For a single final frame, the silhouette score was relatively low (0.06),
reflecting the marginal separation visible in Fig. 3d. Averaging four frames increased the
score to 0.10, and averaging sixteen frames provided a slightly higher value of 0.11. These
results indicate that temporal averaging improves the clustering performance by enhancing
the contrast between the two spatial regions. However, the studied process is inherently dy-
namic, and extended averaging progressively blurs temporal changes. Thus, while temporal
averaging provides a modest gain in sensitivity, the maximum silhouette score of only 0.11
highlights the limited effectiveness of this approach for reliably resolving hydrogen-induced
contrast boundaries.

<figure><img src="image_5.png" /><figcaption>Figure 4: (a) binarized with K-means map of averaged last 4 frames (b) binarized with K-means map of averaged last 16 frames</figcaption></figure>

For additional confirmation, ex-situ SKP mapping of the detection side was performed.
<figure><img src="image_6.png" /><figcaption>Figure 5: SKP potential distribution measured by SKP on the detection side of the PHS membrane near the O-ring on the entry side, used to identify regions affected and unaffected by hydrogen. The scan was performed after cathodic charging at −10 mA cm⁻² for 9000 s on the entry side in 1.6 M NaCl. Measurements were conducted after 2 h of air exposure.</figcaption></figure>

Due to the requirement of an electrolyte-free surface for SKP, simultaneous optical and Kelvin probe measurements were not possible. Therefore, independent experiments were conducted on equivalent samples using identical geometric constraints (same O-ring diameter and position). As with the optical normalized images, the SKP potential maps in Fig. 5 show two zones, with regions opposite the hydrogen-charged area exhibiting negative potentials (ca. −0.3 V vs. 3.4 M KCl Ag/AgCl), while unaffected areas display positive potentials (ca. 0.1 V vs. 3.4 M KCl Ag/AgCl). This aligns with SKP studies on high-strength dual-phase steel, secondary-hardened martensitic steel, aged martensitic stainless steel, and fully ferritic mild steel.⁹,¹²,¹³ In these studies, negative potentials are attributed to Fe(III) reduction to Fe(II) by diffused hydrogen, while positive potentials are attributed to Fe oxidation by atmospheric oxygen in ultrathin ambient electrolyte films. Overall, this body of experimental evidence confirms that the observed changes in surface reflectivity on the detection side are associated with diffused hydrogen and experimentally validate the proposed optical methodology for hydrogen permeation detection. However, the main drawback of optical detection is the absence of a clear boundary between hydrogen-affected and unaffected regions, unlike in the SKP map in Fig. 5, due to the low signal-to-noise ratio in the optical data, as evidenced by the granular pattern observed in the images in Fig. 3.
To clarify, the histogram of pixel intensities from the image at *t* = 9000 s is shown in Fig. 3c, where a single, near-Gaussian distribution is observed. Thresholding this distribution using the K-means automated segmentation tool separates the histogram into two clusters, represented as a binary image in Fig. 3d. Although the binary image provides improved visual distinction between regions affected and unaffected by diffused hydrogen, the granular pattern persists. This limits the potential for detailed analysis, such as defining the onset of hydrogen detection or mapping the spatial evolution of the diffused hydrogen front—both of which are key for quantitative assessment in hydrogen permeation technologies. In this work, we propose a solution to this challenge by retaining the same simple and low-cost optical experimental setup while enhancing the accumulated optical signals using unsupervised ML approaches.

## Enhancement of optical contrast in dynamic ML-based image analysis

In contrast to static image analysis, which relies on pixel intensities from a single frame, this section focuses on dynamic image analysis, which analyzes image sequences. The central idea is that random noise fluctuations affecting a specific pixel or pixel clusters in one frame may not persist in others, enabling the development of intelligent extraction methods that can reveal otherwise hidden patterns. Fig. 6 illustrates the data processing pipeline, which primarily leverages recent advances in unsupervised ML approaches.²⁶,⁵⁰

First, the entire image stack after 9000 s of polarization (Fig. 6a) is decomposed into a collection of per-pixel time series (Fig. 6b). Each time series represents the reflectivity evolution of a single pixel over time, thereby encoding localized temporal behavior associated with hydrogen permeation. A small representative subset of these time series is shown in Fig. 6b to qualitatively illustrate the diversity of intensity dynamics across the field of view.

Next, the time series data are embedded into a 2D latent space using the UMAP dimensionality reduction method (Fig. 6c). The core idea is that UMAP evaluates each entire time
series curve and, based on its internal algorithms, identifies the most prominent features. It
then projects the curves onto the *xy*-plane according to a similarity score derived from these
features. Curves with similar features are placed closer together, while dissimilar ones are
mapped farther apart, based on UMAP's assessment (see Experimental Section for more
details).

In our case, the UMAP algorithm separates all curves into two distinct, dense clusters,
shown as blue and orange circles in Fig. 6c, directly indicating that a clear distinction between
the time profiles can be made. To evaluate the quality of the cluster separation, we also used
the Silhouette Score (see the definition and formula in the Experimental Section), which
yielded a value of 0.9, indicating excellent separation between the orange and blue point
clouds. The reconstruction of the UMAP projection back into the image in Fig. 6d shows
that the blue cluster corresponds to the hydrogen-charging area on the entry side, while the
orange cluster is associated with the surrounding unaffected region. Notably, no granular
pattern is observed in the ML-enhanced image in Fig. 6d, in stark contrast to the thresholded
image in Fig. 3d, providing clear evidence of the effectiveness of our noise reduction pipeline.

The rationale for selecting this specific pipeline is based on the empirical knowledge we ac-
cumulated during our exploration of unsupervised ML for optical signal enhancement.<sup>26,48,50</sup>
This led us to conclude that in most cases, nonlinear (e.g., UMAP) unsupervised dimensional-
ity reduction methods perform markedly better than linear ones (e.g., PCA). For comparison,
PCA was also applied to the same dataset but performed poorly (see inset in Fig. 7b), con-
sistent with our previous works.<sup>26,48,50</sup> To further investigate these differences and validate
our rationale regarding UMAP functionality, we conducted a feature importance analysis for
both UMAP and PCA on this dataset, with the results shown in Fig. 7.

To quantify the contribution of each time-step to the low-dimensional embeddings, we
treated each time-point as a separate feature and used supervised regressors to predict the
UMAP or PCA coordinates from the original time-series data. Specifically, for each embed-
ding dimension, an XGBoost regressor was trained to map the full set of time-step features
<figure><img src="image_7.png" /><figcaption>Figure 6: Schematic overview of the data processing pipeline applied to the time-resolved reflectivity image sequence. (a) Sequential images collected during galvanostatic polarization with representative time stamps annotated. (b) A subset of per-pixel temporal intensity traces extracted to illustrate diverse temporal behaviors. (c) Two-dimensional embedding of the pixel-wise time series using UMAP, followed by K-means clustering into two groups. The annotated clusters highlight spatial segregation corresponding to known experimental boundaries. (d) Reconstructed cluster map revealing distinct spatial domains associated with the clustered temporal dynamics.</figcaption></figure>

to that dimension, and permutation feature importance was computed. In this approach, the values of each feature are repeatedly shuffled, and the resulting increase in prediction error reflects the importance of that feature. The importance scores for individual embedding dimensions were then combined, by using an L2 norm, and normalized for visualization. High importance values indicate that perturbations at those time-steps strongly affect the embedding, revealing which moments in the sequence are most critical for separating the pixel behavior in the reduced-dimensional space.

In a nutshell, the feature importance analysis in Fig. 7 shows the impact (on the *y*-axis) of each datapoint on the outcome of the dimensionality reduction, plotted as a function of datapoint number, which corresponds to time. Both UMAP (Fig. 7a) and PCA (Fig. 7b) exhibit the highest importance values at the initial time interval ($t = 0–1000$ s) and the final time interval ($t = 8000–9000$ s). The key difference between the two algorithms is that the UMAP importance curve also displays several spikes at intermediate times ($t = 2000–6000$ s),
<figure><img src="image_8.png" /><figcaption>Figure 7: Analysis of temporal feature importance in dimensionality reduction. (a) Per-mutation importance scores for each time step derived from XGBoost regressors trained to predict UMAP coordinates from pixel-wise time series. The inset shows the UMAP embedding with two distinct clusters corresponding to pixels with different temporal behaviors. Peaks in the importance curve indicate specific time steps that contribute most strongly to the embedding. (b) Corresponding analysis using PCA coordinates as regression targets. The importance scores are less uniformly distributed, reflecting PCA's limited sensitivity to global temporal features. Insets in both panels display the 2D embeddings used for the regressions, colored by cluster assignment (2 for UMAP and 1 for PCA).</figcaption></figure>

suggesting that particular moments in the image sequence are critical for differentiating pixel behavior, whereas the PCA importance remains near zero during this period. The high importance values in specific time frames for PCA resemble the static image analysis in the previous section, which is not well suited for the present context. In contrast, the broader and more uniformly distributed importance profile of UMAP appears to be a key factor underlying its superior performance.

Estimating sensitivity to hydrogen permeation in the RM setup
<figure><img src="image_9.png" /><figcaption>Figure 8: Temporal progression of hydrogen permeation detected through UMAP-based clustering and electrochemical validation. (a) Selected per-pixel reflectivity time series illustrating signal evolution. Orange dashed lines demarcate cumulative time windows used for truncated UMAP analysis: I (0–1000 s), II (0–3000 s), and III (0–5000 s). (b) UMAP embeddings and K-means clustering for the corresponding time windows, showing improved separability over time. (c) Silhouette score evolution quantifying clustering quality. The score rises sharply after $t_{onset} \approx 3200$ s, marking the optical detection point. (d) The Devanathan–Stachurski measurements illustrating the potential on the entry side (blue curve, left axis) and the OCP evolution on the detection side (orange curve, right axis). Charging begins at 0 s and ceases at 8000 s, with OCP measurements recorded on the charging side both before and after this period.</figcaption></figure>
To evaluate the sensitivity to hydrogen permeation, the results of the current RM methodology were compared in the separate experiment with the evolution of the OCP on the detection side in a Devanathan-Stachurski setup—without a Pd layer on the metal membrane on the detection side—to closely replicate the RM experimental conditions. The rationale is that both OCP and changes in reflected light are highly sensitive to variations in surface oxides, albeit through distinct physical mechanisms: OCP reflects changes in electrochemical potentials, whereas RM captures shifts in refractive indices. This dual approach enables independent cross-correlation for monitoring surface oxide states from two complementary perspectives. Given that the Devanathan-Stachurski measurement is a standard method for hydrogen permeation, it also establishes a benchmark for hydrogen sensitivity testing.

In the case of the RM experiment, the ML pipeline, developed and justified in the previous section, is used here to quantitatively estimate the onset of hydrogen permeation detection as an indicator for estimating sensitivity to hydrogen permeation (Fig. 8a-c). The core idea relies on UMAP analysis of truncated image sequences of varying lengths (marked as time periods I, II, and III in Fig. 8a). Fig. 8b shows UMAP projections for time series of different lengths, revealing gradual point cloud segregation: for 0-1000 s (I), points form a single cloud; for 0-3000 s (II), two clouds appear but are not well separated; for 0-5000 s (III), clearly distinct point clouds emerge. To quantitatively assess point cloud separation for truncated sequences, we employ the silhouette score, previously shown to be a reliable metric in establishing the pipeline.

Note that the focus of this study is not on supervised prediction for generalizing to unseen data, which requires labeled datasets partitioned into training, validation, and test sets. Instead, the task involves unsupervised exploratory data analysis of unlabeled optical datasets. In this context, the silhouette score serves as a suitable internal metric to quantify the compactness and separation between hydrogen-affected and non-affected regions.

As shown in Fig. 8c, the silhouette score remains steady at approximately 0.35 until 3200 s, after which it increases linearly to 0.8 by 9000 s. The initially low values correspond
to the absence of observable changes in the surface film, while the sharp increase indicates
the separation of two distinct zones. This transition marks the optically detectable onset of
oxide film reduction caused by diffused hydrogen.

In contrast, the evolution of the OCP in the Devanathan-Stachurski configuration, as
shown in Fig. 8d (orange curve), indicates behavioral changes much earlier than those de-
tected by the silhouette score. After approximately 500 s of charging, the OCP begins to
decline gradually from -0.75 V, stabilizing at around -1.5 V by 3000 s. This suggests that
the reduction of iron oxides on the detection side by diffused hydrogen begins as early as
500 s, a process not detectable in the current RM setup. However, once hydrogen satura-
tion occurs on the detection side at around 3000 s, optical observations begin to reveal the
presence of hydrogen.

The observed sensitivity limitations are due to the 8-bit pixel depth of the optical camera
and the limited stability of the light source from the commercially available Keyence optical
platform. While these constraints are sufficient for initial proof-of-concept studies of optical
hydrogen permeation in this work, the optical setup will need to be upgraded for follow-
up studies to include a more stable light source and a 12- or 16-bit camera for rigorous
quantitative cross-validation with Devanathan-Stachurski benchmark experiments.

Interpretation of optical signals

This section presents the fitting of experimental optical curves based on the current mecha-
nistic understanding of hydrogen permeation (Fig. 9a), thereby reinforcing the findings and
clarifying the origin of the observed optical signatures.

The dominant factor influencing the optical signal is the thickness and composition of the
oxide film on the detection side. This oxide layer, pre-formed in air at 100°C, was measured
to be approximately 3–4 nm thick and consists of Fe₂O₃ (SI-1; schematized in Fig. 9a). When
hydrogen diffusing from the entry side reaches this oxide, it triggers the reduction of Fe(III)
to Fe(II). This process is counterbalanced by the re-oxidation of Fe(II) through interaction
with atmospheric oxygen, maintaining a dynamic Fe(III)/Fe(II) equilibrium.⁹,¹³,¹⁶,¹⁸ The Fe(III)/Fe(II) balance is controlled by the local availability of hydrogen at the detection-side interface, shifting toward Fe(III) as the hydrogen supply diminishes.

The averaged optical responses of two distinct regions—one influenced by hydrogen (Area 1, Fig. 9b) and one unaffected (Area 2, Fig. 9c)—identified using the UMAP pipeline, evolve consistently with this mechanistic explanation. These responses can be quantitatively described using the Fresnel equation (Eq. 1), with further technical details provided in SI-3.

Initially, both curves in Fig. 9b and c show a slight decrease (0.2%) in normalized intensity from the onset of the experiment up to 3200 s, when hydrogen was first detected. This initial decrease can be attributed to bulk Fe oxidation by atmospheric oxygen, even after the initial surface pre-oxidation was performed. This interpretation is consistent with complementary SKP point measurements (reported in SI-5) over the region unaffected by hydrogen, which show that oxide growth slows down but does not completely stop. The upper x-axis in Fig. 9c indicates that this corresponds to a very minor oxide growth, with an additional thickness on the order of 0.1 nm.

Once the diffused hydrogen reaches the surface at 3200 s, the behavior of the two curves diverges markedly. In the region affected by hydrogen, the normalized intensity increases steadily by ca. 0.4%, corresponding to the reduction of 7–8% of Fe(III) to Fe(II) (Fig. 9b, upper x-axis). In contrast, the region unaffected by hydrogen exhibits an abrupt decrease of 0.9% up to 6000 s of the experiment, after which the signal stabilizes at about 99.1% of the normalized intensity. This trend suggests further oxidation of the Fe bulk, consistent with the growth of an Fe(III) oxide layer of sub-nanometer thickness (Fig. 9c, upper x-axis). The sudden change in growth rate observed at ca. 3200 s may be attributed to the reduction of Fe(III) in Area 1, which could produce a thin layer of water:

$$Fe_2O_3 + H_2 \rightarrow 2FeO + H_2O. \qquad (5)$$

Once generated in Area 1, it can spread to Area 2, thereby reducing the ohmic drop in
<figure><img src="image_10.png" /><figcaption>Figure 9: (a) Schematic representation of oxide film transformation dynamics on the detection side. See text for further details. (b) Experimentally measured reflectivity change in Area 1 (affected by hydrogen; solid blue line, lower *x*-axis) overlaid with the optical fitting associated with the Fe(III) → Fe(II) transformation (dotted blue line, upper *x*-axis). (c) Experimentally measured reflectivity change in Area 2 (unaffected by hydrogen; solid orange line, lower *x*-axis) overlaid with the optical fitting associated with Fe bulk oxidation to Fe(III) oxide (dotted orange line, lower *x*-axis).</figcaption></figure>

the thin-layer electrolyte and accelerating Fe bulk oxidation.

In summary, this study demonstrates that reflective microscopy, when combined with unsupervised machine learning strategies, can transform faint optical signals into reliable indicators of hydrogen permeation. Beyond validating the proof of concept on press-hardened steel, our results suggest that quantification of hydrogen permeation in an optical setup is possible but requires an enhanced optical setup, with detailed attention to pixel depth values and light source stability.

## Conclusions

We introduced a reflective microscopy approach enhanced by unsupervised machine learning for localized detection of hydrogen permeation in press-hardened steel. Subtle reflectivity changes associated with Fe(III) reduction were amplified using dynamic time-series anal-
ysis with UMAP and K-means, enabling spatial segregation of hydrogen-affected regions. Validation by Scanning Kelvin Probe confirmed the correlation between optical signatures and hydrogen-induced oxide reduction. The optical signal onset closely aligned with oxide reduction saturation—observed via independent open-circuit potential measurements in the Devanathan-Stachurski setup—thereby validating the proof-of-concept optical detection and highlighting opportunities for refining hydrogen quantification optics. This RM-ML framework offers a cost-effective, accessible alternative to conventional methods, with potential for future hydrogen permeation quantification and integration into established permeation methodologies.

## Data Availability Statement

The raw and processed data, along with the Python codes used to reproduce the above findings, are available for download at https://zenodo.org/uploads/16363585.

## Declaration of Generative AI and AI-assisted technologies in the writing process

During the preparation of this work, the authors utilized commercially available LLM tools, including ChatGPT-5, to enhance readability and language via API calls in a custom-developed routine available at

https://github.com/Shkirskiy/interactive-proofreader.git. Additionally, ChatGPT-5 was used to assist with Python code editing. All content and code were subsequently reviewed and edited by the authors, who take full responsibility for the final version of the publication.
# Acknowledgement

This work was financially supported by the Agence Nationale de la Recherche (ANR) Jeunes chercheuses, jeunes chercheurs, ANR JCJC, program (OCTAWA project, ANR-22-CE29-0010-01).

# Supporting Information Available

A listing of the contents of each file supplied as Supporting Information is included below.

The following file is available free of charge:

* SI.pdf: This file contains the following sections:

- **SI-1. Surface characterization**: Ellipsometry data showing oxide film growth (approximately 1.5 to 3–4 nm) on press-hardened steel (PHS) upon thermal treatment at 100 °C. XPS analysis confirms that the surface film is composed of $Fe_2O_3$.

- **SI-2. Control experiment**: Optical data from an experiment conducted without hydrogen charging, showing only a minor 0.1% intensity drift and no spatial contrast, confirming that the effects reported in the main text are hydrogen-induced.

- **SI-3. Transfer matrix method for Fe(III)/Fe(II) film**: Theoretical description and equations for the optical model used to interpret reflectivity changes based on a layered Fe(III)/Fe(II) oxide structure.

- **SI-4. Reflectivity changes in RGB channels**: Experimental data showing the reflectivity evolution in the red, green, and blue camera channels for zones affected and unaffected by hydrogen.

- **SI-5. SKP monitoring**: Scanning Kelvin Probe data showing the continuous growth and stabilization of the oxide film on PHS in air over 72 hours.
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TOC Graphic

<figure><img src="image_11.png" /></figure>
Supporting Information: A Novel Method for
Hydrogen Permeation Detection Using Reflective
Microscopy and Machine Learning

Aleksei Makogon,*,† Frédéric Kanoufi,† Varvara Helbert,‡ Flavien Vucko,‡ and
Viacheslav Shkirskiy*,†

†Université Paris Cité, ITODYS, CNRS, 15 Rue Jean Antoine de Baïf, 75013 Paris,
France

‡French Corrosion Institute, RISE (Research Institutes of Sweden), 220 rue Pierre
Rivoalon, 29200 Brest, France

E-mail: aleksei.makogon@cnrs.fr; viacheslav.shkirskiy@cnrs.fr
# Contents

<table><tr><td>SI - 1. Surface characterisation</td><td>S3</td></tr><tr><td>Surface Film Thickness Measurements with Ellipsometry</td><td>S3</td></tr><tr><td>XPS measurements</td><td>S4</td></tr><tr><td>SI - 2. Control experiment</td><td>S6</td></tr><tr><td>SI - 3. Transfer matrix method of a Fe(III)/Fe(II) bi-layer</td><td>S7</td></tr><tr><td>SI - 4. Reflectivity Changes in RGB channels</td><td>S10</td></tr><tr><td>SI - 5. SKP Monitoring of PHS Potential in the Hydrogen-Unaffected Area</td><td>S11</td></tr></table>
# SI - 1. Surface characterisation

## Surface Film Thickness Measurements with Ellipsometry

The thickness of the surface oxide film was determined by spectroscopic ellipsometry using a SENTECH SE 400adv laser ellipsometer operated at a fixed wavelength of 633 nm. Ellipsometry is a well-established, non-destructive optical technique that enables precise determination of thin film thickness and refractive index by analyzing changes in the polarization state of reflected light. The use of a monochromatic wavelength provides high sensitivity for measuring ultrathin oxide layers typically formed on steel surfaces.

To ensure statistical reliability and reproducibility of the data, all measurements were performed five times at randomly selected positions on each specimen, and the averaged value is reported. This procedure minimizes the influence of local inhomogeneities and provides a robust average film thickness. The initial measurements were conducted on clean, untreated samples at room temperature to establish a reference baseline.

Subsequently, the samples were subjected to systematic thermal treatments in an oven at 100°C for progressively longer durations of 30, 60, 90, and 120 minutes. After each heating step, the specimens were allowed to cool naturally to room temperature in air to minimize thermal drift artifacts during measurement. Ellipsometric analysis was then repeated on the same sample after each heating stage, enabling the investigation of the temporal evolution of the oxide layer thickness as a function of annealing time.

The optical model used for data interpretation was based on a two-layer system: a bulk carbon steel substrate and a surface oxide film. The substrate was described with a complex refractive index of $n = 2.757 + 3.392i$.¹ The overlying film was modeled as $Fe_2O_3$, with an optical constant of $n = 2.7925 + 0.1163i$.² This combination has been reported as a suitable approximation for steels with iron oxide layers of nanometric thickness. Fitting the experimental data to this model yielded reliable values for the surface film thickness, enabling a quantitative assessment of oxide growth during thermal exposure.
Overall, this procedure provides a reproducible methodology for monitoring changes in surface oxide thickness under controlled thermal conditions, which is essential for understanding the stability and growth kinetics of protective films on press-hardened steels.

The results are shown in Figure S1.

As shown in Figure S1, the surface film thickness increased with heat exposure, starting from ca. 1.5 nm for the untreated sample and reaching 3–4 nm after 120 minutes. The change between 90 and 120 minutes was relatively small (3.3 nm vs. 3.4 nm), indicating that the oxidation process slows with extended exposure time.

<figure><img src="image_12.png" /><figcaption>Figure S1: Ellipsometry measurements of film thickness on carbon steel before heat treatment and after 30, 60, 90, and 120 minutes of thermal exposure at 100°C.</figcaption></figure>

## XPS measurements

X-ray photoelectron spectroscopy (XPS) measurements were performed using a K-Alpha⁺ spectrometer (Thermo Fisher Scientific, East Grinstead, UK) operated in constant analyzer energy mode, equipped with a micro-focused, monochromatic Al Kα X-ray source (1486.6 eV, spot size diameter: 400 µm) and a flood gun (charge compensation system for insulating samples).

The samples were clipped onto the sample holder and pumped under vacuum overnight. The step size and pass energy were set to 1 eV/200 eV for the survey region and 0.1 eV/40 eV
for the high-resolution regions, respectively. Data acquisition and processing were carried out using *Avantage* software, version 5.9902. The surface chemical composition was determined using manufacturer-provided sensitivity factors.

XPS measurements were conducted to analyze the oxidation state of the surface film. Fig. S2 presents the corresponding spectra before the optical experiment. The spectral interpretation is based on the characteristic binding energies of the Fe 2p core level. The main features can be assigned as follows: the peak observed at 706.7–707.0 eV corresponds to the Fe 2p$_{3/2}$ component of metallic iron (Fe$^0$). The dominant signal in the range 710.8–711.6 eV is attributed to Fe(III) species, characteristic of Fe$_2$O$_3$. In addition, the well-known satellite structures associated with Fe(III) occur at ca. 720 eV, further confirming the presence of iron oxide. Finally, the Fe 2p$_{1/2}$ component of Fe(III) in Fe$_2$O$_3$ is detected at 724.4–725.1 eV.³,⁴

Note that XPS spectra were also recorded after the optical experiment to monitor changes in oxidation states induced by diffusion. However, the spectra showed no detectable differences. A plausible explanation is that, while hydrogen exposure may trigger transient reduction processes, the surface rapidly re-oxidizes once the treatment ends, reverting to a state primarily composed of Fe$_2$O$_3$. This rapid reversion may be driven by atmospheric oxygen, which stabilizes the Fe(III)-rich oxide layer.

In summary, XPS analysis indicates that the surface film consists of an Fe$_2$O$_3$ oxide layer, which is used as the initial surface film composition in optical modeling.
<figure><img src="image_13.png" /><figcaption>Figure S2: XPS measurements of the surface film before the optical experiment.</figcaption></figure>

SI - 2. Control experiment

To confirm the validity of the observations described above, a control experiment was con-
ducted under identical conditions, except without electrolyte and polarization. The experi-
ment lasted 9000 s, during which a microscopy video was recorded under the same imaging
conditions as in the hydrogen exposure experiment. The temporal evolution of the image
intensity is summarized in Figure SI-S3a. A slight increase in intensity of 0.1% can be ob-
served, which can be attributed to drift of the light source and/or the detector. Furthermore,
Figures SI-S3b and SI-S3c present normalized images of the same region at the beginning
and end of the control experiment, respectively. Unlike the hydrogen exposure experiment,
no distinct separation of zones is evident in the control case. The surface exhibits a homo-
geneous granular and noisy appearance, confirming that the observed spatial contrast in the
hydrogen experiment is directly related to hydrogen-induced processes and not to general
interactions with the electrolyte or imaging artifacts.
<figure><img src="image_14.png" /><figcaption>Figure S3: Control experiment without hydrogen exposure. (a) Global intensity evolution during 9000 s of immersion in 1.6 M NaCl without polarization, showing slight brightening (~0.1%), which is lower than in the hydrogen-free region of the main experiment (~0.8%, see Fig. 5 in the main text). (b) First normalized microscopy frame and (c) last normalized frame of the same region. No clear separation of zones is observed, indicating the absence of surface changes without hydrogen.</figcaption></figure>

SI - 3. Transfer matrix method of a Fe(III)/Fe(II) bilayer

For multilayered absorbing films, we employ a numerical approach based on the transfer matrix method (TMM) to simulate the reflectivity of stratified thin-film stacks. This approach enables us to correlate the experimentally measured normalized reflectivity $\frac{I(t)}{I(0)}$ with changes in the optical thickness $\delta$ (associated with the growth of the Fe₂O₃ layer) and variations in the complex refractive indices of each individual layer, such as those occurring during the reduction of Fe₂O₃ to FeO under hydrogen permeation conditions (vide infra).

In this framework, the total reflectivity at normal incidence is calculated by recursively applying the Fresnel reflection coefficients and propagation phase factors across all interfaces.

For a multilayer system composed of $N$ layers with refractive indices $n_j$ and thicknesses $d_j$,
embedded between an ambient medium ($n_0$) and a substrate ($n_{N+1}$), the complex reflection amplitude is given by

$$r = \frac{M_{11} + M_{12} \cdot n_{N+1} - M_{21} - M_{22} \cdot n_{N+1}}{M_{11} + M_{12} \cdot n_{N+1} + M_{21} + M_{22} \cdot n_{N+1}}, \quad (S1)$$

where $M$ is the overall characteristic matrix of the film stack:

$$M = \prod_{j=1}^{N} \begin{bmatrix} \cos \delta_j & \frac{i}{q_j} \sin \delta_j \\ iq_j \sin \delta_j & \cos \delta_j \end{bmatrix}, \quad \text{with} \quad \delta_j = \frac{2\pi}{\lambda} n_j d_j, \quad q_j = n_j. \quad (S2)$$

The corresponding reflectance $R$ is computed as follows:

$$R = |r|^2. \quad (S3)$$

For the specific case of a two-layer stack (Fe₂O₃/FeO on metal), the model simplifies to

$$r_{01} = \frac{n_0 - n_1}{n_0 + n_1}, \quad (S4)$$

$$r_{12} = \frac{n_1 - n_2}{n_1 + n_2}, \quad (S5)$$

$$r_{23} = \frac{n_2 - n_s}{n_2 + n_s}, \quad (S6)$$

$$\delta_1 = \frac{2\pi n_1 d_1}{\lambda}, \quad \delta_2 = \frac{2\pi n_2 d_2}{\lambda}, \quad (S7)$$

$$r_{\text{eff}} = \frac{r_{12} + r_{23} e^{2i\delta_2}}{1 + r_{12} r_{23} e^{2i\delta_2}}, \quad (S8)$$

$$r_{\text{total}} = \frac{r_{01} + r_{\text{eff}} e^{2i\delta_1}}{1 + r_{01} r_{\text{eff}} e^{2i\delta_1}}, \quad (S9)$$

$$R_{\text{total}} = |r_{\text{total}}|^2. \quad (S10)$$
This formalism accounts for multiple reflections, absorption, and interference in stratified thin films and enables direct modeling of complex transformation pathways, such as the growth of Fe₂O₃ and its reduction to FeO.

The code implementing this TMM approach is publicly available on Zenodo at https://zenodo.org/records/16363585.
SI - 4. Reflectivity Changes in RGB channels

Fig. S4 presents the experimentally measured reflectivity changes for all three channels. Panel (a) shows the reflectivity evolution in the region outside the O-ring, while panel (b) corresponds to the region inside the O-ring, which is directly affected by hydrogen. To assess the channel dependence of the reflectivity changes, raw intensity data recorded by the RGB camera are shown in Fig. S4 for the blue, green, and red channels, respectively. While the quantitative modeling in the main text was restricted to the blue channel (λ ≈ 450 nm), similar qualitative trends were observed across all three channels, with minor differences in the absolute values. These differences can be attributed to the wavelength dependence of the refractive index of the monitored Fe(III)/Fe(II) species.

<figure><img src="image_15.png" /><figcaption>Figure S4: Reflectivity changes of press-hardened steel measured with RGB channels. (a) Zone outside the O-ring (unaffected by hydrogen). (b) Zone inside the O-ring (affected by hydrogen).</figcaption></figure>
SI - 5. SKP Monitoring of PHS Potential in the Hydrogen-
Unaffected Area

To determine the effect of new oxide film growth caused by exposure of the press-hardened
steel (PHS) surface to air, the surface potential was monitored at a single point after grinding.
Measurements began ca. 15 minutes after grinding. The potential evolution during air
exposure is shown in Figure S5.

It is well known that contact of a freshly ground surface with air leads to the formation
of an oxide-hydroxide layer, which increases the surface potential due to the potential drop
across the oxide film. After 24 hours of exposure, the potential stabilizes near 0.25 V (SHE).
However, the potential continues to increase slowly even after 24 hours, reaching ca. 0.275 V
(SHE) after 72 hours. This indicates that the kinetics of oxide film growth slow down over
time but do not completely stop.

<figure><img src="image_16.png" /></figure>

Figure S5: SKP monitoring of the PHS potential under ambient conditions (T = 20 ± 1 °C, RH = 60%) over the area unaffected by hydrogen.
References

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(2) Querry, Refractive index of Fe2O3 (Iron sesquioxide, Hematite) - Querry-e — refractiveindex.info. https://refractiveindex.info/?shelf=main&book=Fe2O3&page=Querry-e, 1985; [Accessed 07-08-2025].

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