# Assessment of In-Line particle image velocimetry for turbulence measurements in porous media

A Mure d'Alexis, O Léon, D Donjat, R Roncen, F Mery

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A Mure d'Alexis, O Léon, D Donjat, R Roncen, F Mery. Assessment of In-Line particle image velocimetry for turbulence measurements in porous media. The International Symposia on Applications of Laser and Imaging Techniques to Fluid Mechanics, IN+ Center for Innovation Technology and Policy Research, Instituto Superior Técnico; ADAI Associação para o Desenvolvimento da Aerodinâmica Industrial, University of Coimbra, Jun 2026, Lisbon (Portugal), Portugal. hal-05479608

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# Assessment of In-Line Particle Image Velocimetry for Turbulence Measurements in Porous Media

A. Mure d'Alexis¹*, O. Léon¹, D. Donjat¹, R. Roncen¹, F. Mery¹

¹DMPE, ONERA, Université de Toulouse, 31000, Toulouse, France,

**Abstract** – In-line particle image velocimetry (PIV) is implemented and assessed as a measurement technique for acquiring instantaneous velocity fields within porous structures traversed by turbulent flows. Focusing on triply periodic minimal surface samples, whose geometries are analytically defined, this study evaluates the potential of in-line PIV to maximize optical accessibility relative to conventional light-sheet PIV configurations, while maintaining acceptable particle-image quality despite the unavoidable presence of light-scattering solid surfaces. The primary objective is to assess the feasibility and limitations of in-line PIV when applied through a solid porous matrix, and to identify the methodological adaptations required to obtain reliable velocity fields. This methodological groundwork aims to establish in-line PIV as a robust diagnostic tool for future investigations of turbulent flows within porous media.

## 1. Context

Experimentally probing flow dynamics within porous materials remains a major challenge, particularly when aiming to resolve the spatial distribution of turbulent fluctuations at the pore scale and across multiple pores. Non-intrusive optical diagnostics such as particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) are commonly used in free and wall-bounded flows. However, their application near solid walls is limited by optical obstruction and light-scattering. These effects can severely degrade velocity measurements, restrict spatial coverage, or prevent acquisition inside complex structures (Adrian and Westerweel, 2011).

In porous structures, classical PIV setups (using a laser light-sheet orthogonal to a camera axis) can result in large shadowed regions depending on the geometry. This is particularly illustrated in Figure 1 for the porous structure studied in the present work. Similarly, LDV beams are often blocked when probing complex porous matrices (Mure d'Alexis et al., 2025), or deviated when passing through transparent structures. Such limitations are well documented in studies of optical imaging in heterogeneous media, including index-matched flows and porous materials (Imuetinyan et al., 2024; Wildenschild and Sheppard, 2013).

To overcome these limitations, several strategies have been explored in the literature for optical measurements within porous structures. Zhang et al. (2023) and Khodsiani et al. (2024) used simplified pore geometries, such as ordered arrays of spheres or rods, which allow for easier optical access. Imuetinyan et al. (2024) employed transparent porous media with refractive-index matching (RIM) to facilitate internal visualization. Other studies, such as Seol et al. (2024), restricted measurements to near-wall regions or downstream of the porous material, where optical obstruction is reduced.

Despite promising results, these approaches remain restrictive. RIM experiments require careful tuning of refractive indices, which may vary with temperature or wavelength. Transparent porous materials are typically limited to polymers such as PMMA or hydrogels, which do not faithfully represent the optical, mechanical, or topological properties of real porous matrices. Most importantly, measurements inside porous materials often rely on oversized pores or highly idealized structures. Consequently, certain aspects of pore-scale

<footnote>*arnaud.mure_dalexis@onera.fr</footnote>
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /><figcaption>Figure 1: Schematic of a conventional PIV setup applied to the present porous gyroid structure (left), adapted from Raffel et al. (2024a), and example of a PIV image acquired with this configuration (right), illustrating light-sheet obstruction.</figcaption></figure>

turbulence, such as the conditions described by the Pore Scale Prevalence Hypothesis (PSPH) (Habib et al., 2020), cannot be thoroughly investigated.

## 2. Objective

This study aims to measure velocity fields within a representative complex porous geometry across multiple pore lengths at moderate to high Reynolds numbers, conditions that appear inaccessible via classical optical techniques. To address previous limitations, we investigate an in-line PIV configuration based on the work of Raffel et al. (2024a) and Raffel et al. (2024b). Unlike standard PIV arrangements, the in-line configuration aligns the imaging axis with the light propagation direction, thereby minimizing shadowing and light-scattering effects within the porous matrix.

The physical principles underlying this configuration are closely related to those employed in in-line digital holography and propagation-based imaging, which have demonstrated enhanced penetration in scattering media (Katz and Sheng, 2010). By using a single illumination axis, lateral scattering effects are minimized, allowing deeper probing of complex structures and improved particle imaging within obstructed regions. Moreover, this single-axis alignment greatly simplifies the handling and positioning of different samples, facilitating a wider range of experimental configurations.

This approach is particularly well-suited for investigating structures based on Triply Periodic Minimal Surfaces (TPMS), which can be readily fabricated using additive manufacturing. These geometries combine continuous curvature with high permeability, offering partial optical access that is ideal for observing the development of turbulence within the structure. The potential of this approach was recently demonstrated by Flores-Montoya et al. (2025), further establishing TPMS as a promising candidate for internal flow studies.

The objective of the present study is therefore twofold:

1. to **develop and adapt** an in-line PIV methodology tailored to the challenges of porous media, including scattering, shadowing, and geometric complexity;

2. to **validate** this approach through measurements conducted across multiple pores in a TPMS-based structure, thereby enabling future investigations of pore-scale turbulence mechanisms and the relevance of hypotheses such as the PSPH (Habib et al., 2020).
# 3. Experimental setup

## 3.1 Porous sample

This study focuses on porous geometries based on TPMS, in particular the gyroid structure shown in Figure 2. This structure is chosen for its deterministic properties, geometric regularity, and compatibility with advanced 3D printing techniques such as stereolithography (resin) printing.

For this work, a gyroid porous sample of dimensions 10 cm × 5 cm × 5 cm was manufactured, with a cell size of 5/3 cm. The material’s solid part is defined by the following equation:

<figure><img src="image_4.png" /><figcaption>Figure 2: Porous material dimensions.</figcaption></figure>

$$ \cos(k_x x) \cdot \sin(k_y y) + \cos(k_y y) \cdot \sin(k_z z) + \cos(k_z z) \cdot \sin(k_x x) > \xi, \quad (1) $$

with $\xi = 1.2$, and $k_x = k_y = k_z = 2\pi \times 3/5 \times 10^2 \text{ m}^{-1}$. This cell size was chosen to enable an initial assessment of the feasibility of in-line PIV through such a porous structure, while still retaining significant light-scattering effects from the pore walls.

## 3.2 Experimental setup

The present in-line PIV optical setup is designed with the light source and the camera aligned along the same axis, as shown in Figure 3(a). Unlike conventional orthogonal PIV configurations, this arrangement relies on forward light scattering by the seeding particles, as illustrated in Figure 3(b). Because Mie scattering is strongly anisotropic and peaked in the forward direction, an advantage of this configuration is that it requires lower illumination power than conventional PIV setups, which is favorable for high-speed acquisitions or the use of LED-based light sources. In the present study, pulsed-laser illumination is retained to ensure sufficiently short exposure time and because suitable pulsed LED equipment was not available.

The seeding is provided by a set of Laskin nozzles (PIVPart45 from PIVTEC) producing DEHS particles approximately one micron in diameterr. This size is small enough for the particles to faithfully follow the flow under the expected velocity gradients, yet large enough to scatter sufficient light for clear detection against the residual bright background, as shown in Figure 5, enabling reliable particle identification throughout the flow.

To avoid sensor saturation, the laser intensity was reduced. However, at low power, the beam becomes unstable due to fluctuations in the laser source (Label ① in Figure 3, double-pulse Nd:YAG Evergreen laser, Quantel, 532 nm). A neutral-density filter (label ②) with 5% transmission was therefore used to attenuate the light power in a controlled manner. In addition, a diffusing opal glass window (label ②) with 40% transmission and 10° divergence angle was employed to improve illumination uniformity, at the expense of a slight increase in beam divergence, which in turn slightly degrades subsequent focusing.

To compensate for the divergence introduced by the diffuser, a plano-convex aspheric lens (label ③, Effective Focal Length 50 mm, AR coating 350–700 nm) is placed at an appropriate distance to select a portion of quasi-parallel rays. These rays are then focused upstream of a 100 mm lens (label ④, Milvus Zf.2, Zeiss) to provide collimated light through the porous sample (label ⑤). The light is then focused by a 180 mm lens (label ⑥, Sigma, f/2.8) and partially blocked by a small 3D-printed light trap (label ⑦, 4 mm diameter, 2 mm thickness, black matte) positioned at its focal plane. This trap intercepts only the direct, unscattered light from the source, effectively acting as a high-pass filter in the Fourier domain, before reaching
<figure><img src="image_5.png" /><figcaption>Figure 3: Photograph (top) and schematic (bottom) of the in-line PIV setup used for measurements through the porous medium.</figcaption></figure>

the camera sensor (label ⑧, LaVision, sCMOS). The camera acquires images in a double-frame mode at 15 Hz, with a 15 µs interval between the two laser pulses for each PIV measurement.

### 3.3 Depth of Field

With this in-line configuration, the illumination spans a three-dimensional volume rather than a thin laser sheet as in classical PIV setup. Consequently, the thickness of the region in which particles are in focus and thus detectable is governed by the depth of field (DoF) of the imaging optics. A precise estimation of the DoF is therefore essential to determine the effective measurement volume.

The theoretical DoF of an optical system combined with a digital image sensor can be expressed with the following formulation (Ishiwata et al., 2022), which accounts for the effect of the sensor pixel size:

$$ \text{DoF} \approx K \frac{n\lambda}{2\text{NA}}, \qquad (2) $$

where NA is the numerical aperture of the lens n is the refractive index of the medium between the lens and the object, λ is the illumination wavelength, the coefficient K accounts for the influence of the pixel size relative to the optical system and is calculated as:

$$ K \approx \frac{1}{2} \left( A + B \frac{f_N}{f_C} \right). \qquad (3) $$

In these equations A and B are empirical coefficients, $f_C$ is the cut-off frequency of the optical system, $f_N = 1/(2c)$ is the Nyquist frequency of the sensor, and c is the pixel size of the digital sensor.

Using typical experimental parameters for our setup, this formulation leads to a theoretical DoF of approximately 1.5 mm. This estimation takes into account the finite size of the sensor pixels, which modifies the classical Rayleigh criterion.

To provide a more accurate value, an experimental estimate was obtained using a high-contrast resolution target placed at the focal plane of the imaging optics and translated
<figure><img src="image_6.png" /><figcaption>Figure 4: Determination of the DoF using a focus chart: (a) sharpness curves obtained for each region of interest; (b) regions of interest in the image plane.</figcaption></figure>

along the optical axis in steps of 0.1 mm. For each position, image sharpness was quantified using the spatial standard deviation of the intensity distribution, which provides a robust measure of local contrast. Given an image $I(x,y)$, the sharpness metric is defined as

$$ \sigma_I = \sqrt{\frac{1}{N} \sum_{x,y} (I(x,y) - \mu_I)^2}, \quad \mu_I = \frac{1}{N} \sum_{x,y} I(x,y), \qquad (4) $$

where $\mu_I$ is the mean image intensity and $N$ the number of pixels. A high value of $\sigma_I$ corresponds to a well-resolved pattern (in focus), whereas a decrease of $\sigma_I$ indicates the progressive loss of fine spatial details as the target moves out of the focal plane.

The DoF is determined as the axial range over which the *normalized sharpness* remains above a chosen threshold relative to its maximum value. Using a criterion of 60% of the peak normalized sharpness, the experimentally measured DoF is found to be approximately 3 mm.

## 4. Image preprocessing

Before performing any correlation to estimate velocity fields, the raw images are preprocessed to enhance particle detection and remove artefacts that could compromise PIV analysis. As shown in Figure 5, the raw images exhibit several challenges: the contrast between seeding particles and the background is relatively low due to residual illumination (Raffel et al., 2024a), and additional parasitic scattering occurs on the pore walls. To overcome these limitations, a sequence of preprocessing steps is applied to isolate particle images, suppress background variations, and enhance signal-to-noise ratio. These steps form the basis for the following subsections.
<figure><img src="image_7.png" /><figcaption>Figure 5: Left: example of raw in-line PIV image acquired with the setup shown in Figure 3. Right: zoom on a single porous cell used for detailed analysis.</figcaption></figure>

## 4.1 Butterworth filter

To reduce illumination drift and low-frequency fluctuations while preserving the high-frequency intensity variations generated by convected particles, a temporal Butterworth high-pass filter is applied to each pixel of the image sequence (Sciacchitano and Scarano, 2014). The filtered intensity field is defined as:

$$I_{\text{filt}}(x, y, t) = \mathcal{F}^{-1}[H(\omega) \mathcal{F}(I(x, y, t))], \quad (5)$$

where $I(x, y, t)$ is the raw image, $\mathcal{F}$ and $\mathcal{F}^{-1}$ denote direct and inverse Fourier transforms, and $H(\omega)$ is the transfer function of an n-th order Butterworth high-pass filter:

$$H(\omega) = \frac{1}{\sqrt{1 + \left(\frac{\omega_c}{\omega}\right)^{2n}}}, \quad (6)$$

with $\omega_c = 2\pi f_c$ the cut-off pulsation. This formulation removes slowly varying background illumination and low-frequency artefacts, thereby enhancing the temporal contrast of particle images inside the porous medium. Figure 6(b) shows an example of the filtered image.

## 4.2 Temporal occurrence filtering

To further isolate relevant particle images and remove transient noise, a temporal occurrence filter is applied. For each pixel, the filter counts the number of frames in which its intensity exceeds a threshold $I_{\text{min}}$. Pixels that do not exceed the threshold in at least $N_{\text{min}}$ frames are removed:

$$\text{mask}(x, y) = \sum_{i} [I(x, y, t_i) > I_{\text{min}}] > N_{\text{min}}. \quad (7)$$

This method preserves pixels corresponding to persistent particle traces while eliminating spurious bright spots caused by reflections or detector noise (Sciacchitano and Scarano, 2014). The resulting mask is applied to the images, setting all other pixels to zero (Figure 6(c)).

## 4.3 Connectivity-based masking

After temporal filtering, a connectivity-based mask is applied to eliminate spurious features, using the following steps:
1. Binarization: pixels below a threshold intensity are identified.

2. Labeling: connected regions are labeled using an 8-connectivity scheme.

3. Filtering: regions with an area below a minimum surface threshold or with abnormal mean intensity are removed.

4. Mask application: all rejected pixels are set to zero in the image.

This approach efficiently removes isolated bright spots or extended background structures that are not related to particle motion, as illustrated in Figure 6 (e).

**4.4 Summary of preprocessing steps**

The combined effect of the Butterworth temporal filter, temporal minimum subtraction, and connectivity-based masking produces clean images suitable for velocity estimation using in-line PIV. Figure 6 provides a visual summary of the different preprocessing steps applied to a representative frame:

<figure><img src="image_8.png" /><figcaption>Figure 6: Example of preprocessing treatment</figcaption></figure>

A final mask can be applied manually to remove light scattering emitted by the porous structure in regions far from the edges of the pores, such as the bottom-right area shown in Figure 6(f).

**5. Results**

The effectiveness of the proposed image preprocessing workflow is evaluated by comparing image correlation maps and resulting velocity fields obtained from raw versus preprocessed images across the full camera field of view by applying a continuous, low-velocity test flow across the porous structure. This processing step is carried out using a window-based optical-flow algorithm (FOLKI, Champagnat et al. (2011)) with a window size of 31px, yielding velocity and correlation maps that are directly comparable to those obtained with classical cross-correlation PIV algorithms.

**5.1 Correlation quality**

Figure 7 shows representative correlation maps resulting from the processing of two PIV image pairs. The correlation coefficient ranges from 0 (no correlation) to 1 (perfect correlation). As shown in Figure 7(a), processing the raw images leads to strong spatial heterogeneity, with
<figure><img src="image_9.png" /><figcaption>Figure 7: Correlation maps over the full camera field obtained by processing (a) raw PIV images, showing low and uneven correlation in obstructed regions, and (b) preprocessed PIV images, displaying more uniform correlation in flow regions.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Figure 8: Mean streamwise velocity field $U$ obtained using (a) raw images and (b) preprocessed images.</figcaption></figure>

localized peaks of high correlation caused by intense light scattering from the solid walls of the porous material. These spurious high-correlation regions are undesirable, as they bias the measurements toward artificially low velocity estimates in near-wall regions.

After applying the full preprocessing workflow, the correlation field becomes significantly more homogeneous in the observed pores. The preprocessing does not increase the maximum correlation values; instead, it suppresses spurious correlation peaks related to material-induced light scattering and equalizes correlation levels throughout the measurement region.

As a result, the measured correlation coefficients remain lower than those typically achieved in classical PIV, with values ranging between 50% and 70%. However, they are sufficiently uniform to enable robust and coherent velocity-field estimation throughout the optically accessible regions of the porous structure.

## 5.2 Example of Velocity field

The mean axial velocity fields obtained from raw and preprocessed particle images are shown in Figure 8(a) and Figure 8(b), respectively. Although the two mean fields appear broadly similar, the benefits of preprocessing are most evident in the vicinity of the pore walls. There, the proposed workflow suppresses many artefacts present in the raw-image results, thereby increasing the fraction of the pore-scale flow that is reliably resolved. More detailed illustrations
<figure><img src="image_11.png" /><figcaption>Figure 9: Overview of the experimental wind tunnel developed for turbulence investigation in porous media.</figcaption></figure>

of these improvements will be presented in the final paper.

The resulting velocity field appears coherent and continuous over most of the pore space, revealing the main flow pathways through the material. A reduction of the measured velocity magnitude is nevertheless observed in the vicinity of the pore walls. This effect does not reflect a physical flow deceleration, but rather originates from the PIV interrogation process: the finite interrogation windows partially overlap regions where no seeding particles are present (solid walls), which artificially lowers the measured displacement and thus the velocity. The application of a manually defined spatial mask to exclude wall-adjacent regions from the interrogation will be shown to mitigate this effect in the final paper, and allow a more accurate estimation of near-wall velocities.

**6. Conclusion and Perspectives**

In this study, an in-line PIV measurement methodology was developed and applied to visualize and quantify flow fields through porous media at the pore scale. A dedicated optical setup combining forward light scattering, controlled illumination, and tailored preprocessing techniques was implemented to address the specific challenges associated with measurements through complex porous structures. The proposed preprocessing pipeline, including temporal Butterworth filtering, temporal occurrence filtering, and connectivity-based masking, was shown to efficiently suppress background illumination, parasitic scattering, and noise, thereby enabling reliable particle detection and velocity estimation.

The preliminary results reported here were obtained under loosely controlled flow conditions, with the porous sample placed in an open environment. These initial measurements primarily serve to validate both the optical configuration and the image-processing methodology. In the final paper, the benefits of the proposed preprocessing workflow will be discussed in greater detail, and results obtained under more controlled flow conditions will be presented.

Indeed, following this initial validation, the experimental campaign will be extended to confined-flow configurations, enabled by the recent commissioning of the dedicated test section shown in Figure 9. In this configuration, the flow will be forced through porous samples mounted inside the test section, allowing controlled investigations of turbulence/porous media interactions. A turbulence-generating grid will be installed upstream of the porous structure to impose well-defined incoming turbulent conditions.

Future investigations will focus on TPMS architectures, with the gyroid geometry investigated first. Systematic parametric studies will then be conducted by varying key geometrical parameters, including the orientation of the structure relative to the mean flow, pore size, porosity, and unit-cell scaling. Combined with high-resolution in-line PIV measurements,
this approach will enable a detailed characterization of turbulence evolution across the porous medium, providing new insights into turbulence modulation mechanisms such as attenuation, redistribution, and regeneration of turbulent fluctuations. These results are expected to contribute to a better understanding of flow-structure interactions in architected porous media, with potential implications for applications in flow control, filtration, and heat and mass transfer.

## 7. Nomenclature

<table><tr><td>PIV</td><td>Particle Image Velocimetry</td></tr><tr><td>DoF</td><td>Depth of Field</td></tr><tr><td>ξ</td><td>TPMS structure parameter</td></tr><tr><td>λ</td><td>Wavelength of the illumination</td></tr><tr><td>NA</td><td>Numerical aperture of the lens</td></tr><tr><td>n</td><td>Refractive index of the medium between the lens and the object</td></tr><tr><td>K</td><td>DoF coefficient accounting for the pixel size effect</td></tr><tr><td>A, B</td><td>Empirical coefficients (e.g., A ≈ 1.0, B ≈ 1.1)</td></tr><tr><td>f<sub>C</sub></td><td>Cut-off frequency of the optical system</td></tr><tr><td>f<sub>N</sub></td><td>Nyquist frequency of the sensor, given by f<sub>N</sub> = 1/(2c)</td></tr><tr><td>c</td><td>Pixel size of the digital sensor</td></tr><tr><td>μ<sub>I</sub></td><td>Mean image intensity</td></tr><tr><td>N</td><td>Number of pixels in the image</td></tr><tr><td>σ<sub>I</sub></td><td>Sharpness metric</td></tr><tr><td>I(x, y, t)</td><td>Raw image intensity at pixel (x, y) and time t</td></tr><tr><td>I<sub>filt</sub>(x, y, t)</td><td>Temporally filtered image intensity</td></tr><tr><td>F</td><td>Direct Fourier transform operator</td></tr><tr><td>F<sup>-1</sup></td><td>Inverse Fourier transform operator</td></tr><tr><td>H(ω)</td><td>Transfer function of the Butterworth high-pass filter</td></tr><tr><td>ω<sub>c</sub></td><td>Cut-off pulsation of the high-pass filter</td></tr><tr><td>n</td><td>Order of the Butterworth high-pass filter</td></tr></table>

## 8. Acknowledgements

Co-funded by the European Union (ERC, POROLEAF, 101103502). The views and opinions expressed are, however, those of the authors alone and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. The authors thank Philippe Cornic for his help in designing the pre-processing image filters.

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