Melt-Pool Dynamics Quantification in LPBF via Move Contrast X-Ray Imaging

Comment 1:

The introduction lacks a quantitative performance baseline for Absorption-Contrast X-ray Imaging (ACXI) in melt pool velocimetry; without specifying its minimum detectable velocity or signal-to-noise limitations for flow features, the claimed superiority of MCXI remains insufficiently contextualized.

Response:

We sincerely appreciate this suggestion. The reviewer is correct that establishing a quantitative performance baseline for ACXI is essential for contextualizing the claimed superiority of MCXI.

In conventional ACXI, the Contrast-to-Noise Ratio (CNR) for subtle fluid features is approximately 0.78 (as quantified in Section 3.1 of the manuscript). According to the Rose Criterion, a CNR of at least 3–5 is required for reliable feature detection. These flow structures are therefore statistically invisible in ACXI, precluding any full-field flow analysis. ACXI-based velocimetry traditionally relies on discrete tracer particles, and no established method currently exists for tracer-free full-field velocimetry in standard ACXI — a gap that MCXI directly fills.

Furthermore, even with manual feature tracking in ACXI, a 1-pixel identification error at our imaging frequency (1.087 MHz) propagates to a velocity uncertainty of ~1.09 m/s. MCXI, by leveraging multi-scale frequency characteristics, reduces this to less than 2%, as validated in Section 3.2.

The following text has been added to the Introduction and to Section 3.2 of the revised manuscript:

"Despite these advances, all existing Absorption-Contrast X-ray Imaging (ACXI) approaches share a fundamental limitation: they cannot quantify the continuous full-field velocity distribution of the liquid metal inside the melt pool. This limitation has two distinct origins. First, the melt pool interior presents extremely low absorption contrast. The Contrast-to-Noise Ratio (CNR) for dynamic fluid boundaries in ACXI is approximately 0.78 under the imaging conditions of this study (Section 3.1), well below the Rose Criterion threshold of CNR ≥ 3–5 required for reliable feature detection[22,23], so that subtle internal flow structures are statistically invisible. Second, existing velocity measurement approaches in X-ray imaging rely on tracking discrete identifiable features such as gas pores or spatter particles. Particle Image Velocimetry (PIV) techniques can in principle extract velocity fields, but require the introduction of exogenous tracer particles into the melt, which risks altering local fluid properties and is impractical near the high-curvature keyhole walls where tracers are frequently absent or become trapped. As a result, the continuous, full-field flow pattern of the liquid metal itself—which directly governs heat redistribution, keyhole stability, and pore transport—has remained beyond reach of direct experimental quantification."

"The relative deviation between the optical flow results and the manual tracking reference is within 2% across all tested frames. It is important to note that manual feature-point tracking itself carries an inherent uncertainty: at a frame rate of 1.087 MHz and a spatial resolution of 1 μm/pixel, a ±1 pixel positional identification error corresponds to a velocity uncertainty of approximately 1.09 m/s—25 to 55 times larger than the absolute errors reported in Table 1 (0.02–0.05 m/s). The reported within-2% agreement therefore represents a conservative upper bound on the disagreement between the two methods, not an absolute accuracy claim."

Comment 2:

The methodological description of the Horn-Schunck optical flow implementation omits the convergence criteria, including the iteration number and tolerance, which are essential for assessing the accuracy and reproducibility of the velocity field calculations.

Response:

We agree. Convergence criteria are essential for reproducibility and were inadvertently omitted. The following parameters apply to our implementation of the Horn-Schunck iterative solver (Equations 7–8):

Maximum iterations: 200 per pyramid level (fallback termination criterion).

Convergence tolerance: Normalized L2-norm of successive velocity field updates: ||u^(k+1) − u^k||₂ / ||u^k||₂ < ε = 1×10⁻⁴.

Early stopping: Iteration terminates once the tolerance is met, whichever comes first.

Under the imaging conditions of this study (512×512 pixels, α = 0.1), convergence is typically achieved within 80–120 iterations at the finest pyramid level, corresponding to ~0.5 s per frame pair. The following text has been added to Section 2.2.2:

"Convergence is assessed using the normalized L2-norm of the velocity field update between successive iterations: ||u^(k+1) − u^k||₂ / ||u^k||₂ < ε, where the tolerance ε is set to 1×10⁻⁴. A maximum iteration count of 200 is imposed per pyramid level as a fallback termination criterion. Under the imaging conditions of this study (512×512 pixels, α = 0.1), convergence is typically achieved within 80–120 iterations at the finest pyramid level, corresponding to a wall-clock time of approximately 0.5 s per frame pair on a standard desktop workstation (MATLAB R2022b, Intel Core i7). These parameters were fixed prior to all experimental analyses reported in this manuscript."

Comment 3:

The smoothing factor (α = 0.1) was selected based solely on comparison with feature point tracking, but the manuscript does not address whether this parameter is transferable across different processing conditions or materials, nor does it propose a strategy for adaptive parameter selection.

Response:

We thank the reviewer for raising this important methodological question. The transferability of α = 0.1 is indeed a key concern for the generalizability of our method. We acknowledge the original manuscript was insufficient on this point and have added the following discussion to Section 2.3:

The value α = 0.1 was optimized specifically for Ti-6Al-4V under the experimental conditions used (205 W, 500 mm/s). The optimal α balances: (i) image CNR level; (ii) the characteristic magnitude of flow velocity gradients; and (iii) the relationship between frame rate and inter-frame displacement. Direct application of α = 0.1 to other material systems (e.g., 316L stainless steel, AlSi10Mg) or substantially different laser parameters is not recommended without validation. The following adaptive selection framework has been added to Section 2.3:

"It is important to note that the transferability of α = 0.1 across different material systems or processing conditions cannot be assumed a priori. The optimal α represents a balance between the velocity gradient magnitude (which scales with melt pool flow speed and laser power) and the image contrast-to-noise ratio (CNR). As a practical guideline, we propose the following adaptive selection strategy: (i) estimate the image CNR from a static background region; (ii) compute the expected maximum inter-frame displacement =/ (pixel_size × frame_rate); (iii) select α according to the empirical relationship , where = 7.78 and correspond to the Ti-6Al-4V reference conditions in this study. This framework provides an initial estimate that should be refined through validation against trackable feature points whenever they are available in the dataset. For conditions significantly deviating from those in this study (e.g., α-Al alloys with higher thermal diffusivity or substantially different laser power densities), a dedicated calibration step is strongly recommended.

"

Comment 4:

The demonstration of near-equal positive and negative momentum in the melt pool does not quantify the residual momentum imbalance or account for momentum exchange with the solid substrate and vapor ejection, which would provide a more complete verification of the conservation argument.

Response:

We thank the reviewer for this valuable observation. We have added the following quantitative analysis to Section 3.3:

Residual momentum imbalance: In the X-direction, the residual imbalance is |49.7% − 50.3%| = 0.6%; in the Y-direction it is |50.3% − 49.7%| = 0.6%. Both values are well below the measurement uncertainty (<2%) and confirm that the extracted velocity field is free of systematic directional bias.

Boundary momentum exchange: (i) Solid substrate: The solidification front velocity (~0.5 m/s) is more than one order of magnitude lower than the peak internal flow velocity (~12 m/s), contributing <4% to the total momentum budget — a secondary effect within our statistical framework. (ii) Vapor ejection: Under the quasi-steady melt-pool conditions of the dataset, vapor ejection introduces a net upward momentum of approximately 2–3% of the total, explaining the slight positive Y-direction bias (0.6%) observed in Figure 2(b).

The following text has been added to Section 3.3 of the revised manuscript:

"From a physical perspective, the LPBF melt pool is a locally closed fluid system, where internal flow is jointly driven by surface tension gradients (Marangoni convection), recoil pressure, gravity, and buoyancy, forming a complex three-dimensional flow field [12]. In a closed recirculating system with no net external momentum input, conservation of mass and momentum requires that the time-averaged positive and negative momentum components in any given direction remain approximately balanced. The near-equal distribution of positive and negative momentum fractions observed in Figure 2(a),(b) (~49.7%/50.3% in X, ~50.3%/49.7% in Y) is consistent with this physical expectation, and provides an internal self-consistency check demonstrating that the extracted 2D projected velocity field is free of systematic directional bias. While a 2D projection cannot constitute a rigorous proof of three-dimensional momentum conservation, this result supports the physical plausibility of the calculated velocity field and confirms the absence of systematic algorithmic drift."

Comment 5:

The interpretation of the Quasi-stationary Stagnation Zone (QSSZ) as a region of local force equilibrium is presented without quantitative estimates of the recoil pressure, capillary pressure, and hydrostatic pressure, thereby limiting the mechanistic insight into the claimed dynamic balance.

Response:

We sincerely thank the reviewer for this insightful suggestion. We fully agree that a mechanical analysis is vital for validating the QSSZ interpretation. We provide the following quantitative force balance analysis, which has been incorporated into the Discussion section of the revised manuscript.

The QSSZ is first established as a direct observational fact from MCXI frequency-domain images: according to the fundamental principle of move contrast imaging, image contrast in MCXI reconstructed images originates from the relative motion of material components: regions where constituents undergo no relative motion, or only extremely weak motion, appear as black or near-zero-contrast areas. The temporal frequency amplitude in the QSSZ region approaches the noise floor prior to any optical flow computation, confirming near-zero material motion independently of any algorithmic smoothing.

We then provide the following pressure estimates for the QSSZ location (keyhole mid-wall, not the laser-irradiated bottom):

Peak vs. Local Recoil Pressure (Pᵣ): At the laser-irradiated keyhole bottom (T ≈ 3560 K, near boiling point), the peak Pᵣ ≈ 0.1–1 MPa (from Pᵣ ≈ 0.54×p_atm×exp[Lᵥ(T−Tᵦ)/(RᵦTTᵦ)]). However, the QSSZ is located on the mid-wall, where: (i) multiple reflections attenuate the local energy density (~44% of initial energy remains after two bounces at ~34% absorption per reflection); (ii) a steep lateral temperature gradient exists. Since Pᵣ decays exponentially with temperature, a drop of 300–400 K reduces the local Pᵣ to approximately 10–30 kPa.

Capillary Pressure (Pᵧ): Pᵧ = γ/R, where γ ≈ 1.5 N/m for liquid Ti-6Al-4V at ~1600 K. Using our measured keyhole curvature R ≈ 50–100 μm near the QSSZ boundary, Pᵧ ≈ 15–30 kPa.

Hydrostatic Pressure (Pₕ): Pₕ = ρgh ≈ 4000 × 9.8 × (200–400) × 10⁻⁶ ≈ 8–16 Pa. This is four orders of magnitude smaller than Pᵣ and Pᵧ, and is negligible.

These estimates confirm that a localized dynamic equilibrium is established at the QSSZ between the locally attenuated recoil pressure (~10–30 kPa) and the capillary pressure (~15–30 kPa). The following text has been added to the Discussion section:

"The mechanical origin of the QSSZ can be elucidated through a quantitative force balance analysis. While the peak recoil pressure (Pᵣ) at the laser-irradiated keyhole bottom (T ≈ 3560 K) reaches 0.1–1 MPa, the QSSZ is spatially localized on the mid-keyhole wall, where multiple reflections and the shadowing effect significantly attenuate the local energy density, reducing the local Pᵣ to approximately 10–30 kPa. Simultaneously, the local capillary pressure (Pᵧ = γ/R) is estimated at 15–30 kPa based on the measured curvature and surface tension. The hydrostatic pressure (Pₕ ≈ 8–16 Pa) is negligible. The convergence of local Pᵣ and Pᵧ to the same order of magnitude creates a localized 'cooling-weakening zone' where the net driving force vanishes, consistent with the near-zero velocity measurements and the stabilization of the QSSZ area observed in Figure 3(e)."

Comment 6:

The division of the keyhole evolution cycle into three stages is descriptive, but the analysis does not establish quantitative correlations between the duration of each stage or the critical aspect ratio for stratification and the controllable laser parameters, reducing the predictive utility of the proposed framework.

Response:

We thank the reviewer for this important observation. We acknowledge that establishing quantitative correlations between stage durations and controllable laser parameters would substantially enhance the predictive utility of the proposed framework. However, this study is built upon a single-condition open-source dataset (Zhao et al. [21], 205 W, 500 mm/s), which does not permit the construction of a multi-parameter statistical correlation across different P-V conditions.

The primary scientific contribution of this work is to establish the MCXI-based full-field velocimetry framework and to reveal the three-stage physical mechanism — a capability that was previously inaccessible with ACXI. Establishing quantitative P-V phase diagrams of critical stage parameters across a systematic matrix of laser conditions constitutes an important and logical next step, and we have explicitly added this as a future research direction in the Discussion and Conclusions sections of the revised manuscript.

Comment 7:

The quantitative pore pinch-off velocities are compared to simulations, but the manuscript does not discuss how these experimental measurements could be used to refine or validate the physical sub-models (e.g., surface tension, recoil pressure) within existing computational models.

Response:

We thank the reviewer for pointing out this important translational dimension of our results. The following discussion has been added to the Discussion section of the revised manuscript:

"Beyond direct numerical validation, the measured pinch-off kinematics provide quantitative constraints for refining physical sub-models in computational frameworks. First, the collision velocity of ~8 m/s, combined with the measured neck width at pinch-off (~10–20 μm from MCXI images) and the known dynamic viscosity of liquid Ti-6Al-4V (μ ≈ 0.005 Pa·s), yields a capillary number Ca = μV/γ ~ 0.025, enabling back-calculation of the effective surface tension γ_eff at the pinch-off temperature. Discrepancies between this back-calculated value and the temperature-dependent surface tension model used in simulations (typically dγ/dT ≈ −0.26 mN/m·K for Ti-6Al-4V) would identify systematic errors in the thermophysical property databases employed. Second, the ~1–2 μs acceleration window inferred from the MCXI velocity sequence places a quantifiable test on the accuracy of Hertz-Knudsen evaporation models near the boiling point. These experimental benchmarks are intended to provide the additive manufacturing simulation community with directly actionable data for sub-model calibration."

Comment 8:

The conclusions do not explicitly translate the identified three-stage keyhole dynamics and critical porosity conditions into actionable strategies for process control, such as closed-loop laser power modulation, limiting the practical impact of the findings.

Response:

We fully agree with the reviewer that translating fundamental physical findings into actionable engineering strategies is critical for demonstrating practical impact. The following content has been added to the Discussion and Conclusions sections:

"The quantitative findings of this study translate directly into actionable strategies for LPBF process control. First, the identification of the critical J-shaped aspect ratio threshold (d/h = 1.31 for pore-generating cycles versus d/h = 0.69 for stable cycles) provides a morphological criterion that can be incorporated into real-time process monitoring systems: when in-situ imaging or proxy sensors detect the onset of stratified flow at the keyhole tail, a brief laser power increment (~+10–20% power, ~2–5 μs duration) can be triggered to maintain sufficient recoil pressure and prevent the keyhole from crossing the critical aspect ratio threshold. Second, since pore pinch-off consistently occurs during the late contraction phase (~23–27 μs within a ~24 μs cycle), time-resolved power modulation synchronized to the predicted keyhole evolution cycle could suppress pore nucleation events with minimal perturbation to overall energy input. Third, the elevated porosity risk at scan initiation and termination supports the use of power ramp-up and ramp-down profiles at scan path endpoints, with ramp durations matched to the measured expansion-phase timescale (~5 μs). These control strategies constitute a physically grounded roadmap for closed-loop laser parameter optimization aimed at keyhole porosity suppression."

Comment 1:

The main concern is that the novelty is not clearly demonstrated. The authors position MCXI as a significant advance over absorption contrast imaging (lines 46-55), but the actual contribution seems to be the combination of an existing contrast enhancement approach with a well-established optical flow method. The manuscript does not clearly explain what fundamentally new capability is achieved compared to prior work that already uses high-speed X-ray imaging and motion analysis. The Introduction cites a large number of references, but these are grouped and not discussed individually. For example, the blocks [1-3], [4-7], [26-29], [30-32], [33-35] and especially [8-15] & [16-21] are presented without explaining what each group contributes or what gap remains. As a result, the motivation feels overstated.

Response:

We sincerely thank the reviewer for this critical and constructive evaluation. We acknowledge that the original manuscript did not sufficiently articulate the fundamental novelty of the contribution, and that grouped citations without individual explanation obscured both the state of the art and the remaining gap. We have substantially revised the Introduction to address all aspects of this comment.

On the novelty of the MCXI–optical flow framework:

The key point is that this work is not a mere combination of existing tools. MCXI is not a simple contrast enhancement algorithm—it applies frequency-domain filtering to time-series pixel intensity data, selectively retaining target-motion signals while suppressing static background noise, enabling CNR improvements of ~10× over ACXI at the same keyhole boundary (confirmed in Section 3.1 ). Crucially, prior MCXI implementations (refs [24]–[29]) extracted motion signals only qualitatively; none derived quantitative velocity fields. Similarly, optical flow methods have never been applied to LPBF melt-pool imaging because standard ACXI images lack the trackable texture required. The combination of MCXI—which makes the invisible visible—with the Horn–Schunck optical flow framework achieves, for the first time, tracer-free full-field pixel-level velocity measurement of the LPBF melt-pool interior. This has been made explicit in the revised Introduction:

“Despite these advances, all existing Absorption-Contrast X-ray Imaging (ACXI) approaches share a fundamental limitation: they cannot quantify the continuous full-field velocity distribution of the liquid metal inside the melt pool. This limitation has two distinct origins. First, the melt pool interior presents extremely low absorption contrast. The Contrast-to-Noise Ratio (CNR) for dynamic fluid boundaries in ACXI is approximately 0.78 under the imaging conditions of this study (Section 3.1), well below the Rose Criterion threshold of CNR ≥ 3–5 required for reliable feature detection[22,23], so that subtle internal flow structures are statistically invisible. Second, existing velocity measurement approaches in X-ray imaging rely on tracking discrete identifiable features such as gas pores or spatter particles. Particle Image Velocimetry (PIV) techniques can in principle extract velocity fields, but require the introduction of exogenous tracer particles into the melt, which risks altering local fluid properties and is impractical near the high-curvature keyhole walls where tracers are frequently absent or become trapped. As a result, the continuous, full-field flow pattern of the liquid metal itself—which directly governs heat redistribution, keyhole stability, and pore transport—has remained beyond reach of direct experimental quantification.”

On the grouped citations [16]–[21] (in-situ synchrotron X-ray imaging):

The original manuscript cited refs [16]–[21] as a block without distinguishing their individual contributions. We have revised this paragraph to individually describe each work and the residual gap:

“In situ synchrotron X-ray imaging has provided unique and transformative insights into LPBF melt-pool dynamics and defect formation mechanisms [16-21]. Studies by Parab et al. [16], Leung et al. [17], and Cunningham et al. [18] established ultrafast imaging platforms and revealed keyhole formation thresholds, morphological transitions, and defect dynamics with sub-microsecond temporal resolution. Zhao et al. [21] further identified the critical keyhole-tip instability as the primary mechanism of porosity generation. Despite these advances, all existing Absorption-Contrast X-ray Imaging (ACXI) approaches share a fundamental limitation: they cannot quantify the continuous full-field velocity distribution of the liquid metal inside the melt pool. ”

The two distinct origins of this limitation—low CNR of internal flow structures and the absence of trackable tracer texture—are then individually articulated, with the CNR quantification explicitly referenced to the Rose Criterion [22,23].

On the grouped citations [8]–[15] (process maps, simulations, and laser welding):

This has been made explicit in the revised Introduction:

"Over the past decade, research has shifted from empirical Power–Velocity process maps and post-mortem defect analysis [8–10] toward understanding the microscale physical mechanisms that underlie defect formation. High-fidelity numerical simulations have revealed the complex multi-physics of melt flow, keyhole instability, and pore generation [11–14], and analogous studies in laser welding have further demonstrated the critical role of transient internal flow in keyhole dynamics [15]. However, these models require experimental velocity-field data for calibration of key sub-models such as surface tension and recoil pressure—data that have remained experimentally inaccessible."

Comment 2 :

The validation of the method is also too limited. The authors base their accuracy claim on four feature points, which is not sufficient to demonstrate robustness. The comparison with manually tracked velocities (lines 236-243) is reasonable as a first step, but manual tracking itself introduces uncertainty, which is only briefly acknowledged (lines 250-253) and not quantified. There is no comparison with alternative velocity extraction techniques or with numerical simulations beyond qualitative agreement. The statement that the method achieves “high accuracy” within 2% should therefore be treated more cautiously.

Response:

We thank the reviewer for these precise observations. We address each sub-issue separately.

On the limited number of feature points:

We wish to clarify that Table 1 in the manuscript presented a representative subset of the full validation dataset for brevity. To directly address the reviewer's concern, we provide here the complete validation dataset as Table R1, comprising all feature points tracked across different frames throughout the 30 image sequence. Across this full set, the relative deviation between the MCXI–optical flow result and the manual tracking reference remains consistently below 2% in all cases. The imaging data (Zhao et al. [21]) were acquired at 1.087 MHz in a keyhole-mode LPBF environment where gas pores and spatter particles — the only available natural tracers — appear intermittently and are frequently consumed by the solidification front or ejected from the imaging plane. This physical scarcity of trackable features is a constraint shared by all prior ACXI-based velocimetry studies in LPBF.

On the absence of comparison with alternative velocity extraction techniques or numerical simulations:

We agree this is an important concern and wish to clarify why direct methodological comparison is not feasible in this configuration. Standard Particle Image Velocimetry (PIV) requires seeding the melt with exogenous tracer particles — which is physically impractical in a LPBF keyhole environment operating at ~3560 K with high-curvature interfaces, and would alter the local fluid properties being measured. Digital Image Correlation (DIC) is restricted to surface displacements and cannot access internal melt pool flow. To our knowledge, no established tracer-free full-field velocimetry benchmark exists for this imaging configuration, which is precisely the gap this work aims to fill. It is also instructive to note that the velocity measurements reported in the original dataset publication — Zhao et al. [21] — were themselves obtained by manually computing pixel displacements of identifiable features divided by the known frame interval, with no automated full-field method applied. The fact that even the state-of-the-art reference study in this field relied on sparse manual tracking further confirms that no superior alternative benchmark is currently available against which to compare the proposed method.

On the manual tracking uncertainty and the 2% accuracy claim:

In our validation procedure, the manual tracking velocity was computed specifically along the principal direction of maximum velocity of each feature point — the direction in which inter-frame displacement is largest and the positional identification of a high-contrast feature (gas pore) is most reliable. For the feature points in Table 1, the inter-frame displacement along this direction ranges from approximately 3 to 4 pixels. For a high-contrast feature identified to sub-pixel precision, a conservative positional uncertainty of ±0.5 pixels per frame is appropriate, yielding a displacement uncertainty of ±0.5 pixels and a corresponding velocity uncertainty of approximately 0.5/3.5 ≈ 14% in the worst case. The MCXI–optical flow velocity was extracted as the maximum velocity component along the same direction at the corresponding pixel, ensuring a controlled and consistent comparison basis.

Under this aligned comparison protocol, the within-2% agreement between the two independently derived velocities — well within the ~14% uncertainty of the manual reference itself — confirms that the optical flow result is fully consistent with the best available experimental ground truth under these imaging conditions, and exhibits no systematic directional bias. The 2% figure therefore does not represent an absolute accuracy claim, but rather a conservative upper bound on method disagreement. To reflect this more carefully, we have revised the accuracy statement in Section 3.2 as follows:

"The relative deviation between the MCXI–optical flow result and the manual tracking reference is within 2% across validated feature points, representing a conservative upper bound on method disagreement. Both velocities were evaluated along the principal direction of maximum displacement, where inter-frame displacements are largest and positional identification of high-contrast features is most reliable. This level of agreement, well within the inherent uncertainty of the manual tracking reference, confirms that the proposed method reproduces the available experimental ground truth without systematic bias."

Comment 3:

Several claims go beyond what the data can support. For example, the statement that the velocity field “rigorously validates system momentum conservation” (lines 291-2945) is too strong. A near-equal distribution of positive and negative velocity components in a 2D projection does not constitute a rigorous validation of conservation laws.

Response:

We thank the reviewer for this precise observation.

 We agree completely. The near-equal distribution of positive and negative velocity components in a 2D projection does not constitute a rigorous proof of three-dimensional momentum conservation. All instances of 'rigorously validates/verifies momentum conservation' have been replaced throughout the manuscript with the following formulation:

"...consistent with the physical expectation for a closed recirculating flow system, providing an internal self-consistency check demonstrating that the extracted 2D projected velocity field is free of systematic directional bias. While a 2D projection cannot constitute a rigorous proof of three-dimensional momentum conservation, this result supports the physical plausibility of the calculated velocity field and confirms the absence of systematic algorithmic drift."

Comment 4:

Similarly, the introduction of the “quasi-stationary stagnation zone” (lines 332-334) is interesting, but it is not clear whether this feature reflects a real physical phenomenon or an artifact of filtering and smoothing in the optical flow calculation. The paper does not provide enough evidence to distinguish between these possibilities.

Response:

We thank the reviewer for raising this important concern.

We acknowledge that this distinction was not made explicitly, and have substantially revised Section 4.1 to address it. We provide three lines of evidence that together support the physical origin of the QSSZ.

First, the QSSZ is identifiable directly in the raw MCXI frequency-domain images—prior to any optical flow computation—as a region of near-zero temporal frequency amplitude approaching the noise floor. This low-signal region is not introduced by optical flow smoothing; it is present in the input data before velocity calculation begins.

Second, the spatial character of the QSSZ is inconsistent with what would be expected from a smoothing artifact. Algorithmic smoothing due to the regularization parameter α would produce a diffuse, geometry-independent velocity reduction that broadens gradually from high-gradient boundaries. Instead, the QSSZ is sharply localized to the keyhole mid-wall region, away from the high-irradiance tip, and has a well-defined boundary adjacent to the high-speed zone. This geometry-specific localization reflects the underlying laser energy-deposition pattern rather than numerical regularization.

Third, the temporal evolution of the QSSZ area (Figure 3(e))—rapid initial growth followed by stabilization—matches the physically expected dynamics of keyhole expansion reaching a morphologically quasi-steady state. A smoothing artifact would not exhibit this physically interpretable temporal signature.

“A Quasi-Stationary Stagnation Zone (QSSZ) is identified directly from the MCXI frequency-domain amplitude images as a spatially localized region where the temporal-frequency amplitude approaches the noise floor—prior to any optical flow computation. According to the fundamental principle of move contrast imaging, image contrast in MCXI reconstructed images originates from the relative motion of material components: regions where constituents undergo no relative motion, or only extremely weak motion, appear as black or near-zero-contrast areas. The low-amplitude region visible in Figure 3(b) and (d) (marked by the triangle) therefore constitutes a direct imaging observation that material motion within this zone is negligible. This near-zero contrast region is present in the input data before velocity calculation begins, confirming that the QSSZ is a genuine physical feature of the flow field and not an artifact introduced by optical flow smoothing.”

Comment 5:

The discussion of pore formation raises similar concerns. The authors argue that pore formation is driven primarily by local pressure imbalance and surface tension effects (lines 449-453), and they dismiss vortex-driven mechanisms by referring to low Reynolds numbers (lines 462-465). However, this argument is not developed in sufficient detail. The flow field is inferred from 2D projections, and the limitations of this assumption are acknowledged but not fully addressed. As a result, the physical interpretation remains somewhat speculative.

Response:

The reviewer is correct that the original Reynolds number argument lacked explicit calculation. We have added the full quantitative estimate to Section 5.3. Using a measured exterior flow velocity of V ≈ 0.8 m/s, a characteristic melt-pool width of L ≈ 200 μm, and the kinematic viscosity of liquid Ti–6Al–4V of ν ≈ 0.5 × 10⁻⁶ m²/s, the Reynolds number is Re = VL/ν ≈ 320, well below the threshold at which coherent vortex structures are expected to form(2000). This quantitative estimate makes the argument self-standing.

We also accept the reviewer's point regarding the 2D projection constraint. We have revised all causal claims in Section 4.3 from definitive language ('proving that...') to appropriately qualified language ('consistent with a mechanism in which...'). We have explicitly acknowledged that out-of-plane vortical components cannot be excluded from 2D imaging data alone, and that the physical interpretation is accordingly qualified. The measured pinch-off velocity (7.98–8.04 m/s) is now presented as providing experimental support for the velocity scale of the pinch-off event, independent of the specific driving mechanism.

“This process partially aligns with the porosity generation mechanism revealed by Yu and Zhao [39] through high-fidelity simulations. However, the physical mechanism inferred in the present work differs from their analysis, which attributed pore detachment to a vortex driven by the combined motion of the keyhole tail and the surrounding melt. In the present measurements, the flow velocity of the melt pool outside the keyhole is below 0.8 m/s. Using a characteristic length of L ≈ 200 μm (melt-pool width) and the kinematic viscosity of liquid Ti–6Al–4V of ν ≈ 0.5 × 10⁻⁶ m²/s, the Reynolds number of the exterior melt flow is Re = VL/ν ≈ (0.8 × 200 × 10⁻⁶) / (0.5 × 10⁻⁶) ≈ 320, well below the threshold at which coherent vortex structures are expected to form(2000[42]). This quantitative estimate suggests that vortex-driven momentum transfer is unlikely to account for the observed pinch-off kinematics under the present conditions, and that the capillary-pressure-dominated collapse mechanism is more consistent with the measured data. We acknowledge, however, that the present measurements are based on 2D projections of a three-dimensional flow field, and that out-of-plane vortical components cannot be excluded from the imaging data alone. The collision velocity of 6–8 m/s predicted by the simulations of Yu and Zhao is in close quantitative agreement with the measured values in this work (7.98–8.04 m/s), providing experimental support for the velocity scale of the pinch-off event regardless of the underlying driving mechanism.”

Comment 6:

Structurally, the manuscript would benefit from a clearer separation between results and discussion. Section 4 mixes observation with interpretation throughout. A dedicated Discussion section would help clarify what is directly supported by the data and what is an interpretation.

Response:

We thank the reviewer for this structural suggestion and fully agree. The revised manuscript has been restructured as follows:

Section 4 (Results): Presents quantitative measurements directly supported by data — velocity field evolution, QSSZ area measurements, three-stage keyhole dynamics, and pore pinch-off kinematics.

Section 5 (Discussion): Contains physical interpretations, including the QSSZ force balance analysis, the mechanistic explanation of three-stage destabilization, the Reynolds number analysis for pore formation, and the process control implications.

This reorganization clearly delineates what is a direct experimental result and what is a physical interpretation.

Comment 7:

Regarding self-citation, there is a noticeable concentration of references to MCXI-related work authored by the same group or closely affiliated researchers ([22-29]). This is expected to some extent, since the method originates from this research line. However, the manuscript relies heavily on these sources to define the technique, while offering limited comparison with independent studies. The balance should be improved by citing and discussing alternative or competing approaches from other groups.

Response:

We appreciate this observation. The concentration of references [22-29] is inherent to establishing the MCXI technique, as no independent reimplementations exist. However, we accept the reviewer's broader point and have added the following discussion of independent alternative approaches to the Introduction and Discussion:

Particle Image Velocimetry (PIV) adapted for X-ray imaging can in principle provide velocity fields, but requires exogenous tracer particles that risk perturbing local fluid properties and cannot access the keyhole interior. Digital Image Correlation (DIC) provides full-field surface displacement but is limited to the sample surface. The optical flow methods we employ have an extensive independent literature [32–35] — the benchmarking work of Barron et al. [32], the iterative framework of Lucas and Kanade [33], and the fluid-dynamics extensions of Heitz et al. [34] — and we have strengthened the connection to these independent foundations in the revised manuscript.

Comment 8:

Figure 1 needs to be revised for readability. The scale markers are too small and difficult to discern, especially when viewed at standard zoom levels. This makes it hard to interpret the spatial dimensions of the features being analyzed. The authors should enlarge the scale bars and ensure that their labels are clearly legible.

Response:

We thank the reviewer for this observation. Figure 1 has been revised in the updated manuscript with enlarged scale bars (100 μm, font size ≥ 10 pt, high-contrast background), enlarged axis labels with physical units, and spatial dimensions of key features annotated directly on the images. All figures have been regenerated at ≥ 300 dpi to ensure legibility at standard print and screen zoom levels.

Comment 9:

There are clear inconsistencies in reference numbering. Reference [25] appears after [23], reference [39] appears after [32], and reference [38] appears after [36]. This violates the required sequential order of numerical citations and must be corrected throughout the manuscript.

Response:

We sincerely apologize for this error. All reference numbers have been corrected throughout the manuscript to strictly follow the order of first citation in the text. The reference list has been renumbered accordingly, and all in-text citations have been verified to match.

We sincerely thank all three reviewers for their careful reading and constructive comments. The detailed feedback has significantly improved the quality, rigor, and clarity of the manuscript. We have revised the manuscript accordingly and provide point-by-point responses below. All changes to the manuscript are highlighted in the revised version for easy reference.

Comment 1:

Please emphasize more precisely in the Abstract as well as in the Introduction the scientific novelty and industrial contribution of your investigation.

Response:

We thank the reviewer for this suggestion. We acknowledge that the original manuscript did not articulate the novelty and industrial contribution with sufficient clarity. The Abstract and Introduction have been revised to explicitly highlight: (1) the fundamental novelty — the first tracer-free full-field pixel-level velocity measurement of the internal LPBF melt pool, which was previously inaccessible by any ACXI-based method; (2) the industrial contribution — the provision of quantitative velocity-field data and critical aspect ratio thresholds that directly enable closed-loop laser power modulation strategies for keyhole porosity suppression.

The revised text added to the Introduction reads:

"To address this challenge, this work proposes a quantitative analysis framework that couples Move Contrast X-ray Imaging (MCXI) with the Horn–Schunck global optical flow method. By coupling MCXI — which converts previously invisible internal melt flow into detectable dynamic signals — with the Horn–Schunck optical flow method — which translates those signals into quantitative pixel-level velocities — the present work achieves, for the first time, tracer-free full-field velocity measurement of the LPBF melt-pool interior."

Comment 2:

I would suggest adding a methodology framework figure that will present more clearly the investigation steps of your paper.

Response:

We thank the reviewer for this suggestion. While adding a new methodology framework figure is beyond the scope of the current revision timeline, we have revised the Introduction to include a more structured and explicit description of the analysis pipeline. The revised paragraph clearly presents the three-step workflow: (1) raw X-ray image acquisition, (2) MCXI frequency-domain filtering to extract motion signals, and (3) Horn-Schunck optical flow computation to derive pixel-level velocity fields. This textual description serves as a clear methodological roadmap for readers.

Comments 3, 4, 5, 6, and 7:

I would suggest to describe more detailed experimental setup. Please add one subchapter for this purpose. Describe experimental procedure, as well as input proces parameters and corresponding responses.

Please, describe how did you perform experimentations. What kind of experimental plan you applied. Please, express in specific tables variable as well as constant process parameters. How did you define variable process parameters values?

Please, add more figures of experimental samples.

I would suggest to add validations tests that will make your research more relevant.

I would suggest to develop (if possible) equations that would be able to describe relations between inputs and output. Correspondingly, response surface plot that visualise that relations.

Response:

We sincerely thank the reviewer for these detailed suggestions. We would like to clarify an important aspect of this work: the manuscript is primarily a methods contribution focused on developing and validating the MCXI-based full-field velocimetry framework. The experimental data are drawn from a publicly available open-source dataset (Zhao et al. [21]), which was originally collected and published as an independent study. We did not perform the X-ray imaging experiments ourselves.

As a result, it is not possible for us to report additional experimental samples, expand the experimental design to multiple parameter sets, or generate response surface plots — as all data originate from a single fixed-condition dataset (205 W, 100 μm spot, 500 mm/s scan speed). The experimental conditions are fully specified in that published work [21].

In response to the reviewer's suggestion, we have added a more complete description of the experimental setup and imaging parameters in the data declaration section of the revised manuscript, including the laser source, imaging temporal and spatial resolution, and material system:

"The raw image data used in this paper originate from the open-source dataset [21], which reports in-situ high-speed synchrotron X-ray imaging experiments of a Ti-6Al-4V alloy laser melt pool. The experiment utilized synchrotron X-rays as the light source. Laser parameters: power 205 W, spot diameter ~100 μm, scanning speed 500 mm/s. The temporal resolution of the imaging data is 1.087 MHz, and the spatial resolution is 1 μm/pixel."

Comment 8:

Please add in the Conclusions the limitations and constraints of your paper as well as open directions for future investigations.

Response:

We thank the reviewer for this suggestion. The Conclusions section has been expanded to explicitly address the limitations of the proposed method and future research directions. The following text has been added:

"Although the proposed method achieved excellent results, certain limitations remain: the quality of move contrast images directly affects optical flow accuracy; the smoothing factor α lacks automatic adaptability across different material systems and processing conditions; boundary handling may lose information at the melt pool edges; and 2D projection analysis cannot capture 3D flow components. Future work could combine GPU parallel computing to enhance computational efficiency, leverage deep learning for adaptive optimization of the smoothing factor, further improve MCXI temporal resolution, and expand toward quantitative analysis of 3D velocity fields. Additionally, establishing systematic correlations between the identified three-stage keyhole dynamics and controllable laser parameters across a matrix of P-V conditions represents an important next step for translating the present findings into predictive process design tools."