Build-Height-Synchronized Fringe Projection System

• The build-height-synchronized fringe projection system is a structured-light technique that actively synchronizes projector–camera geometry with rising layer height in laser DED.
• It projects sinusoidal fringes and uses phase demodulation to achieve in-situ, layer-wise surface reconstruction with an accuracy of ±46 μm compared to microscope measurements.
• The system integrates calibrated repositioning, rotation-based measurement, and geometry-driven anomaly detection (LPD and NCR) for real-time quality assurance in additive manufacturing.

Searching arXiv for the cited DED fringe projection and related dynamic fringe projection papers. A build-height-synchronized fringe projection system is a structured-light module whose projector–camera geometry and working distance are actively adjusted in step with the nominal layer height, so that the focal plane and triangulation baseline remain constant across layers. In laser powder-blown directed energy deposition (DED), where the measurement surface rises layer-by-layer, this synchronization is used to preserve phase-to-height conversion fidelity and enable in-situ, layer-wise surface reconstruction of each newly deposited layer. In the reported implementation for laser-DED, the approach achieves a reconstruction accuracy of ${\pm}46\ \mu\text{m}$ on DED surfaces, supports absolute surface height measurements, and enables annotation-free identification of common deposition anomalies such as lack of fusion and poor surface finish directly from reconstructed morphology (Hu et al., 31 Aug 2025).

1. Definition and measurement rationale

In laser DED, the measurement surface rises layer-by-layer, unlike powder bed fusion where the bed is lowered and optics can remain at a fixed standoff. As the standoff, angle of incidence, focus, field of view, and shadowing conditions change with build height, unsynchronized optics degrade triangulation fidelity and phase-to-height conversion. A build-height-synchronized fringe projection profilometry module is therefore defined as a system in which the projector–camera geometry and working distance are actively adjusted in step with the nominal layer height, so the focal plane and triangulation baseline remain constant across layers (Hu et al., 31 Aug 2025).

The module projects sinusoidal fringes and demodulates their phase to reconstruct a full-field height map at micrometer lateral sampling. Because synchronization preserves the calibrated phase-to-height mapping, the reconstructed surface can be interpreted as absolute surface height rather than only relative topography. This enables traceable geometric evidence of anomalies, including height deviation, lack of fusion, and poor surface finish, on each layer. The reported motivation is not only metrology fidelity but also the linking of process signatures to certifiable part geometry, thereby supporting quantitative quality assurance and eventual closed-loop control (Hu et al., 31 Aug 2025).

The central misconception addressed by this formulation is that fixed optical geometry is sufficient for all additive manufacturing modalities. The DED case is explicitly different because the build grows upward into the optical working volume. The synchronized architecture is therefore not an incidental mounting choice; it is the mechanism by which calibration validity is maintained as the part height changes.

2. Optical architecture and synchronized mechanics

The reported hardware configuration combines a DLP projector LC3010-RGB10/OF (Keynote Photonics, USA), native resolution $1280 \times 720$, and a CMOS camera Alvium 1800 U-1242m (Allied Vision, Germany) with a $50$ mm lens (Edmund Optics 86574), native resolution $4128 \times 3008$. The projector is operated in the blue channel for shorter wavelength sensitivity and higher SNR. Measurements are acquired through a laser safety observation window (Kentek ACRX-BB2) providing OD 6+ broadband attenuation and particularly strong rejection in the blue ($200$–$532$ nm). Blue-channel projection benefits from the window’s suppression of external blue light, improving measurement stability. No additional polarizers are specified (Hu et al., 31 Aug 2025).

Element	Specification	Function
Projector	LC3010-RGB10/OF, $1280 \times 720$	Blue-channel fringe projection
Camera	Alvium 1800 U-1242m, $4128 \times 3008$	Fringe image acquisition
Lens	Edmund Optics 86574, $50$ mm	Imaging optics
Window	Kentek ACRX-BB2, OD 6+	Laser safety and blue-light suppression
Actuator	FUYU FSK40F200-10C7	Synchronized module repositioning
Controller	Arduino Uno	Actuator control

Geometrically, the camera optical axis is approximately normal to the region of interest, while the projector is oriented at a $15^\circ$ angle relative to the camera axis. The calibrated working distance is $1280 \times 720$0 mm. At that distance, the field of view is approximately $1280 \times 720$1 mm $1280 \times 720$2 $1280 \times 720$3 mm, corresponding to an effective lateral resolution of $1280 \times 720$4; the typical captured area during experiments is about $1280 \times 720$5 mm $1280 \times 720$6 $1280 \times 720$7 mm, sufficient for a $1280 \times 720$8 mm $1280 \times 720$9 $50$0 mm build (Hu et al., 31 Aug 2025).

The module operates inside a sealed DED chamber and is rigidly mounted on a precision linear actuator. Because vertical clearance is limited, the module is installed laterally. After each layer, a multi-axis rotary stage rotates the circular substrate so that the freshly deposited surface faces the FPP module. In this rotated measurement configuration, the increase in build height appears as a lateral offset within the FPP frame. The synchronization law is

$50$1

where $50$2 is the initial lateral offset, $50$3 is the layer index, and $50$4 is the nominal interlayer step used in the experiment. The actuator resolution of $50$5 is used to maintain the calibrated working distance and scale as the build grows (Hu et al., 31 Aug 2025).

The print–measure loop proceeds layer-wise: deposit the layer in the standard build orientation, rotate the build plate to face the laterally mounted FPP module, project the fringe sequence and acquire images for reconstruction, then rotate back to the print orientation and continue the build. Measurements are taken immediately after deposition and platform rotation, when the laser is off and thermal emissions are reduced relative to the active melt pool. Exposure is controlled by the camera, and HDR acquisition is not required for the surfaces measured in the study (Hu et al., 31 Aug 2025).

3. Calibration, phase retrieval, and height reconstruction

Camera intrinsic calibration is performed with MATLAB’s Camera Calibration Toolbox using a checkerboard. Focal length, principal point, and distortion are estimated and used to undistort imagery. Lateral pixel scaling is established by imaging a $50$6 mm-pitch checkerboard inside the chamber; at a $50$7 mm standoff this yields $50$8 (Hu et al., 31 Aug 2025).

Phase-to-height calibration uses a $50$9 angle gauge block placed on the build plate. A $4128 \times 3008$0 mm segment along the slope is used to correlate unwrapped phase to analytically derived height, and a least-squares linear fit yields the phase-to-height constant $4128 \times 3008$1. Surface height is then reconstructed by

$4128 \times 3008$2

where $4128 \times 3008$3 is the unwrapped phase and $4128 \times 3008$4 is surface height (Hu et al., 31 Aug 2025).

The phase-shifting formulation is expressed with the generic PSP equations

$4128 \times 3008$5

and

$4128 \times 3008$6

A conventional phase-shifting algorithm is used; the wrapped phase $4128 \times 3008$7 is spatially unwrapped to obtain $4128 \times 3008$8. No multi-frequency temporal unwrapping is required due to continuous surfaces and interlayer timing. Camera lens distortion is corrected prior to phase demodulation to preserve geometric fidelity. Because synchronized repositioning holds the module pose relative to the surface constant for each measurement, the projector–camera geometry can be effectively represented by the single linear phase-to-height calibration constant $4128 \times 3008$9 rather than by a layer-specific recalibration (Hu et al., 31 Aug 2025).

The point-cloud generation stage begins by segmenting the printed region from the surrounding build plate using Otsu’s thresholding. Pixel coordinates are mapped to metric lateral coordinates using the calibrated pixel-to-length scale, and the segmented region becomes a $200$0D point cloud. Statistical outlier removal is then applied: for each point, the mean distance to its $200$1 nearest neighbors is computed; the global mean $200$2 and standard deviation $200$3 are formed; and points with neighborhood distance above

$200$4

are discarded. Surface normals are estimated on the denoised cloud, and height and normal maps are visualized. Layer-wise datasets are inherently aligned by known stage rotation and actuator offsets used during synchronization (Hu et al., 31 Aug 2025).

4. Geometry-derived anomaly metrics

The anomaly-detection framework operates directly on the reconstructed surface morphology and does not require manual labeling. Two complementary geometry-based point cloud metrics are defined: Local Point Density (LPD) and Normal-Change Rate (NCR). Their intended division of labor is explicit: LPD highlights poor surface finish, while NCR identifies lack-of-fusion features (Hu et al., 31 Aug 2025).

For a point set $200$5, LPD counts neighbors within a fixed radius:

$200$6

with $200$7 mm. Low $200$8 highlights sparse sampling, including voids, steep local slopes, occlusions, and filtered noise, while high $200$9 maps material accumulation or smoother overbuilt regions. In the DED context, LPD is reported to sensitively reflect poor surface finish, including powder residues of approximately $532$0–$532$1 and path undulations, and to highlight deposition discontinuities at hatch turnarounds and raster–wall junctions (Hu et al., 31 Aug 2025).

NCR measures local normal variation within a larger neighborhood. For point $532$2 with normal $532$3 and neighbors within $532$4 mm,

$532$5

The absolute dot product compares normals independent of orientation. High NCR indicates abrupt curvature transitions typical of lack of fusion, conical depressions, or collapse. A multi-threshold segmentation is applied in which a higher NCR threshold isolates anomaly cores and a lower threshold captures transitional boundaries, yielding hierarchical segmentation of defects without manual labels (Hu et al., 31 Aug 2025).

False-positive suppression is handled procedurally rather than by a learned classifier. Thresholds are selected from NCR distributions on nominal regions to minimize false alarms, and morphological consistency across layers together with agreement between NCR and LPD is used to reduce spurious detections caused by benign features such as scan overlaps. This makes the framework explicitly annotation-free and geometry-driven rather than dependent on supervised defect labels (Hu et al., 31 Aug 2025).

5. Validation, experimental findings, and comparative position

Baseline accuracy is established with staircase gauge blocks (Mitutoyo 516-946-26), which yield a vertical RMSE of $532$6. Validation on DED surfaces is performed against a commercial focus-variation $532$7D microscope, the Bruker Alicona InfiniteFocus G4, and reports RMSE $532$8 in absolute height relative to the microscope. The lateral sampling is approximately $532$9. For deviation statistics over $1280 \times 720$0 points, with $1280 \times 720$1 bins over the $1280 \times 720$2–$1280 \times 720$3 mm range, $1280 \times 720$4 of points lie within $1280 \times 720$5 mm, $1280 \times 720$6 within $1280 \times 720$7 mm, and $1280 \times 720$8 within $1280 \times 720$9 mm (Hu et al., 31 Aug 2025).

Validation quantity	Value
Gauge-block vertical RMSE	$4128 \times 3008$0
DED surface RMSE vs microscope	$4128 \times 3008$1
Lateral sampling	$4128 \times 3008$2
Within $4128 \times 3008$3 mm	$4128 \times 3008$4
Within $4128 \times 3008$5 mm	$4128 \times 3008$6
Within $4128 \times 3008$7 mm	$4128 \times 3008$8

The experimental anomaly study inserts laser-off segments of $4128 \times 3008$9 mm randomly into hatch toolpaths to generate six- and twelve-anomaly layers over a $50$0 area; scan direction alternates $50$1 between layers, and anomalies are spaced sufficiently to avoid thermal overlap. Within this setting, LPD maps show density disruptions at melt pool termination sites, hatch turnarounds, and raster–wall interfaces. Micro-scale particulates are visible and corroborated by focus-variation microscopy, including an example with $50$2 lateral extent and approximately $50$3 height. NCR maps robustly localize elongated, elliptical anomalies aligned with scan direction, and incidental geometric defects such as interlayer misalignments are also captured (Hu et al., 31 Aug 2025).

Pixel-wise distance mapping between segmented anomaly regions and the nearest programmed laser-off centers reveals tails extending opposite the scan direction. The reported attribution is ongoing powder/gas impingement and thermal inertia during laser-off events. No ROC or PR curves are reported; the evidence is instead framed in terms of reliable qualitative localization, morphology, spatial extent, and quantitative reconstruction fidelity (Hu et al., 31 Aug 2025).

Relative to other sensing modalities, the synchronized FPP approach is described as achieving micrometer-scale lateral sampling and tens-of-microns vertical RMSE over a large field without interrupting production, while using active illumination that is robust to texture variations. It avoids the multiple-pass registration overhead of laser line scanners, does not require surface preparation as in DIC, and provides direct geometric evidence rather than proxy melt pool signals such as coaxial imaging or pyrometry (Hu et al., 31 Aug 2025).

6. Control integration, related dynamic fringe projection, and scope

The reconstructed outputs are intended for control as well as inspection. The synchronized FPP system delivers absolute layer height and curvature maps that can drive adjustments to laser power, powder feed, travel speed, hatch spacing, or standoff; trigger corrective remelting or localized repair passes; or halt the build when NCR or LPD exceed thresholds. The interlayer print–measure loop enables near-real-time feedback on a per-layer cadence. The computational pipeline—phase demodulation, segmentation, statistical outlier removal, normal estimation, and LPD/NCR evaluation—runs on standard hardware, although specific timing metrics are not reported (Hu et al., 31 Aug 2025).

A related line of work in dynamic digital fringe projection addresses a different failure mode: in phase-shifting profilometry, any motion during the acquisition of fringe patterns can introduce errors because the method assumes both the object and measurement system are stationary. A motion-induced error reduction algorithm based on the motor’s encoder and the pinhole model of the camera and projector performs pixel-wise correction of motion-induced disparity and phase-shift error, enables $50$4D shape measurement with only three fringe patterns, and is reported to reduce errors even in non-uniform motion (Jeon et al., 2024). This suggests a technical complementarity: the DED-specific synchronized system primarily stabilizes geometry across layers by repositioning between deposition events, whereas motion-aware PSP methods are relevant when acquisition must occur during stage motion or under residual vibration.

The limitations of the synchronized DED configuration are explicitly line-of-sight and surface-condition dependent. A single lateral view at $50$5 projection can suffer from self-occlusion in steep geometries, and multi-view FPP would improve coverage. Specular reflections and high-temperature emission are mitigated by measuring after deposition and by using blue-channel projection through a window that suppresses external blue light, but extreme surfaces may still challenge phase quality. Rigid mounting and actuator repositioning maintain the baseline, yet any drift would affect the phase-to-height linearity captured in $50$6. The rotation-based measurement mode also requires access and consistent rotation; complex parts may therefore need alternative orientations or additional views (Hu et al., 31 Aug 2025).

The reported potential improvements are multi-view synchronized FPP, polarized illumination, high dynamic range capture, multi-frequency phase unwrapping for discontinuities, and curvature-tensor metrics beyond NCR for richer anomaly characterization. In terms of applicability, the synchronization concept is less necessary in PBF-LB because FPP is already mature for fixed-height beds, but it reinforces the importance of maintaining focus and optical scale for high-fidelity areal inspection. The method is presented as transferable to wire-arc AM and other DED variants with adjustments for brighter arcs and surface emissivity; synchronized repositioning and multi-view coverage are identified as particularly valuable for tall, bead-like geometries. Powder-blown stainless steel builds demonstrated robust performance in the reported study, while reflective alloys or very rough beads may require refined exposure and filtering (Hu et al., 31 Aug 2025).