Measure board edge curvature with line scan imaging

Uneven board edges create two different problems: capturing the complete boundary and turning thousands of edge samples into useful cutting information. For an industrial inspection station, begin with calibrated edge coordinates rather than a curvature number alone. This guide explains how to image both lateral edges, synchronize samples with board travel, and report bow, width and local curvature. It also separates what a top-view silhouette can measure from underside contours and height variation that require additional views.

1. Decide which edges and measurements you need

For the two lateral edges visible from above, a single overhead line scan camera can capture both boundaries. Its sensor line spans the board width, perpendicular to travel. Motion supplies the second image dimension.

The resulting image represents the board's projected outline. It does not automatically describe its entire cross-section. Establish these definitions before selecting hardware:

• Lateral edge profiles: left and right boundaries in the board plane.
• Upper and lower edge contours: boundaries associated with the top and underside surfaces, which may differ on a tapered edge.
• Height or twist: out-of-plane geometry that a silhouette alone cannot resolve.

If the required cutting boundary lies underneath an overhanging upper surface, the overhead view may hide it. Additional underside or oblique views may be necessary. If the requirement is actual height, use a calibrated depth-measurement method; cleaning a laser-derived height profile is a separate problem from extracting a silhouette.

For edge straightening, specify the useful outputs first: minimum usable width, edge deviation from a proposed cut, maximum bow and the longitudinal positions of defects. Local curvature can supplement these measurements, but it should not replace the original edge coordinates.

2. Arrange the camera, board and illumination

Place the sensor line across the widest expected board envelope, including lateral wander. Keep the inspection region clear of supports that would hide either edge. A gap between transport supports can provide a transmission view, provided the mechanical arrangement supports the board safely.

Backlighting often gives a simpler boundary than reflected illumination because the board appears as a silhouette. However, bark fragments, hanging fibers and translucent material can still complicate the edge definition. Reflected lighting may be necessary where a transmission view is impractical, but grain and surface markings can create competing transitions.

Keep the measurement plane consistent. A height change alters magnification with conventional perspective optics, so a warped board can produce apparent width changes. Calibrate and validate across the permitted height range rather than assuming every board occupies the calibration plane.

Use two cameras when the required width and detail cannot be covered adequately by one sensor, or when different surfaces need separate views. Provide overlapping coverage where practical and calibrate both cameras into the same board coordinate system. Synchronization alone does not establish their geometric relationship.

3. Choose spatial sampling before acquisition speed

Define lateral sampling from the smallest feature that must influence the cutting decision. Define longitudinal sampling from the shortest edge variation you need to retain. They need not be equal.

The basic relationships are:

Consider an illustrative inspection width of 500 mm across 4096 pixels:

That is a sampling calculation, not a measurement-accuracy claim. Lens blur, edge contrast, calibration error and board movement also affect performance. The field-of-view calculation guide explains how coverage and sensor geometry interact.

Suppose board speed is 1000 mm/s and the chosen longitudinal interval is 0.25 mm:

Use an encoder tied to actual board travel where possible. A conveyor encoder is only equivalent when belt motion reliably represents board motion. Slip changes the longitudinal scale even if acquisition timing is otherwise correct.

For varying speeds, trigger lines at fixed travel increments using supported camera or acquisition-hardware functions. Confirm trigger limits, exposure behavior and missing-trigger handling in the selected equipment documentation. The line-rate setup procedure covers acquisition timing in more detail.

4. Select components around coverage and contrast

Start with line scan cameras and the camera finder. Compare required pixel count, supported triggering, usable line frequency and interface throughput. Do not choose by pixel count alone.

The LS-LCM-0005 is a mono GigE camera with an 8K line length and M72 lens mount. The LS-LCM-0080 is a mono GigE camera with a 4K line length and M42 lens mount. Their catalog summaries establish different starting points, not a complete application qualification.

All 2 share: Mono / colour Mono. Values as printed in each product's data sheet; open a part for its drawing and full specifications.

For the earlier example, an uncompressed monochrome stream with one byte per pixel has this approximate payload:

Protocol overhead, additional channels and pixel packing affect the actual interface requirement. Use the camera bandwidth planning guide when checking the full acquisition path.

Choose line scan lenses through the lens finder using sensor length, magnification, working distance and mount compatibility. The LS-LSL-0150 lists a 40 mm focal length and 60 mm image circle. Confirm its mechanical interface, focus range and performance at the intended magnification before pairing it with a camera.

The line scan optics selection guide explains why image-circle coverage and edge sharpness matter across long sensors.

For line scan lights, use the lighting finder to identify candidates for contrast trials. The LS-LSC-0131 lists dimensions of 975 x 22 mm and a 24 V supply. Physical dimensions alone do not establish illuminated coverage or suitability for transmission imaging.

Treat these as component candidates, not a verified matched system. Confirm illumination geometry and exposure performance using representative boards. The exposure and illumination guide explains why electrical power alone cannot predict usable edge contrast.

5. Calibrate into board coordinates

Use longitudinal position as x and lateral position as y, both expressed in millimeters. Store the left and right boundaries as y_left(x) and y_right(x).

A practical calibration sequence is:

1. Establish the measurement plane. Position a dimensionally known target where the relevant board contour will pass.
2. Calibrate the lateral mapping. Measure known target positions across the complete sensor line, including both ends.
3. Check distortion. Fit an appropriate mapping and test it against target positions withheld from the fit.
4. Calibrate longitudinal travel. Compare accumulated encoder distance against an independently measured travel distance under representative conditions.
5. Align additional views. Use shared reference features to transform their coordinates into the same physical system.
6. Validate across height and speed. Repeat measurements at the permitted operating extremes.

Do not apply a single millimeters-per-pixel factor if residual distortion exceeds your tolerance. Equally, avoid adding a complicated distortion model without enough independent calibration data.

Separate the machine coordinate system from the board coordinate system. A fixed board yaw introduces a linear slope into each edge profile. Removing that slope can help describe bow, but retain the original coordinates for cutting-path alignment.

Changing yaw during acquisition is more serious: it can resemble real curvature. Mechanical guidance or an independently validated motion estimate is needed to distinguish those effects.

6. Extract a continuous edge without inventing one

Begin with a background capture and representative samples spanning normal appearance variation. For transmission imaging, estimate the background intensity along the sensor line and normalize gradual illumination variation before detecting transitions.

Process each acquired line using the expected board region:

• Identify candidate board-to-background transitions.
• Select the left and right boundaries using expected order, width and continuity.
• Refine transition positions with a local fit when contrast and optical sharpness support it.
• Attach confidence values based on contrast, transition width and competing candidates.
• Mark ambiguous samples invalid rather than forcing a plausible contour.

Subpixel fitting improves numerical position estimates under favorable conditions; it does not remove optical or calibration errors.

Define the physical edge you intend to measure. A silhouette detector might follow a projecting fiber, while a cutting planner may need the boundary of solid material. Those are different definitions. Validate the selected rule against accepted and rejected examples before applying morphological cleanup.

Use continuity constraints in physical units. For example, reject jumps exceeding the maximum physically credible edge change between adjacent samples, but leave room for genuine notches. An aggressive filter can erase exactly the defect the station should identify.

Preserve sample positions across acquisition blocks. The frame-boundary handling guide explains how block processing can otherwise omit edge information near image boundaries.

7. Separate bow, width and local curvature

Calculate useful geometric summaries before differentiating noisy edge data:

Choose the reference line deliberately. An endpoint chord measures deviation relative to the ends. A fitted straight line describes overall alignment. A proposed cutting line answers a manufacturing question. Their maximum deviations will generally differ.

For a calibrated planar edge y(x), curvature magnitude is:

Use consistent units. Coordinates in millimeters produce curvature in inverse millimeters. Multiply that value by 1000 to express it in inverse meters.

As a worked example, approximate a gently bowed edge by a circular arc with chord length L = 2000 mm and sag b = 8 mm:

This is an arc approximation, not a valid replacement for an irregular boundary. Report the measured maximum deviation alongside any fitted radius.

For local curvature, fit a polynomial or spline over a declared physical window and differentiate the fitted curve. A 20 mm window and a 100 mm window describe different scales of shape. Select the window from the smallest manufacturing-relevant bend, then document it with every curvature output.

Avoid publishing very large radius values near straight sections. A small curvature uncertainty produces a large radius uncertainty there; deviation and curvature confidence are more informative.

8. Reduce the image stream to manageable data

Retain calibrated contours as the primary measurement record. A useful per-board record includes longitudinal positions, both edge coordinates, validity flags, calibration identifier and processing settings.

The example board length requires:

That is about 64 kB for edge coordinates alone. The corresponding uncompressed monochrome image contains:

The contour record also needs metadata and confidence information. If positions are not recoverable from a fixed sampling interval and a valid origin, store them explicitly.

Keep diagnostic images for commissioning, rejected boards and selected audit samples. Saving only fitted curvature values makes later fault analysis difficult.

When simplifying contours, use a maximum geometric-deviation limit rather than dropping every fixed number of samples. Preserve sharp notches and invalid regions. Never connect across an unknown interval without flagging the interpolation.

9. Verify performance and recognize the limits

Build an acceptance set containing straight references, known bowed outlines, narrow notches and representative rough edges. Compare reported positions against an independent reference method whose uncertainty is suitable for the tolerance.

Repeat passes at different speeds and lateral positions. If the same board produces different geometry, investigate travel scaling, board motion, height variation and edge visibility before adjusting the curvature filter.

Set separate acceptance limits for:

• Lateral coordinate error across the inspection width.
• Longitudinal distance error over a full board.
• Repeatability of maximum deviation and minimum width.
• Invalid-sample fraction and maximum unobserved interval.
• Detection of the smallest manufacturing-relevant notch or bend.

The usual single-camera answer is wrong when the required contour is hidden, boards change height beyond the validated range, or material slips relative to the travel encoder. More processing cannot recover an unseen boundary or an unknown motion history.

If boards stop for inspection, an area capture may be simpler. For alternative acquisition arrangements, the moving-web acquisition comparison explains when a dedicated line sensor is not the only option.

10. Check requirements before ordering

Use this short specification checklist to keep component selection tied to the measurement:

• Boundary definition: identify lateral, underside or solid-material contours explicitly.
• Coverage: include maximum board width, wander and calibration margins.
• Sampling: state lateral spacing, travel increment and maximum speed.
• Optics: confirm sensor coverage, mount, focus range and permitted height variation.
• Illumination: prove edge contrast at the required exposure using representative material.
• Synchronization: confirm encoder resolution, trigger compatibility and slip assumptions.
• Processing: define invalid-data handling, smoothing window and contour simplification tolerance.
• Outputs: retain edge coordinates alongside width, deviation and curvature summaries.
• Acceptance: agree on reference measurements, repeatability limits and failure handling.

Begin the hardware review with the camera configurator. If underside visibility, board motion or edge definition remains uncertain, send those requirements through applications support before committing to a camera and lens combination.