Line scan illumination uniformity: fix the dark band across wide webs

An 8K line scan camera looks at a 1500 mm wide web from 900 mm above it. The surface reads as even to the eye and a hand-held meter shows 9500-10500 lux across it. Yet every frame carries a band along the scan direction — dark across the middle third under one light, dark at both edges under another. This page is for anyone commissioning wide-web line scan inspection. You will learn why the meter and the camera disagree, how to read the true profile from the image, how long the light must be, when the lens image circle is the cause, and how far flat-field correction can carry what remains.

Why does a lux meter read even light while the camera shows a band?

A lux meter sums the light landing on one small patch of the web surface. The band in your image is built from the light's intensity profile along the scan line and the lens's angle response — two things a surface reading never shows. Most meter heads average over a diffuser 10-40 mm across, and few people sample 1500 mm of web densely enough to find a 500 mm trough. The readings already matter on their own: a 9500-10500 lux spread is 10%, and 10% at 8-bit mid-scale is 128 × 0.10 = 13 grey levels — more than most defect thresholds tolerate before any band is added.

Direction is the second blind spot. A light that dumps most output straight down and little at 40° off axis can light every patch you point the meter at. The camera, which integrates a cone of angles at every column, records a trough. The camera shares the inspection's geometry, so its own image is the instrument to trust.

What does the band's shape tell you about the cause?

A band that is symmetric about the web centre and identical in every frame is geometry. Two cameras sharing one light and showing the same band point at the light or the lens, not at the sensors. Sort the symptom by shape before touching anything:

• Dark middle third — a 500 mm trough on this web: a seam where two tubes or bar lights meet, or a gap between them. Fix it with spacing, not software.
• Dark toward both edges, smoothly: wide-angle shading. The light is short relative to the web, the lens is near its image-circle limit, or both. The arithmetic follows.
• Dark only over the last few hundred columns, falling fast: vignetting from an image circle smaller than the sensor.
• A band that moves, flickers or changes with line speed is not illumination — work through how to set the line rate of a line scan camera instead.

Symmetric is the workable case: predictable, measurable and correctable. Asymmetric means a crooked mount or a failing LED segment, and no correction frame should be asked to hide that.

How do you measure the light profile the camera actually sees?

Scan a uniform matte target — a sheet of white paper on the roller is enough — at production speed and exposure. Then plot the mean grey value of each of the 8192 columns; that plot is the only profile that matches what the inspection sees. Any line scan camera with 8K resolution will do it — for example the LS-LCM-0099, an 8K 10GigE model with an M72 mount — and the analysis needs only the camera's capture tool and a spreadsheet.

1. Run the target under the light at production speed, exposure and current.
2. Capture at least 10 frames and average them to suppress pixel noise.
3. Compute one mean value per column, then divide by the overall mean so the plot reads as a ratio.
4. Classify the shape: a smooth dome peaking at the centre is light-side shading, a notch or step is a seam, a fast drop over the last columns is the lens.

At 1500 mm / 8192 = 0.18 mm per pixel the plot's horizontal axis maps directly onto the web. A workable commissioning target is a raw profile within ±10% peak-to-peak for defect detection, and within ±5% when the system also measures.

Why do wide webs darken toward the edges even under good lighting?

At 750 mm half-width and 900 mm working distance the web edge sits 39.8° off axis. There a light much shorter than the web delivers about 45% of its centre irradiance, and a diffuse surface loses about 35% more in the lens.

For this geometry:

• θ = arctan(750 / 900) = arctan(0.833) = 39.8°, so cos θ = 0.768.
• Light side: 0.768³ = 0.45 — a short central light behaves like a point source, and edge irradiance falls to 45% of centre.
• Lens side: 0.768⁴ = 0.35 — the standard cos⁴ estimate of image irradiance for a diffuse surface at angle θ through a conventional lens.
• Stacked: 0.45 × 0.35 = 0.16, edges near 16% of centre.

The cos³ term is a lighting problem: an emitting window that spans the full field lights every point from nearly straight overhead and collapses it to almost nothing. The cos⁴ term is a geometry problem no light can fix, because it depends only on the angle at which the lens sees the surface. Splitting the web across two cameras halves the angle — arctan(375 / 900) = 22.6°, and cos⁴(22.6°) = 0.73 — which is why very wide single-camera fields are corrected rather than lit flat. The 35% figure is what correction has to rescue, and the next section prices that rescue in noise.

How long must the line light be for a 1500 mm web at 900 mm working distance?

Make the emitting window longer than the field by 10-20% at each end — 1800-2100 mm of light for a 1500 mm field. Then every web point is lit from nearly straight overhead and the cos³ term disappears. The margin covers roll-off at the window's ends, mounts that sit back from the emitting length, and a few millimetres of normal web wander. Height then sets brightness rather than uniformity: irradiance falls with the square of the mounting distance, while a full-span light stays uniform at any practical height.

One window beats two, because a seam cannot form inside it. Where nothing long enough exists, two lights end to end work well: the line scan lights category runs lengths from a few hundred millimetres past a metre, and the light finder filters by length, wavelength and voltage. The LS-LSC-0017-L25 is a 1092 mm, 24 V line scan light. The LS-LSC-0131 measures 975 × 22 mm on a WS20 4-pin connector, and the LS-LSC-0657 runs 970 mm in white. Two of them end to end give 1092 mm + 975 mm = 2067 mm of housing — about 15% past the 1800 mm target — with the overlap trimmed until the column plot shows no step.

Give each half its own channel on a lighting controller so the seam is balanced in current, not by shimming mounts. Length is not the only budget: a fast line also needs the wattage, and how much power a fast line scan light really needs works that side out.

Could the lens and its image circle be the cause instead?

Vignetting darkens the extreme pixels first and never the middle third. If the column plot falls steeply only over the last few hundred columns, check the image circle before buying light: an 8K sensor with 7 μm pixels spans 8192 × 7 μm = 57.3 mm, and the lens must cover all of it.

With m = 57.3 mm / 1500 mm = 0.038, the focal length works out to f = 0.038 × 900 mm / 1.038 = 33 mm — a short focal length paired with a large image circle, an unusual combination worth matching deliberately. How to calculate a line scan camera's field of view covers the method, and line scan lens selection for 4K, 8K and 16K cameras compares lens classes per sensor.

The calculator above runs the same arithmetic from your own working distance. A lens for this sensor needs an image circle of at least 57.3 mm. The LS-LSL-0150 is a 40 mm line scan lens with a 60 mm image circle in an M58/M72 mount.

That 60 mm circle clears the 57.3 mm sensor by 1.3 mm per side, which works, and more circle leaves more mounting tolerance. Match mount to camera — an M58 lens on an M72 camera takes the correct adapter — and the line scan lenses category filters the rest of the class by image circle and mount.

When does flat-field correction help, and when does it fail?

Flat-field correction divides each column by its own mean on the uniform target, so it fixes multiplicative shading exactly — provided nothing in the frame has clipped and the factor stays modest. Above a factor of about 2 the lifted zones lose real quality: shot noise scales with the correction factor, so a column lifted 2× carries twice its noise and half its signal-to-noise ratio.

This geometry is why correction alone disappoints. With the light spanning the web, the residual edge response is the cos⁴ term at 0.35, and the needed factor is 1 / 0.35 = 2.9 — nearly three times the noise in the edge zones before the sensor's own noise is added. With the cos³ term present too, the factor is 1 / 0.16 = 6.3, and correction is hopeless as the primary fix.

Conditions that make correction work:

• Keep the brightest columns at or below 80% of saturation, so every column has at least 1.25× of headroom upward.
• Keep the darkest columns several times above the noise floor; lift small factors, not large ones.
• Correct in 12-bit raw and map to 8-bit afterwards: a 2.9× noise multiplication that is invisible in 12-bit becomes visible after 8-bit quantisation.
• Re-capture after any change of light, height, current or lens position, and on a schedule tied to LED ageing — why strobe mode extends LED lifetime explains the drift you are correcting. If headroom is tight, pixel binning buys exposure margin at the same line rate.

Which fix do you apply first?

Work in this order: measure the column profile, remove any notch with light spacing and per-channel current trim, span the web to remove the light-side dome, correct the remaining cos⁴ shading in 12-bit, and replace the lens only if the falloff hugs the extreme pixels. Each step costs little and the next builds on its result.

1. Measure: column-mean plot on a uniform target at production settings — every later decision reads from it.
2. De-seam: a notch or step near the middle gets the lights overlapped and the two controller channels balanced until the step is under 2-3 grey levels.
3. Span: a dome peaking at the centre gets the window lengthened to the 1800-2100 mm this field needs, mounted as low as camera clearance allows.
4. Correct: the remaining smooth falloff gets flat-field in 12-bit raw, factors kept near or below 2.
5. Replace: a steep drop over the last columns only gets a lens whose image circle properly covers 57.3 mm.

Then make it stay fixed: re-shoot the profile after any mechanical or electrical change and on a schedule that matches your LED drift, so the correction frame never goes quietly stale. If a band ever appears that is asymmetric or moves with speed, stop adjusting the light — it is timing, and the band-shape section above routes it.

If you are sizing a light for a wide web right now, send the web width, line speed and working distance through the contact page. The wider family of lighting problems lives on the lighting topic page.