Corners going dark on a new camera build is one of the most common lens faults, and it has three sources: the lens's image circle is smaller than the sensor, the iris is wide open, or it is the natural cos-fourth falloff every lens shows. The three call for different fixes — a different lens, a higher f-number, a shading profile — and guessing wrong costs a week of bench time. This guide gives you the diagonal arithmetic, the cos-fourth numbers, a ten-minute white-target test and the decision for each case.
What vignetting looks like
On an area scan camera, vignetting shows as a smooth darkening toward the corners. Hard black corners with a visible circular boundary are a worse, separate fault: the lens is not covering the sensor at all. On a color camera the falloff usually brings a tint, because the red, green and blue channels dim by different amounts toward the edge. On a line scan camera the same optics compress into two dark bands at the ends of every line, which on a web line reads as dark edges on every product. If moving or swapping the light moves the dark region, the cause is illumination rather than the lens; the shading correction fix for uneven brightness covers that case.
Cause 1: the image circle is smaller than the sensor
A lens forms a sharp disc of fixed diameter, the image circle, and pixels outside it receive no light. Catalogs rate the circle by sensor format: a 2/3" lens covers about 11 mm, a 1" lens about 16 mm. The mount guarantees nothing — a C-mount thread fits any C-mount camera regardless of what the optics behind it cover.
The check is one Pythagoras line. A 1" sensor measures 12.8 × 9.6 mm, so sqrt(12.8^2 + 9.6^2) mm = sqrt(163.84 + 92.16) mm = 16.0 mm diagonal. A 2/3"-format lens covers an 11 mm circle, radius 5.5 mm, while the corner sits 8.0 mm out. Everything beyond 5.5 mm stays black: (16 − 11) / 16 = 31% of the diagonal is unexposed. No gain setting recovers a pixel that got zero photons, so this fault is fixed at the ordering stage or not at all. The diagonal for each format is tabulated in what 1 inch and other sensor sizes mean and the lens sensor format guide.
Cause 2: natural cos-fourth falloff
Even a perfectly matched lens dims its corners. Light reaching the edge travels at an angle theta to the axis, and four cosine factors compound: the exit pupil is foreshortened once, the slant path adds two more, and the light lands on the flat sensor obliquely once. Irradiance falls as cos(theta)^4:
Worked example, 2/3" sensor (11 mm diagonal) with an 8 mm lens: theta = atan(5.5 / 8) = 34.5 degrees, cos(34.5) = 0.824, and 0.824^4 = 0.46. The corners sit near 46% of the centre, about 1.1 stops down. Lengthen the focal length and the angle collapses:
| Focal length | Corner angle | cos(theta)^4 | Corner level |
|---|---|---|---|
| 8 mm | 34.5° | 0.46 | -1.1 stops |
| 12 mm | 24.6° | 0.68 | -0.55 stops |
| 25 mm | 12.4° | 0.91 | -0.13 stops |
| 50 mm | 6.3° | 0.98 | -0.03 stops |
Treat the figures as the geometric estimate: strong retrofocus or pupil-compensated designs shift real lenses away from pure cos-fourth by tens of percent. The trend is reliable, and it names the worst combination: a short focal length on a large sensor. The field angle itself is what the lens field of view article works through.
Cause 3: the aperture term, wide open
On top of cos-fourth, a lens at its widest f-number clips the oblique bundles at the barrel or front aperture, trimming the corners further. This is the only term you can tune at the bench: stop the iris down two to three stops and most of it disappears, while the cos-fourth share stays exactly where it was. The cost is depth of field and, eventually, diffraction, so choose the working f-number with the aperture and depth of field guide instead of by trial.
The white-target test that separates the causes
Point the camera at an evenly lit white target — a sheet of paper under your production light works — set the exposure so the centre sits near 75% of full scale, and plot a pixel profile through the centre from corner to corner. Three signatures, three diagnoses:
- A hard cut to black at a fixed radius: image circle smaller than the sensor. Twice that radius is the circle you are missing.
- A smooth bowl matching the cos-fourth figure for your focal length: natural falloff, correct it with shading.
- A dip that visibly shrinks when you stop down two stops: aperture clipping on top.
Mixed cases are common, and you read them from the outside in: black first, aperture second, cos-fourth last.
Fix the circle: match the lens format to the sensor
The decision rule is one line: the lens's rated image circle must meet or exceed the sensor diagonal, with one format of headroom where you can get it. Headroom buys tolerance for mounting error, and the same field of view on a larger sensor needs a longer focal length, which softens the cos-fourth term as a bonus.
C-mount fixed lenses from 1/2" to 1.1" sensor format, with the image circle each is built to:
| Specification | LS-FFL-1023 | LS-FFL-0679 | LS-FFL-0602 | LS-FFL-0567 |
|---|---|---|---|---|
| Mount | – | C-mount | C-mount | C-mount |
| Format | – | 2/3" | 1" | 1.1" |
| Resolution | – | 6.0 Megapixel (2.4 μm pixel size) | 10 Megapixel | 20 Megapixel |
| Focal length | – | 35 mm | 8.5 mm | 16 mm |
| Aperture | – | F2.8 Manual iris | F2.4 Manual iris | F2.8-22 |
| M.O.D. | – | 0.2 m | 0.1 m | 0.1 m |
| Size | – | dia. 33 x 30.6 mm | dia. 80 x 67.1 mm | – |
| Weight | – | 50 g | 270 g | – |
| Filter thread | – | – | M77 x P0.75 | M35.5 x P0.5 |
| Price | $249.00 | $219.00 | $429.00 | $679.00 |
Values as printed in each product's data sheet; open a part for its drawing and full specifications.
Match the row to your sensor diagonal and step up a format whenever the margin is thin. The machine vision lens category filters by sensor format and image circle, the lens finder narrows by the same facets, and the lens configurator walks sensor, working distance and resolution in one pass.
Fix the falloff: flat-field shading correction
When corners sit within a factor of two of the centre, a shading profile is the right tool. Capture a uniform white reference at your final lighting, lens, iris and working distance, compute the per-pixel gain that divides the dip out, and apply it to every frame. Many line scan cameras ship the function, and in software it is a single image division — dividing one image by another for flat-field correction shows the working. Re-shoot the reference whenever the set-up changes, because the profile is a picture of your exact geometry, not of the lens alone.
Two limits set how far to push it. Correction multiplies noise by the same gain it applies to signal, so a corner restored from 30% carries 3.3 times the noise, and a hard circle mismatch stays black because gain times zero is zero. On color, correct each channel's profile separately, then re-run white balance. Profiles are the last 20-30% of a falloff problem, not a substitute for coverage.
Line scan: the dark ends of the line
On a line scan camera the sensor is a single row, so the image circle only has to span the line length along the scan direction, and that length is easy to misjudge. Multiply pixels by pitch: 8K at 7 µm is 56 mm, 16K at 5 µm is 16,000 × 5 µm = 80 mm, and 16K at 3.5 µm is 56 mm again. A lens built for a 45-60 mm circle cannot light an 80 mm line, whatever the adapter claims. Buy by line length, not by mount; the line scan lens category sorts by it, and the line scan field of view article covers the geometry along the web.
The LS-LSL-0023 is a 16K 5 µm line scan lens, 116 mm focal length, V-mount.
- Sensor format
- Large format
- Mount
- V-mount
- Image circle
- 60-90 mm
- Focal length
- 100 mm +
If the dark band on your web moves when the light moves, it is the illuminator rather than the lens, and the line scan illumination uniformity guide walks that diagnosis.
Checks before you order
Work this list before the purchase order, not after the first images:
- Sensor diagonal in millimetres from the camera data sheet, and a lens image circle at or above it.
- For line scan, line length from pixels times pitch, and a lens specified for that length class.
- The f-number you will actually run: two to three stops down from wide open for flat corners, checked against the depth of field you need.
- A white-target profile at final lighting, iris and distance — it doubles as your coverage proof and your shading reference.
- Color work planned for per-channel correction and a white balance afterwards.
If the first two lines disagree, change the lens now; every downstream fix trades noise for brightness. Send sensor diagonal, working distance and target field of view through the lens configurator, or reach us through the /contact/ page and we will check the circle against your camera before you order.
Questions
How much vignetting can flat-field correction remove?
Roughly one stop cleanly: a corner at half the centre level needs 2x gain, which also doubles its noise, so the corrected corner carries one stop less signal-to-noise than the centre. A corner at 25% costs two stops. Black stays black at any gain, so an undersized image circle cannot be corrected at all. Capture the reference at final lighting, aperture and working distance, and re-shoot it whenever any of those change.
Does stopping down the aperture fix vignetting?
It fixes the aperture term only, the extra corner loss from shooting wide open. Two to three stops down, that share is usually gone, while the geometric cos-fourth falloff stays exactly the same, because it comes from the field angle, not the iris. On a 2/3" sensor with an 8 mm lens, even at F5.6 the corners remain near the 46% the cos-fourth table predicts, so check depth of field before stopping down further.
Why are the corners of my color image tinted instead of just dark?
The red, green and blue channels do not fall by the same amount toward the edge, so the corner drifts in color even after an overall gain fix. Correct each channel's profile separately, matching red and blue to green, then re-run white balance. The result is three equally dim channels, not three bright ones: the cast disappears while the underlying loss of light stays, which is why coverage still matters.
What image circle does a 16K line scan camera need?
Multiply pixels by pixel pitch: 16,000 × 5 µm = 80,000 µm = 80 mm of sensor length, so the lens must be specified for an 80 mm line, and a 60 mm class optic will not cover it. The circle only has to span the line along the scan direction, not a two-dimensional diagonal, which is why line scan lenses are rated by line length. Choose one length class above your sensor for margin.
Can I fix a 2/3 inch lens on a 1 inch sensor in software?
No. Pixels outside the 11 mm image circle received no light, so no gain, profile or debayering recovers them; the corners are true zeros, not dim values. The fix is a lens whose rated circle meets the 16 mm diagonal, such as a 1 inch format model. If the replacement cannot reach the same field of view at the new working distance, move the camera back and accept the resolution trade instead.