Sensor Size and Lens Compatibility in Machine Vision: Image Circle, Vignetting, and Relative Illumination
How to match a lens to a sensor: coverage math, vignetting mechanisms, and the relative illumination curve that combines them.
A lens matches a sensor when its image circle diameter equals or exceeds the sensor diagonal, with margin left for corner sharpness. That comparison is necessary but not sufficient: after coverage you still check mechanical vignetting, aperture-dependent optical vignetting, the fixed cos4 falloff of the projection, and chief ray angle (CRA) match to the sensor's microlens array. This page covers all four. For sensor format dimensions, naming conventions, and diagonal charts, see the CMOS sensor size guide.
How do I know if a lens covers my sensor?
Compare the lens image circle diameter to the sensor diagonal. If the image circle equals or exceeds the diagonal, coverage is sufficient; if it is smaller, the sensor corners fall outside the illuminated area and record black. Calculate the diagonal from the active area, not from the format name. Both a mechanical fit (mount and flange distance) and an optical fit (image circle, CRA, relative illumination) have to hold, and a correct mount does not rule out vignetting.
For a 1/2-inch sensor with a 6.4 × 4.8mm active area: diagonal = √(40.96 + 23.04) = √64 = 8.0mm. That sensor needs an image circle of at least 8.0mm plus margin. Round the diagonal up and the lens's rated image circle down before comparing, so a borderline pairing is judged conservatively.
Sensor format reference and minimum image circle
Sensor formats Commonlands lenses cover, from 1/4-inch to 1.1-inch, with the minimum image circle each needs for full coverage.
| Sensor format | Typical active area (mm) | Diagonal (mm) | Minimum image circle | Typical lens class |
|---|---|---|---|---|
| 1/4" | 3.2 × 2.4 | 4.0 | 4.0mm+ | M12 |
| 1/3" | 4.8 × 3.6 | 6.0 | 6.0mm+ | M12 |
| 1/2.9" | 5.6 × 3.2 | 6.4 | 6.4mm+ | M12 |
| 1/2.7" | 5.3 × 4.0 | 6.6 | 6.6mm+ | M12 |
| 1/2.5" | 5.8 × 4.3 | 7.2 | 7.2mm+ | M12 |
| 1/2" | 6.4 × 4.8 | 8.0 | 8.0mm+ | M12 or C-mount |
| 1/1.8" | 7.2 × 5.4 | 9.0 | 9.0mm+ | M12 or C-mount |
| 1/1.7" | 7.6 × 5.7 | 9.5 | 9.5mm+ | M12 or C-mount |
| 2/3" | 8.8 × 6.6 | 11.0 | 11.0mm+ | C-mount |
| 1" | 12.8 × 9.6 | 16.0 | 16.0mm+ | C-mount |
| 1.1" | 13.3 × 11.3 | 17.5 | 17.5mm+ | C-mount |
Active area varies by manufacturer and model even within one format label, so use the exact width and height from the sensor datasheet. Look them up in the image sensors database.
What causes vignetting in machine vision?
Vignetting has three mechanisms, each with a different fix. Mechanical vignetting is physical clipping: the image circle is smaller than the sensor diagonal, so corner pixels get no light regardless of aperture.
Optical vignetting is aperture-dependent roll-off, from off-axis bundles seeing a smaller effective aperture. It is worst wide open and improves as you stop down, which a C-mount iris ring lets you do. Most M12 lenses have no iris and are fixed at manufacture. Natural falloff follows the cos4 law and does not respond to aperture at all.
At a 20° half-angle, cos4 gives about a 22% drop. At 30°, the drop is about 44%. At 45°, it reaches about 75%. The half-angle that matters for corners is the diagonal one set by the sensor, not the horizontal field, so a lens with a 30° horizontal half-angle has a larger corner angle and a larger worst-case loss. This holds for rectilinear projection. Wide-angle and fisheye designs beat the raw figure with deliberate distortion and pupil aberration, so treat it as their worst case.
How to tell the three vignetting mechanisms apart when choosing a Commonlands lens: match the symptom to its mechanism and fix.
| Symptom | Likely mechanism | First check | Fixable by stopping down? |
|---|---|---|---|
| Hard black corners, sharp boundary | Mechanical vignetting | Compare image circle to sensor diagonal | No; a different lens is required |
| Smooth radial falloff, improves stopped down | Optical vignetting | Measure relative illumination at multiple F-numbers | Yes, on C-mount with an iris ring |
| Smooth radial falloff, unchanged stopped down | Natural (cos4) falloff | Calculate expected falloff from the corner (diagonal) field half-angle | No; it is governed by projection geometry, not aperture. Magnitude depends on lens design (rectilinear vs. wide-angle/fisheye) |
| Corner darkening with color shift | CRA mismatch (see below) | Compare lens CRA curve to sensor microlens spec | No; brightness correction does not fix color error |
Flat-field correction can normalize any of these in software, but it amplifies corner noise and cannot restore contrast or color that CRA mismatch removes. Where corner quality drives the pass/fail decision, minimize vignetting in the optics first and treat correction as cleanup for residual non-uniformity, not the primary fix.
What is relative illumination in a lens?
Relative illumination is the normalized brightness at a field position, expressed as a ratio to the on-axis illuminance. A lens at 70% relative illumination in the corner delivers 30% less light there than at center under the same exposure. It is the umbrella curve that combines mechanical vignetting, optical vignetting, cos4 falloff, and CRA mismatch. It is not a synonym for any one of them.
A low distortion spec does not buy corner brightness: a lens under 0.2% distortion can still sit at 50% relative illumination at the corner, so check both specs separately for dimensional work.
What feeds the relative illumination curve on a Commonlands M12 or C-mount lens, and what changes each contributor.
| Contributing mechanism | What it changes | What fixes it |
|---|---|---|
| cos4 roll-off | Illuminance falls as the fourth power of the cosine of the field half-angle under rectilinear projection; wide-angle and fisheye designs can beat this raw figure with deliberate distortion and pupil aberration | Largely fixed by projection geometry for rectilinear designs; accept it or choose a longer focal length, or a lens whose projection is intentionally engineered to reduce it |
| Optical (aperture) vignetting | Oblique ray bundles see a reduced effective aperture | Stop down the iris on C-mount; most M12 lenses are fixed at design |
| Mechanical (image-circle) vignetting | Illuminated cone smaller than sensor diagonal | Use a lens with a larger rated image circle |
| CRA mismatch | Principal ray angle at the corner mismatches sensor microlens design | Select a lens with a CRA profile matched to the sensor spec |
| Filter/window stack | Coating passband shifts and higher Fresnel loss at the oblique angles corner rays actually see, plus added aberration in converging light | Use AR-coated optics rated for the lens's CRA range; budget filter stack into the CRA analysis |
Does CRA matter once the image circle is large enough?
Yes. Chief ray angle (CRA) is the angle at which the principal ray reaches the sensor at a given field position: near zero at center, larger and oblique at the corners. CMOS sensors have microlens arrays shaped for a specific CRA profile that varies with field height. If the lens CRA at the corner does not match, the microlenses steer light away from the photodiode and corner sensitivity drops.
Request the lens CRA profile at 0°, half-field, and full-field, and compare it against the sensor's microlens CRA at the same heights. A full-field mismatch beyond the sensor's rated CRA acceptance tolerance produces measurable corner shading, and that tolerance is sensor-specific, so read it from the sensor datasheet rather than assuming a threshold. This data is not always in a headline datasheet. Ask the manufacturer if it is missing. Commonlands supplies CRA data where available for its M12 and C-mount lenses.
Fisheye fill factor: the intentional exception to the coverage rule
Standard lenses are specified so the image circle covers the sensor diagonal. Fisheye systems deliberately vary that ratio, because a fisheye still has a defined image circle; what changes with sensor choice is how much of the projection the sensor captures. A complete circular image needs the circle to fit inside the sensor's short dimension, not just the diagonal, so a circle can clear the diagonal and still be clipped top and bottom.
How a Commonlands fisheye lens fills different sensors, set by the image-circle-to-sensor ratio.
| Fill mode | Image circle vs sensor | What the sensor sees | Typical use |
|---|---|---|---|
| Circular fisheye | Image circle smaller than the sensor's short dimension | Complete circular image with black corners; maximum fisheye FOV visible | 360-degree imaging, panoramic capture |
| Full-frame fisheye | Image circle at or just above sensor diagonal | Fisheye content fills the frame edge to edge | SLAM, robotics, surround-view systems |
| Cropped fisheye | Image circle larger than sensor diagonal | Sensor captures only the central region; narrower effective FOV, less apparent distortion | Compact embedded builds using a wide fisheye at moderate FOV |
Commonlands product examples across formats
These Commonlands lenses show how image circle, sensor format, and mount scale together, and where vignetting and relative illumination differ.
Lens picks by sensor format
For a rectilinear lens the coverage test is one comparison: the image circle has to reach the sensor diagonal. This table maps common formats to a Commonlands lens whose published image circle clears that diagonal, reusing the diagonals from the reference table above.
| Sensor format | Diagonal (mm) | Example sensors / use | Recommended Commonlands lens | Lens image circle |
|---|---|---|---|---|
| 1/4" | 4.0 | Low-cost surveillance, webcams | CIL343 4.4mm M12 | 8.8mm-9.7mm; oversized for 1/4" |
| 1/3" | 6.0 | Security cameras, drones | CIL062 6mm M12 | 9.0mm |
| 1/2" | 8.0 | Compact cameras, drones | CIL085 8mm M12 | 8.9mm |
| 2/3" | 11.0 | Global-shutter machine vision | CIL522 12mm C-mount | 11.4mm |
| 1" | 16.0 | Global-shutter machine vision | CIL544 25mm C-mount | 17.6mm |
The CIL544 covers 1.1-inch sensors, the top of the Commonlands C-mount range. For larger formats such as 4/3-inch or APS-C, large-format C-mount lenses from Fujinon, Kowa, or Edmund Optics are the standard options.
Frequently asked questions
These answers apply to any lens and sensor pair. Commonlands lists image circle in millimeters for its M12 and C-mount lenses, so coverage is a direct comparison.
Does CRA matter once the image circle is large enough?
Yes. Chief ray angle describes the angle at which light exits the lens at the sensor corners. If it does not match the sensor's microlens array design angle, the microlenses cannot direct that light onto the photodiode efficiently. The result is corner shading or color drift even when the image circle fully covers the sensor. Mismatch is most common with wide-angle M12 lenses on high-resolution sensors.
Can flat-field correction fix lens vignetting?
Flat-field correction normalizes brightness by dividing each pixel by a gain factor from a reference white image, and it removes the visible appearance of corner darkening. It cannot restore photons or signal-to-noise ratio that were never collected: a corner receiving 50% of center illumination has its signal and its noise amplified by the same gain factor, so corner SNR is unchanged by the correction. It is still worse than center SNR, but no worse than the uncorrected corner.
Is a larger image circle always better?
No. A lens designed for a larger format needs a larger optical group, which adds mass, cost, and mount size. If your sensor diagonal is 7.2mm, a lens rated for 17.6mm adds weight and cost for a benefit that is usually small on that sensor.
Oversizing does reduce optical vignetting and seats the active corners in a better-corrected zone of the image circle, but it does not reduce cos4 falloff, since the field angles on the sensor are set by focal length and sensor size, not by the lens's rated format. Match image circle to sensor diagonal with a 10-15% margin rather than defaulting to the largest available option.
Can a 1/3-inch lens work on a 1/2-inch sensor?
Typically not without vignetting. A 1/3-inch format lens has an image circle around 6.0mm, and a 1/2-inch sensor has a diagonal around 8.0mm. The sensor corner sits at a radius of 4.0mm (half the 8.0mm diagonal) while the illuminated circle's edge is at a radius of 3.0mm, so the corners fall about 1mm outside the circle, producing dark or black corners that cannot be recovered in software without sacrificing resolution.
Why do fisheye lenses behave differently on different sensor sizes?
A fisheye lens has a defined image circle like any other lens. What changes with sensor choice is how much of that projection reaches the sensor. Circular fisheye with black borders occurs when the image circle is smaller than the sensor's short dimension, so the full circle sits inside the frame with corners unlit.
Full-frame fisheye occurs when the image circle is at or just above the sensor diagonal, filling the frame edge to edge. A sensor whose short side is smaller than the image circle, while the diagonal is larger, clips the circle top and bottom, so engineers pair a given fisheye lens with a sensor sized relative to its rated circle depending on which fill mode they want.
Need help matching a lens to your sensor?
Commonlands publishes image circle specifications, and where available relative illumination and CRA data, for our M12 and C-mount lenses. Send us your sensor part number and working distance and we will point you to lenses that clear coverage with margin.