Optical aberrations in machine vision lenses: how stopping down helps

A machine vision image can be in perfect focus and still unusable: edges smear, contrast drops, and the inspection algorithm gets the blame. More often than not the fault is optical aberration, and the fastest fix is the aperture ring, not new software. Closing an entocentric lens to f/4-f/8 removes the marginal rays behind most blur terms, and the improvement follows third-order optics closely enough to predict. This page names each aberration by the symptom it prints in the image, shows why the gain ends near f/8, and works a 16 mm, 20 MP example end to end, so you can set the working aperture by arithmetic instead of trial and error.

Which aberrations the iris actually fixes

The iris sits between the lens groups and trims the cone of rays that forms every image point. Third-order optics names each blur term after how fast it grows with the marginal ray height ρ, the steepness of that cone: spherical aberration grows with ρ³, coma with ρ², and astigmatism, field curvature and the defocus from longitudinal color grow with ρ. Closing from f/2.8 to f/8 divides the ray height by 8 / 2.8 = 2.86, so each term shrinks by the square or cube of that factor.

The ÷ factors follow directly from the scaling: 2.86³ = 23, 2.86² = 8.2, 2.86¹ = 2.9. Real lenses deviate from ideal third-order behavior, but the ranking — spherical falls fastest, distortion not at all — holds across FA designs, which is why one turn of the ring fixes so many soft images.

Why the sweet spot sits at f/4 to f/8

Stopping down moves two blur sources in opposite directions. Aberration blur falls with the powers of 1/N above; diffraction blur rises in a straight line with N. For entocentric FA lenses feeding 2/3-inch through 1.1-inch sensors, the curves cross between f/4 and f/8, and that band is the standard sweet spot: below it aberrations dominate, above it diffraction eats the gain.

At f/5.6 the diffraction disk is about 7.5 µm across; at f/11 it is 14.8 µm. The diffraction limit and aperture effects guide works the diffraction side of this trade-off in detail. The crossover also shifts with pixel size — sensors with pixels under 3 µm meet diffraction earlier — which is why the Nyquist limit and camera resolution guide belongs in the same decision.

Steep cones and dense pixels are where aberrations bite hardest, so the extremes of the lens range show it first. Two lenses in the catalog mark the two ends: an 8.5 mm design for 1-inch sensors, and a 16 mm design built for 20 MP on the 1.1-inch format:

Worked example: working aperture for a 16 mm, 20 MP 1.1-inch set-up

The case: the LS-FFL-0567, a 16 mm lens with an aperture range of F2.8-22, rated for 20 MP sensors in the 1.1-inch format. That sentence quotes the datasheet; every number below it is derived here, with the arithmetic shown.

• λ = 550 nm — mid-visible green, the standard reference wavelength for monochrome sensors.
• Sensor geometry — by the type convention of 16 mm of diagonal per inch of format, the 1.1-inch class runs a 17.6 mm diagonal; assume the common 3:2 aspect. (What the inch classes mean, physically: the lens sensor format explainer.)
• Rule — d = 2.44 × λ × N.

Pixel pitch: a 3:2 diagonal splits by √13 = 3.606, giving 17.6 × 3 / 3.606 = 14.6 mm wide and 17.6 × 2 / 3.606 = 9.8 mm tall — an area of 143 mm², or 143,000,000 µm². Divided by 20,000,000 pixels that is 7.15 µm² per pixel, so the pitch is √7.15 ≈ 2.7 µm.

Wide open, the 1.4-pixel disk is not what you see — the lens's own aberration blur is, which is why FA lenses look soft at maximum aperture even though the disk math looks harmless. Sweep f/4, f/5.6 and f/8 while a focus metric watches a fixed target: sharpness climbs, then flattens near f/5.6-f/8. Past f/8 the disk passes 4 pixels and grows about 40% per stop. The decision: run this pairing at f/5.6-f/8 for inspection work; move to f/11-f/16 only when part height forces the depth of field; leave f/22 to presence checks, where an 11-pixel blur circle is tolerable and measurement is not the goal.

Depth of field grows in proportion to N at fixed magnification, so f/8 holds twice the depth of f/4 on this set-up — the payment you get back for the lost resolution. Size that margin before you commit with the depth of field calculator.

What stopping down cannot fix

Distortion is a mapping error: the lens bends straight lines, and the amount is set by field height alone, not by f-number. Stop from f/2.8 to f/22 and the picture frames exactly the same bowed geometry, only darker and sharper. The fixes live elsewhere: read the datasheet distortion figures the way the geometric vs TV distortion guide describes, and when the tolerance still misses, correct the mapping with the lens distortion correction workflow.

Lateral color ignores the ring for the same reason: red and blue form images at slightly different magnifications, the offset grows toward the corners, and no f-number moves it. Only lens correction or per-channel calibration removes it.

Flare and ghosting are stray light, not aberration. A bright highlight smears a streak across the frame whatever the iris does; that takes a shroud, better coatings or moved lighting, and the blue streak diagnostic separates the two cases at the bench.

The cost of every stop: light, exposure and motion blur

Each stop doubles N and halves the light. From f/2.8 to f/8 is three stops (2.8 → 4 → 5.6 → 8), so the sensor receives one-eighth of the light: a 0.5 ms exposure becomes 4.0 ms. A part moving 100 mm/s then smears 4.0 ms × 0.1 mm/ms = 0.4 mm across the frame — often worse than the aberration you were fighting. The alternatives are 8× the light or 3 stops of gain, about +18 dB, which costs signal-to-noise ratio. How iris, exposure and gain interact is the subject of the automatic iris, exposure and gain guide, and the light-gathering arithmetic behind f-numbers is in the M12 lens light-gathering note.

Name the aberration before turning the ring

• Whole field soft at f/2.8, tightening by f/5.6 — spherical aberration. Stop down; you are on the right side of the crossover.
• Comet-tailed points away from center, sharp on axis — coma. Stop down; a comet that survives f/8 points to a tilted or decentered element, not the aperture.
• Edge detail sharp in one direction only — astigmatism. Stop down; if it persists past f/8, plan a lens change.
• Straight lines bow at every f-number — distortion. The ring cannot help; see the previous section.
• Color fringes that flip sides through focus — longitudinal color. Stop down, and set focus at the working aperture.
• Low contrast everywhere plus bright streaks from highlights — flare. Fix lighting and shading, not the iris.

Sweep rather than guess: step through the ring positions while a reliable sharpness metric watches a fixed target, and take the position where the metric flattens, one stop before it falls again.

Focus at the working aperture, then lock it

Residual spherical aberration pulls the marginal-ray focus off the paraxial one, so best focus can shift as you close the iris. Focus with the ring already at the working position, not wide open. The ring is also a mechanical part: on a vibrating machine a loose iris ring walks a stop at a time and the image drifts soft over weeks. Set it, lock it, and mark it — the lens locking screws guide covers the screws and the clearance they need inside a housing.

Before ordering, check three datasheet lines: the aperture range brackets f/5.6-f/8 with room on both sides; the printed distortion figure fits the measurement tolerance; the image circle covers the sensor format with margin.

When the usual answer is wrong

The f/4-f/8 band is a rule for entocentric FA lenses with an iris. Fixed-magnification designs are corrected for one design aperture, and the datasheet f-number is a constant of the optics: the LS-FFL-1023, for instance, ships fixed at F13.4 for 0.5× work at a 150 mm working distance, already at its corrected best. Tune such a lens with light and exposure, never with an aperture setting it does not have.

When the enemy is distortion or color rather than blur, a telecentric lens beats any amount of stopping down: the entocentric vs telecentric guide sorts the choice, and the telecentric distortion and telecentricity explainer decodes its datasheet. The LS-TCL-0574 is that class in practice: 0.4× magnification at a 227 mm working distance on a 1.2-inch sensor.

And when the line runs fast, the trade can reverse. If f/8 demands 4 ms and motion blur allows only 1 ms, open up toward f/4 and buy the better-corrected lens instead: blur paid in hardware beats blur paid in smear.

The decision, case by case

• Image soft wide open, sharpest at f/5.6-f/8 — normal behavior. Set the ring at the flattest point of the sweep, lock it, and refocus there.
• Still soft or comet-tailed at f/8 — the ring is exhausted. Check for a decentered element, then move up a correction class.
• Straight lines bow at every stop — distortion. Choose a low-distortion or telecentric lens, or calibrate the mapping.
• Motion blur forcing exposures below the sweet spot's budget — add light or a better lens; do not chase sharpness into a longer exposure.
• Blur growing again past f/8 — diffraction has taken over. Come back one or two stops and accept the depth of field loss.

Compare models with these lines in front of you: aperture range, distortion figure, image circle, resolution rating. The machine vision lenses category holds the range, the lens finder filters it by sensor and focal length, and the lens configurator steps through the whole chain. The lenses topic page collects the optics guides around this one, and if a sweep never flattens, bring the image set to us through the contact page.