Spherical aberration in machine vision lenses: spot it and fix it

A lens can be perfectly focused and still soft. When the rim rays and the centre rays of the same lens meet at different points along the axis, no focus position lands every ray on the sensor at once. That defect is spherical aberration, and it is the usual reason a machine vision lens looks mediocre wide open, right in the middle of the field where no other aberration should touch it. Here you get the ten-minute bench test that confirms it, the arithmetic that sets how far to stop down before diffraction takes over, and the rule for when the honest fix is a corrected or telecentric lens.

What is spherical aberration in a machine vision lens?

Spherical aberration is the on-axis defect in which rays entering near the rim of a lens cross the axis closer to the lens than rays through its centre, so one spherical surface has no single true focus. It is geometry, not damage: incidence angle grows toward the rim of a spherical surface, so a positive lens bends its rim rays harder and they meet the axis before the paraxial focus.

At the sensor, placed at the compromise position, a sharp central image is superimposed with a defocused rim image. The result is uniform softness and lost edge contrast everywhere, including dead centre — the spot pure spherical aberration leaves is a round halo, not the comet of coma or the cross of astigmatism, which live off-axis. If the middle of your field never quite snaps wide open, this is the first suspect; the optical aberrations guide covers the off-axis cast.

Two exponents drive every number on this page. Third-order theory puts the transverse blur at the cube of the ray height in the pupil, and the longitudinal focus spread at its square. Halve the aperture and the blur scale falls eightfold; nothing you clean, tighten or refocus removes it, because it is ground into the surface.

How do you test for it on the bench in ten minutes?

The bench test takes ten minutes: focus wide open on a centred pinhole target, close the iris two stops, and refocus — if the sharpest focus moves and the image sharpens, you were looking at rim rays that never had a common focus. You need the camera, the lens, a stable focus stage, and a backlit pinhole or a fine dark edge centred in the field.

1. Open the iris to its smallest f-number, focus for peak sharpness, and write down the stage reading.
2. Close the iris two stops without touching focus, and look: a still-soft image that sharpens after you refocus is rim blur being excluded.
3. Write down the new best-focus position. The distance from the first reading is the focus shift, in micrometres or focus-ring marks.
4. Step one stop at a time to the planned working aperture and note where visible sharpening stops.

Read two numbers out of the test. The focus shift is your calibration liability: it tells you how much best focus moves each time exposure control or an operator changes the aperture. The stop where sharpening ends is your working f-number — past it, the cube law has collected the easy wins and diffraction starts charging.

If the centre stays crisp wide open and only the corners blur, the defect is off-axis — coma, astigmatism or field curvature — and this test will not move it. Diagnose that with the aberrations guide linked above instead.

How many f-stops should you stop down?

Start with one to two f-stops and no more: third-order optics makes the ray blur grow with the cube of the aperture radius, so halving the diameter cuts that blur roughly eightfold, and past two or three stops diffraction eats the gain. The first two stops do the work: they delete the rim rays that carry the worst blur under the cube law, and the image usually stops improving visibly somewhere between two and four stops down. Beyond that point each stop adds diffraction faster than it removes aberration.

Every stop also halves the photons. Budget exposure or LED drive before you commit: two stops of correction means four times the light, four times the exposure or four times the strobe energy.

The bench test hands you the answer for your specific lens, so run it rather than assuming a number. An iris with real range makes the test quick:

On a 1.1", 20 MP station the LS-FFL-0567 covers the whole F2.8-22 span, so the test and the working stop both live inside one lens.

What does each stop cost you in light, diffraction and depth of field?

Every stop halves the light and grows the diffraction spot about 40%, while depth of field grows in the same proportion — at f/5.6 and 550 nm the Airy disk is 7.5 µm wide, which is 2.2 pixels on a 3.45 µm sensor. Light is the simple cost: aperture area falls as 1/N². Diffraction is the hard floor: once the Airy disk exceeds about two pixels, the sensor rather than the lens sets the blur. Depth of field is the refund: it grows in the same proportion as f-number, so the stops that cost light pay you depth.

The ceiling is the stop button: keep the Airy disk at or under two pixels and stopping down still buys sharpness; cross it and you are blurring on purpose. The diffraction limit and aperture guide works the same formulas from the lens side.

Worked example: 35 mm lens on a 5 MP 2/3" camera

Example inputs, typical of a 5 MP 2/3" station: pixel pitch 3.45 µm, sensor width 8.8 mm, 550 nm light, target field of view 88 mm, exposure cap 4 ms on a static part.

A 35 mm, 2/3", 6 MP C-mount lens fits this station:

Magnification is m = 8.8 / 88 = 0.1. Working distance is WD = f × (1 + m) / m = 35 mm × 1.1 / 0.1 = 385 mm. Wide open at f/2.8 the centre reads soft at every focus position; the two-stop test confirms rim blur, so the station runs at f/5.6:

• Aberration blur: aperture diameter halves, so the transverse blur scale drops by 2³ = 8×.
• Light: two stops cost 2² = 4× exposure, so the programme goes 1 ms → 4 ms, inside the cap.
• Diffraction: d = 2.44 × 0.55 µm × 5.6 = 7.5 µm = 7.5 / 3.45 = 2.2 pixels, right at the two-pixel line.
• Ceiling check: N ≤ 2 × 3.45 / (2.44 × 0.55) = 5.1, so f/5.6 is the last usable stop. At f/8 the spot grows to 2.44 × 0.55 × 8 = 10.7 µm = 3.1 pixels and the image degrades.
• Depth of field: with c = 2 px = 6.9 µm, DOF at f/2.8 is 2 × 2.8 × 0.0069 mm × 1.1 / 0.01 = 4.3 mm; at f/5.6 it is 8.5 mm, enough to hold ±4 mm of part height variation.

Decision: run this station at f/5.6 and 4 ms, and keep the gains — eightfold less aberration blur, 8.5 mm of depth of field, diffraction still at 2.2 pixels. Stopping to f/8 would buy depth the part does not need and pay in real blur.

Wavelength moves the ceiling. Blue light at 460 nm puts the f/5.6 spot at 2.44 × 0.46 × 5.6 = 6.3 µm, or 1.8 pixels, and usually raises edge contrast on bare metal and pale plastics — the LED colour guide picks the wavelength for your part.

When should you buy a corrected lens instead of stopping down?

Buy a corrected or aspheric design when the two-stop fix leaves you short on any of three budgets: blur must stay under one pixel, exposure cannot rise fourfold, or best focus must not move when the aperture changes. Corrected designs spend extra elements and aspheric surfaces on exactly this error, which is why an entry FA lens can look ordinary wide open while a measurement-grade design snaps at the same aperture. Each failure mode names its buyer:

• Gauging under one pixel: 2.2 pixels of diffraction at f/5.6 already exceeds a sub-pixel edge budget. If the tolerance needs it, no stop position will do; you need a design that is sharp wide open.
• Motion-capped exposure: if 4 ms blurs the part, the two-stop fix is unaffordable at any price of light. A corrected lens at f/2.8-f/4 keeps exposure where motion allows.
• Iris-dependent focus: if exposure control varies the aperture between frames, best focus wanders by the shift you measured. Keep auto iris out of a gauging station — the automatic iris guide explains how exposure and focus are coupled.

There is a fourth case: depth of field beyond the ceiling. If the part needs ±8 mm at a pixel pitch whose ceiling is f/5.1, stopping down cannot deliver it — you are past the point where the iris is the right tool, and a lens designed for the job is. That is the telecentric lens for gauging decision, and for a measurement station it is usually worth it.

Do telecentric lenses solve spherical aberration?

No lens built from spherical surfaces escapes the defect entirely, but machine-vision telecentric lenses are multi-element designs corrected so rim and centre rays meet at one focus, which is the same correction you would otherwise buy aspheric elements for. Telecentricity itself is a chief-ray property: it holds magnification constant across depth of field, which is what stops a gauging result drifting when a part sits 2 mm nearer or farther. Aberration correction is a separate property, and the two travel together in measurement optics because gauging needs both — which is why the telecentric lenses category carries both as standard.

For the trade between ordinary and telecentric designs, see entocentric vs telecentric lenses; for how their remaining distortion is specified, see the telecentric distortion guide. The catalog's corrected telecentrics span the common ranges:

All 3 share: Mount C-mount. Values as printed in each product's data sheet; open a part for its drawing and full specifications.

The LS-TCL-2118 covers a 2/3" sensor at 1x from a 108 mm working distance; the LS-TCL-1422 reaches 0.166x on a 1" sensor from 258 mm; the LS-TCL-0811 gives 1.36x at 73 mm working distance and carries a coaxial light port for surface and mark inspection.

Which lens should you order for your station?

For a static inspection with 3.45 µm pixels or coarser and light to spare, run the two-stop fix at the diffraction ceiling; for sub-pixel gauging, capped exposure or a moving iris, order a corrected or telecentric lens and lock its aperture. Work the checklist in order; the first line that fails names the purchase:

• Two-stop test on the real part. Record focus shift and the stop where sharpening ends. Why first: both later numbers come from it.
• Diffraction ceiling. N ≤ 2p / (2.44λ): 3.45 µm pixels at 550 nm stop at f/5.1; 2 µm pixels stop at f/3.0. Why: past the ceiling, stopping down blurs more than it corrects.
• Depth of field. Compare DOF at the working stop with part height variation. Why: DOF ≈ 2Nc(1+m)/m² is what the stops buy back.
• Exposure cap. Every stop doubles exposure or LED drive; two stops need 4×. Why: motion blur undoes the optical gain.
• Mechanics. Lock the iris and the focus rings after setup — the lens locking screw guide shows why a drifting ring silently moves calibration.

Three outcomes cover most stations. Static part, coarse pixels, light to spare: stop down two stops from wide open, refocus, add light, done. Gauging with a sub-pixel budget, or depth past the ceiling: order a corrected telecentric sized by sensor width over field of view, and run it at its design aperture. Moving parts or a wandering exposure controller: corrected glass at a locked aperture and fixed exposure, because stability is the specification.

The machine vision lenses catalog and its finder filter by sensor format, working distance and resolution, and the lens configurator walks the same numbers this page used. If the two-stop test on your part says corrected glass, start the search there — the test cost you ten minutes and just saved you a lens.