Chromatic aberration in machine vision lenses: fix colour fringing

Colour fringes along black-and-white edges, red and blue edges that never sharpen together, an image that stays soft however carefully you focus: that is chromatic aberration, and every simple lens has it. Refractive index falls as wavelength grows, so the focal length of a lens is shorter in blue light than in red. Below you get the two-minute test that shows whether a lens is colour-corrected, the formula and numbers that size the error at your aperture, and a decision path: one LED colour, an achromat, an apochromat, or an IR-corrected design. It is written for anyone who specifies the lens and the light together.

The decision up front

• One LED colour is enough for your inspection — use a red or blue bar light with a monochrome camera. With a single narrow wavelength in the scene, red-versus-blue focus differences cannot exist and chromatic aberration is gone. This is the least-cost fix: change the light, keep the lens.
• White light is required (colour inspection, colour camera, human review of the image) — buy an achromatic lens at minimum, corrected to bring red and blue to one focus. Choose an apochromatic lens when you measure colour or run a high-resolution sensor near its limit.
• You illuminate in infrared — specify an IR-corrected lens. A visible-corrected lens refocuses strongly at 850 nm or 940 nm.
• You already own an uncorrected lens — stop down two stops to blunt the axial fringing, pay in light, and accept the lateral fringe at the frame edge. On a moving line this trade usually fails; the worked example shows why.
• Before any purchase — run the refocus test below. It costs two minutes and tells you what you actually own.

Two errors, one cause

The refractive index of optical glass falls as wavelength increases — for a typical crown glass by about 0.008 between the blue line at 486 nm and the red line at 656 nm. Shorter wavelength, higher index, stronger bending: blue light focuses closer to the lens than red. From that single fact, two image errors follow.

Longitudinal (axial) chromatic aberration: the focal point moves with wavelength. Hard light-dark transitions gain colour fringes and the whole image loses contrast, because at any focus setting at least two colours are out of focus.

Lateral (transverse) chromatic aberration: magnification moves with wavelength. Red and blue images of the same object come out different sizes, so the fringe grows toward the frame edge. Wide-angle designs show it first, and no aperture change reduces it — it is a geometry error, not a focus error.

On a monochrome camera the fringes are grey rather than coloured. The contrast loss is identical.

Vd is the Abbe number of the glass, about 64 for a typical crown. m is the magnification and N the set f-number; the (1 + m) term converts focal-length spread into sensor-side defocus at finite magnification.

The two-minute refocus test

1. Light the target with red light only — a red LED bar, roughly 620-630 nm.
2. Focus critically on a black-white edge, then lock the focus ring.
3. Change nothing but the light: switch to blue.
4. Read the result. If the image went soft and the focus ring has to move, the lens is not colour-corrected; the travel you needed is the axial error made visible.
5. Repeat with your infrared source. The shift is larger again, because index keeps falling through 850 nm and 940 nm.

How big the error actually is

For a single uncorrected lens element, the axial spread between blue 486 nm and red 656 nm is the focal length divided by the Abbe number:

• 16 mm lens: Δf ≈ 16 / 64 = 0.25 mm
• 35 mm lens: Δf ≈ 35 / 64 = 0.55 mm
• 50 mm lens: Δf ≈ 50 / 64 = 0.78 mm

Real multi-element machine vision lenses sit between this singlet bound and a true achromat, so treat f/64 as the worst case your bench test can reveal. An achromatic lens brings two wavelengths — red and blue — to one focus; the residual secondary spectrum is of order f/2000, about 8 µm on a 16 mm lens. An apochromatic lens brings three or more wavelengths (blue, green, red) to a common focus and corrects spherical aberration at multiple wavelengths at the same time.

The lateral error at the frame edge is the image height divided by the Abbe number: about 1.6% between red and blue. At the edge of a 14.6 mm-wide sensor that is 7.3 mm × 0.016 ≈ 0.11 mm, or about 40 pixels of 2.74 µm — a fringe you can see from across the room.

Worked example: white light on a 20 MP camera

The example lens is the LS-FFL-0567: a 16 mm C-mount machine vision lens with an F2.8-22 range, a 16-22 mm image circle and a 20 MP rating on a 1.1-inch sensor.

Assume a 1.1-inch sensor 14.6 mm wide with 2.74 µm pixels — about 5,300 pixels across — and a part that needs a 58 mm field of view:

• Magnification: m = 14.6 / 58 ≈ 0.25×
• Working distance: WD = f × (1 + m) / m = 16 × 1.25 / 0.25 = 80 mm
• Object-side pixel: 2.74 µm / 0.25 = 11 µm on the part

A white LED spans the whole visible range, so take the singlet bound: Δf = 16 / 64 = 0.25 mm. The colour blur on the sensor is b = Δf × (1 + m) / (2 × N); at F2.8 that is 0.25 × 1.25 / (2 × 2.8) = 0.056 mm. Across the aperture range:

Read the table as the decision. Wide open, the white-light image carries 20 pixels of colour mush. Closed all the way to F22 the fringe shrinks below three pixels but never reaches zero, and every stop costs light: an exposure of 200 µs at F2.8 needs 200 × (11 / 2.8)² ≈ 3,100 µs at F11. On a part moving 150 mm/s that is 0.46 mm of motion — 42 object pixels of blur. The cure kills the image. Strobing the light shortens the effective exposure, but the pulse then has to carry the energy.

An achromatic lens in the same station has Δf ≈ 16 / 2000 = 8 µm, so b = 0.008 × 1.25 / 5.6 ≈ 1.8 µm at F2.8 — under one pixel, sharp wide open. That is the whole argument for paying for correction: it buys back the aperture.

Why stopping down is only half an answer

Stopping down deepens depth of field, so the axial blur shrinks in proportion to 1/N — visible line by line in the table above. Two things stop it from being a fix:

1. Lateral colour does not respond to aperture at all. Different colours make different-sized images; no iris changes that geometry. The frame-edge fringe stays.
2. Diffraction arrives first. The Airy disc diameter is 2.44 × λ × N: at 550 nm and F22 that is 29 µm, about 11 pixels on this sensor. You would trade 2.6 pixels of colour blur for 11 pixels of diffraction blur.

Read how stopping down helps the other aberrations alongside the diffraction limit at the same aperture: together they set the window of usable f-numbers, and colour correction widens that window from the wide end.

The least-cost fix is one wavelength

A colour LED emits a band roughly 20-30 nm wide. Inside such a band there is no red-versus-blue focus split, so with a monochrome camera and a single red or blue light, chromatic aberration cannot form an image defect. Why monochromatic lighting wins covers the contrast side of the same choice, and which LED colour gives the best contrast settles the wavelength by the defect, not by habit.

A red bar such as the LS-BAR-1168 — 423 x 40 mm, diffused, 24 V — drops into a station in place of its white equivalent such as the LS-BAR-1276 at 372 x 28 mm, also 24 V, with no change to the mechanical layout.

One caution: a white LED is a blue chip plus phosphor, so white light already contains the full visible span. White light is the problem, not a neutral default — reach for it only when the application needs true colour. The bar lights finder lists every model with its colour options, in sizes from under 50 mm to over 400 mm.

When white light is required: achromat, apochromat, IR-corrected

When the part must be seen in true colour, the correction moves into the lens:

Check the resolution class of the lens against the sensor before anything else — a corrected lens that cannot resolve the pixel count wastes both halves of the budget. The machine vision lenses finder filters by sensor format, image circle and resolution, and the lens step of the configurator walks the same choice from your field of view and working distance. Choosing the lens focal length comes first, and matching lens format to sensor decides whether the corners ever see the corrected field. Two classes from the same catalogue make the budget point:

All 2 share: Mount C-mount. Values as printed in each product's data sheet; open a part for its drawing and full specifications.

Infrared moves focus the furthest

Refractive index continues to fall from red into the near infrared, so the focus shift between a visible setting and 850 nm exceeds any shift within the visible band — which is why step 5 of the refocus test is the most dramatic. The bar light range includes 850 nm and 940 nm versions, so the situation is common.

If the station runs IR only, refocus at the IR wavelength and check whether the resolution survives. If the camera must work in visible light and IR — day operation plus IR at night, or visible plus through-plastic IR — the lens must hold focus across both bands, which is exactly what an IR-corrected design delivers. Ambient visible light leaking into an IR station is also out of focus relative to the IR image; a band-pass filter such as the LS-LXR-0225, 850 nm with an M30.5 x 0.5 thread, blocks it at the lens and sits in the lens accessories range.

For colour cameras in mixed light, near-infrared contamination and IR-cut filter options covers the other half of the problem.

Checks before you order

• Run the red/blue refocus test on the lenses you already own; record the focus travel each one needs.
• Fix the light colour first. If one LED colour gives the contrast you need, an uncorrected lens may already be sharp enough.
• Work the blur budget: aim for b under two pixels at your working f-number. Achromat residuals of order f/2000 clear that bar easily.
• For IR stations: refocus test at the actual wavelength, IR-corrected lens, band-pass filter against ambient.
• Match image circle and resolution class to the sensor before comparing anything else.
• On moving parts, compute the exposure cost of any stop-down before choosing it — the arithmetic is above.
• Bench-test the final lens and light pair on real parts before the purchase order.

When the usual answer is wrong

• "A monochrome camera fixes it." It does not. The fringe turns grey and the contrast loss stays. What removes the error is the light, not the sensor.
• "Short lens, small error." The absolute spread scales with focal length, but the relative spread Δf/f is constant, and short wide-angle designs put lateral colour at the frame edge first. An 8 mm lens such as the LS-FFL-1582, a 2/3-inch C-mount design with a 57.6° field of view, will show corner fringes that look like a focus fault — expect them and buy the correction.
• "We will refocus for each colour." Sequential red and blue exposures with refocusing change the magnification too, by that same 1.6%. Red and blue edge coordinates then disagree, which is a measurement error no single focus setting can hide.

Start with the two-minute refocus test — it tells you whether you need to spend anything at all. Then take your working distance and field of view to the lens finder or the full system configurator, with the light colour decided first.