Bandpass filter for machine vision: CWL and FWHM explained

Daylight through rooflights and the shop's high-bay LEDs add a background to every frame. When you cannot strobe the light, or strobing leaves ambient inside the pulse, the fix is spectral: a bandpass filter matched to the LED's peak wavelength, mounted in front of the lens. This explainer gives you the four numbers on the filter data sheet, the arithmetic that turns them into a bandwidth choice, and the two traps that turn a good filter into a dark image: tilt and fast lens cones. You will leave able to write CWL, FWHM and blocking on the order line, and to say why each number is what it is.

What a bandpass filter passes and blocks

A bandpass filter transmits one wavelength band and attenuates everything else. Two numbers define the band. The central wavelength (CWL) is the midpoint between the two wavelengths where transmission has fallen to half its peak. The full width at half maximum (FWHM) is the distance between those two half-power points; a data sheet that says 'bandwidth' means the same number. A filter specified as 470 nm CWL with 30 nm FWHM passes roughly 455-485 nm at half transmission or better, and a modern hard-coated filter reaches 85-95% transmission at the peak.

Outside the band, the data sheet speaks in optical density (OD), a base-ten log scale:

OD 3 passes 0.1% of the light it blocks, OD 4 passes 0.01%, OD 6 passes 0.0001%. Machine vision bandpass filters usually block at OD 3-4; fluorescence sets push to OD 6 so the excitation light cannot bleed into the image.

Widths sort into classes:

For where these bands sit between 365 nm and 1550 nm, see wavelength ranges of light in machine vision.

How much ambient light it removes

Two mechanisms add up. Inside the band, the filter passes ambient exactly as it passes your light: daylight's photon flux per nanometre is roughly flat across the visible (within about a factor of two from 400 to 700 nm), so a 30 nm band passes about 30/300 = 10% of visible daylight. Outside the band the blocking floor applies: with OD 4, the remaining 90% of the spectrum is cut by 10,000 times.

The lamp changes the arithmetic. A warm lamp at 3000 K radiates its peak near 966 nm (Wien: 2.898 × 10^6 nm·K ÷ 3000 K ≈ 966 nm), so a 470 nm band catches little of it. White LED high bays are blue-rich, with the pump peak near 450 nm, so a blue bandpass cuts less of them; if the cell lives under white LEDs, measure the ambient wavelengths before you count the savings.

Strobing and filtering reject different photons, so they multiply. A pulse filling 1/20 of the frame time already cuts ambient 20-fold; the filter then removes most of what arrives during the pulse. How to measure the combined result is in strobed lighting ambient rejection, and the ambient light rejection specification shows how to write the number into an acceptance test.

Sizing the bandwidth: formula and worked example

Here is the sizing logic, and it runs against the instinct to buy the narrowest filter. A coloured LED is not a line source: its glow spans roughly 15-40 nm FWHM depending on colour (red runs narrow, green wide). The filter must cover that glow plus the drift between light and filter, or you are throwing away LED photons.

The LED bin is the tolerance band the light's peak wavelength is sold within, commonly ±3 to ±5 nm because LED makers sort production into bins. Hard-coated filter CWL tolerance is commonly ±2 nm. The tilt shift comes from the next section; a bracket mounted square contributes under 1 nm.

Worked example — 470 nm deep-blue LED, bracket mounted within 5° of square:

• LED data sheet: peak 470 nm, bin ±3 nm, spectral FWHM 25 nm.
• Filter: CWL 470 nm ± 2 nm. Tilt shift at 5°: sin 5° = 0.087, (0.087 / 1.7)² = 0.0026, shift ≈ 470 × 0.0013 ≈ 0.6 nm.
• Drift sum: 3 + 2 + 0.6 = 5.6 nm.
• Required FWHM ≈ 25 + 2 × 5.6 = 36.2 nm — order 40 nm.
• If the nearest catalogue width is 30 nm, the band covers the LED's central bulk but clips the half-power edges: expect a visible light loss and check the exposure budget before committing. Do not drop to 10 nm for rejection's sake: a 10 nm band on a 25 nm LED passes about 10/25 = 40% of the LED's photons even perfectly aligned, and the daylight it admits shrinks by the same factor, so the image goes darker, not cleaner.

For the 40 nm choice, in-band daylight is 40/300 ≈ 13% of the visible band, and everything else meets the OD 4 floor. Pick the LED colour first — which LED colour gives the best contrast — then size the filter to it.

The tilt trap: angle of incidence shifts the band

An interference filter is a stack of thin coatings, and its band moves toward shorter wavelengths as light arrives off normal:

At 470 nm with n_eff 1.7, a 15° tilt shifts the band by about 5.5 nm (sin 15° = 0.259, (0.259/1.7)² = 0.0232, shift ≈ 470 × 0.0117 ≈ 5.5 nm) and peak transmission drops as well. That is enough to walk the LED peak off a 25 nm band.

The same physics acts inside a lens cone. The marginal ray half-angle is roughly arcsin(1/(2N)) for f-number N:

The decision: with a 10-25 nm filter, stop down to f/4 or slower, or use a telecentric lens, whose nearly parallel rays are the closest thing to a perfect filter mounting. For the worked 470 nm example, the cone at f/2.8 adds 2.6 nm to each side, so the requirement becomes 25 + 2 × (3 + 2 + 2.6) = 40.2 nm — right at the limit of a 40 nm part; at f/4 it lands at 25 + 2 × (3 + 2 + 1.3) = 37.6 nm, comfortably inside. Off-axis rays from a wide field arrive at still larger angles, so corners shift a little further than the table; tight fields and longer working distances shrink the difference. Coating temperature moves the band by roughly 0.01-0.03 nm per °C, so a factory's seasonal swing stays under 1 nm and only matters next to an oven.

Bandpass against the other filters

Filters overlap in their jobs, so here is who does what:

Three of these have their own pages: attenuation without spectral selectivity is the ND filter's optical density sizing, the glare case is the polarizer's cost in f-stops, and the IR-under-daylight case starts at near-infrared wavelength selection. If low contrast comes from reflections rather than ambient, start with stray light diagnosis before ordering glass.

Fluorescence and colour separation

With a monochrome sensor and sequenced red, green and blue lights, bandpasses in front of the lens keep each frame to a single colour channel — the structure the multi-wavelength sequencing guide builds on. Why monochrome-plus-filter beats colour for contrast is covered in monochrome camera with optical filter.

Fluorescence is the bandpass's specialist job. A UV or violet LED excites the material, the material glows back at longer wavelengths (the Stokes shift), and the camera images that glow through a bandpass on the lens while a shortpass on the light keeps the excitation clean. The glow is orders of magnitude dimmer than the excitation, which is why fluorescence sets block at OD 6.

Checks before you order

Work the list before the order goes in:

• Wavelength: CWL equals the LED's nominal peak, and you read the bin off the light's data sheet rather than trusting the catalogue colour name.
• Width: FWHM at least the LED spectral FWHM plus twice the sum of bin, CWL tolerance and tilt shift — 36-40 nm in the worked example above.
• Blocking: OD 4 outside the band for a factory cell; OD 6 for fluorescence.
• Peak transmission: 85% or better; every 10% lost is a small fraction of a stop, and losses add up across the path.
• Placement: on the lens front thread, square to the axis, not between lens and sensor where the cone converges at 7-21° at working apertures.
• Sensor: monochrome for a narrow band; the note on colour sensors in the FAQ explains why.
• Thread: match the lens's front thread to the filter holder or a step ring — the thread is where filters get sent back.

Everything else in the optical path — light extension cables, diffuser plates, mounting parts — sits in the lighting accessories category, with the accessories finder for a filtered view.

The decision, per case

• Visible LED task with ambient you cannot strobe away: bandpass matched to the LED, FWHM from the formula — 40 nm for the 470 nm worked example — OD 4 blocking, mounted square, at f/4 or slower or on a telecentric lens.
• IR task where colour carries no information: a longpass daylight-cut filter, with its wider tolerances and more light.
• Too much light, no ambient problem: ND, not bandpass.
• Shiny parts: polarizer first; add the bandpass afterwards if ambient survives the geometry changes.
• Fluorescence: shortpass on the light, bandpass on the lens, OD 6 blocking.

Pick the light first; the configurator below walks the LED choice, and the lenses topic page collects the rest of the optics guides. If a specific light-and-filter pairing needs a second opinion before you commit, contact the applications team.