How many lumens for machine vision lighting: a worked example

A lumen rating cannot, by itself, tell you whether a light will produce a usable image. Exposure is decided by illuminance at the part, your exposure time, the lens f-number and the pixel pitch of the sensor — so the same 1,000 lm light can be blinding at 100 mm and useless spread across a metre of belt. The calculation below answers the question in two steps: convert lumens to lux at the part, then lux to photons on the pixel, and check the result against the sensor's absolute sensitivity threshold. Worked end to end, it tells you when almost any light will do and when you need strobing.

Why lumens alone cannot answer the question

A lumen measures total light output as the human eye weighs it, with peak sensitivity at 555 nm. A machine camera has no eye: its sensor turns photons into electrons according to its own quantum-efficiency curve. What sets your grey levels is the number of photons landing on each pixel during the exposure, and that number is set by four things — the light's flux, the area it covers, the exposure time and the f-number.

The area term alone moves the answer by two orders of magnitude. Spread 1,000 lm bare in all directions and the illuminance at 300 mm is about 880 lx; concentrate the same flux into a 32° cone and the lit circle at 300 mm is 172 mm across, about 43,000 lx — roughly 50× more. This is why beam shaping matters more than the raw lumen figure, and why two lights with the same lumen rating can behave nothing alike over the same part. Compare spot lights by beam angle and working distance first.

The worked numbers below use a plain white bench spot, a blue spot with a focusing lens, and a compact high-output unit — the three ways a small field usually gets covered:

Step 1: lumens to lux at the part

Take the full beam angle from the light's data sheet and the working distance from your layout. The cone formula assumes the flux is spread evenly across the beam; real beams peak on axis and fade toward the edge, so treat the result as the average over the circle and expect field corners to sit up to a factor of two lower. The same lumens-to-lux conversion physics drives room and workbench lighting sums — the units do not change between a factory floor and a vision station. Beam angles like the 32° printed on the LS-SPT-0024 are typical for compact spot lights.

For the 1,000 lm, 32° example light:

Two levers follow from the formula. Halve the working distance and illuminance quadruples; halve the beam angle and the lit area drops by four, so lux quadruples at the same distance. Once the lit circle is larger than your field of view, illuminance follows the inverse-square law, and a 10% working-distance error already costs about 17% of the light.

Step 2: lux at the part to photons on the pixel

Here ρ is the part's diffuse reflectance (0.8 for a white label, about 0.1 for dark plastic), τ the lens transmission and m the magnification, which you can ignore when the field is large compared with the sensor. The constant converts lux-seconds to photons per square metre at 555 nm: 1 lx equals 1/683 W/m² there, and one 555 nm photon carries 3.58×10⁻¹⁹ J. A white LED's broad spectrum actually delivers about twice this many photons, so the calculation is conservative.

The camera side needs only two published numbers: quantum efficiency and absolute sensitivity threshold, both on any mono area scan camera sold with EMVA 1288 data — reading EMVA 1288 performance data walks through both. A 20 MP mono USB3 model such as:

Worked example: one spot light, three production cases

Setup: white diffuse part, ρ = 0.8; mono sensor with 5.9 µm pixels, a common pitch on 2-3 MP global-shutter sensors (illustrative); lens f/2.8 with transmission 0.9; magnification small. Target: mid-grey at half of a typical 10,000-15,000 e⁻ full well, so 5,000 e⁻ per pixel.

1. Required photons: 5,000 e⁻ ÷ 0.6 QE = 8,333 photons per pixel.
2. Photons per lx·s on one 5.9 µm pixel: 4.09×10¹⁵ × (5.9×10⁻⁶)² = 1.42×10⁵.
3. Required sensor exposure: 8,333 ÷ 1.42×10⁵ = 0.059 lx·s.
4. Back through the lens, with 4N² = 31.4 for f/2.8: E_part = 0.059 × 31.4 ÷ (0.8 × 0.9 × t).
5. At t = 10 ms: E_part ≈ 260 lx.

Scaled to any exposure and f-number:

Now three production cases, with the example light delivering 43,000 lx (1,000 lm, 32° cone, 300 mm working distance):

The 100 µs figure is not arbitrary: at 300 mm/s the part moves 300 mm/s × 100 µs = 30 µm during exposure, about a third of the 82 µm object pixel a 200 mm field gives across 2,448 pixels. Object-space pixel size shows how to get that pixel for your own field, and exposure time vs shutter speed covers the blur budget. The f/8 in the third case buys depth of field for a part that is not flat — check what your part's height spread actually requires before paying the eightfold light penalty:

For the third case the fix is geometric, not a bigger lumen number. Move the light from 300 mm to 150 mm: 4× the illuminance gives 172,000 lx, still 1.2× short. Narrow the beam from 32° to 16°: another 4×. A 2× pulsed overdrive on top of either closes the gap with margin, and strobing is exactly the tool for it.

So the decisions: for the static station, choose by coverage and uniformity, not flux. For the belt at 100 µs, the 1,000 lm, 32° spot at 300 mm fits with 1.7× margin — verify the distance at production height. For f/8 plus 100 µs, treat illumination as the design problem and solve it with working distance, beam angle or pulsed overdrive.

The floor: threshold, full well and why gain is no substitute

Two sensor numbers bound the whole calculation. The floor is the EMVA 1288 absolute sensitivity threshold — the mean photon count at which signal equals noise — typically 4-8 photons on modern global-shutter mono sensors. The 8,333-photon target sits about a thousand times higher, so with artificial lighting the noise floor is never what limits you; motion blur and depth of field are. The ceiling is full well, roughly 10,000-15,000 e⁻ for a 5.9 µm pixel, which is why the example aims at 50% and keeps headroom for bright texture.

Raising gain is not a substitute for photons: gain amplifies signal and noise together, so a 30 e⁻ pixel stays noisy at any gain. Set exposure and illuminance first, as in exposure before gain, then interpret the raw values your driver reports with exposure and gain units.

Where the lumen model breaks

Coloured and infrared light

Lumens are weighted for human vision: 683 lm/W at 555 nm, roughly 180 lm/W at 630 nm, about 30 lm/W at 455 nm, and essentially zero at 850 nm. A mono silicon sensor ignores that weighting and responds by its own QE curve, which still has real response at 850-940 nm. So an infrared light can print close to zero lumens and still be the strongest unit in the build, and a 1,000 lm red rating carries several times the radiometric watts of a white one at the same rating. For coloured lighting, size in watts and compare against the sensor's QE at that wavelength; never rank lights of different colours by lumens for a mono camera.

Specular and dark parts

The ρ term assumes diffuse reflection. Polished metal and glass ignore it: they return the light at the mirror angle, so the model's answer can be wrong by orders of magnitude in either direction. The law of reflection decides whether that lobe belongs in the lens (bright field) or out of it (dark field), and on machined surfaces the scattered fraction is the signal itself — see lighting for metal surface defect inspection. Fix the geometry first, then set the level empirically from the image.

Ambient light

A production floor runs 300-500 lx of task lighting and direct sun runs about 100,000 lx — and both land on your part. At f/2.8 and 10 ms, room light alone on a white part already puts the example pixel near its full well, which tells you how little flux a static station really needs. What a dedicated light buys is contrast, uniformity and strobe control, not raw level; the reasoning in stable 2D vision inspection systems and the day and night license plate case both rest on that. To beat ambient, pulse the light and shorten the camera exposure to match: a 100 µs pulse inside a 150 µs exposure collects 500 lx × 0.15 ms = 0.075 lx·s of room light against the strobe's 26,000 lx × 0.1 ms = 2.6 lx·s — about 35:1 in your favour.

Making the number hold in production

Drive the light from a lighting controller rather than a fixed supply: LED output tracks drive current, so current regulation holds grey levels steady across the day, and pulsing keeps heat and aging down. Fire the pulse so it fully covers the camera's exposure window — a pulse that starts late or ends early truncates exposure without telling you, and a few microseconds of rise time matter at 100 µs scales, as strobe rise time explains. Pulsed overdrive — current above the continuous rating for tens-of-microseconds pulses — multiplies illuminance by 5-10× within duty-cycle limits, which is the hidden strobe technique.

Triggering the light from the camera's exposure, instead of free-running it, also removes flicker and level drift between frames; the trigger and lighting-stability guide walks the wiring logic. On margin: LEDs are rated to L70 — 70% of output at the end of rated life — so keep at least 1.4× illuminance in hand and re-check grey levels at maintenance intervals. For pulsed stations, pick a spot built for high luminance and short-pulse drive:

Checks before you order

• Write down exposure time, f-number and part reflectance first — they, not lumens, set the requirement.
• Compute required illuminance with the scaling formula, then delivered lux from the beam angle at the measured working distance, part present.
• Bench-run at production exposure with gain off; a good part should sit mid-grey in the histogram.
• Walk the real field of view: cone-edge falloff can cost a factor of two at the corners.
• Keep at least 1.4× margin for LED aging, plus the working-distance tolerance.
• For blue, red or infrared lighting, sanity-check in watts against sensor QE — a lux meter reads near zero in IR.

Start with the lights finder to filter spot lights by size and wavelength, or configure a lighting station around your camera. The lighting topic page collects the geometry and wavelength guides this calculation builds on, and you can send a specific layout to us through the contact page.