How to measure 500 micron laser-drilled holes with machine vision

Laser drilling hands inspection a narrow question: is this hole, nominally 500 µm across, inside its ±50 µm band, and is it round? That is a gauging task, and four numbers settle it — object-space pixel size, field of view, working distance and edge contrast. This guide sizes the camera, lens and light for a 500 µm ±50 µm hole, works the arithmetic end to end, and draws the line between a standard entocentric build and a telecentric one. You leave with a parts list, the checks that keep it honest, and the cases where this sizing is wrong.

How small must one pixel be to gauge a 500 µm hole to ±50 µm?

Size it for 5 µm per pixel in object space or finer: the working rule — measurement resolution one tenth of the tolerance — puts a 50 µm tolerance at a 5 µm pixel, which spans the nominal hole with 100 pixels and leaves headroom for sub-pixel edge fitting and calibration drift.

The one-tenth rule is the working standard in vision metrology: pixel = tolerance / 10, so 50 µm / 10 = 5 µm. The same budget governs every dimensional measurement of small parts; only the numbers change.

Stricter shops allocate against the whole band: pixel = band / 60, so 100 µm / 60 = 1.7 µm. Use that number when the gauge's full spread must sit inside a tenth of the band — certification work, not routine inspection.

Sub-pixel edge fitting makes the statistical term small: on a clean backlit edge, gradient interpolation repeats to 0.1-0.2 px, which is 0.5-1.0 µm at 5 µm per pixel. Scale, distortion and focus then own the error budget, and the later sections handle exactly those. Once a magnification is chosen, object space pixel size follows from magnification by a one-line division.

The diameter itself needs enough pixels to fit a circle: treat 20 pixels as the floor and 100 as the point where roundness becomes reportable. At 5 µm per pixel the 450 µm reject limit still spans 90 pixels.

What field of view and camera resolution does that allow?

At 5 µm per pixel, a 4000 × 3000 sensor covers at most a 20 × 15 mm field of view; a 5 MP sensor manages about 12 × 10 mm, which serves one hole at a time but not a hole plus its fiducials.

Decide what must share the frame before opening a lens catalog. In the worked example below, the hole's position is checked against fiducials up to 15 mm apart, so the field is 20 × 15 mm and the sensor needs 4000 × 3000 pixels. Fewer pixels buy a smaller field, never a coarser measurement.

A 1/1.7-inch optical format is nominally 7.4 mm wide, so 4000 pixels across it are about 1.85 µm each. Small pixels like those shift part of the burden onto the lens, which the next section addresses.

The LS-CMR-0166 is a 12 MP USB3 camera with a 1/1.7-inch sensor, 4000 × 3000 pixels and 30 fps. Its rolling shutter costs nothing here, because gauging runs on a stationary part between laser shots; if your part cannot stop, start from the global-shutter models in the camera finder. Choose mono over colour: a Bayer pattern splits a fine edge across three pixel sites and softens exactly the transition being fitted.

The camera behind the worked example:

The camera resolution calculator turns any other field size into a pixel count the same way.

Which focal length and working distance give that field?

On a sensor nominally 7.4 mm wide, a 20 mm field of view means 0.37x magnification, and a 35 mm focal length delivers it at about 130 mm working distance — the pairing to order for a cell with that much clearance.

The arithmetic for the example cell, assuming a 20 mm field and 130 mm of clearance between part and chamber wall:

1. m = 7.4 mm / 20 mm = 0.37
2. f = 130 mm × 0.37 / 1.37 = 35.1 mm, so order a 35 mm lens
3. check: WD = 35 mm × 1.37 / 0.37 = 129.6 mm, effectively the 130 mm assumed
4. object-space pixel = 20 mm / 4000 px = 5.0 µm
5. the hole spans 500 µm / 5.0 µm = 100 pixels; the 450 µm reject limit spans 90

More clearance moves the focal length, not the sampling: at 200 mm, f = 200 × 0.37 / 1.37 = 54 mm, a 50 mm-class part from the lens finder. The focal length choosing guide works the same trade for other sensors, and the working distance and field of view formula covers the reverse route, starting from a fixed lens.

The LS-FFL-0679 is a 35 mm, 2/3-inch, 6 MP C-mount machine vision lens with an 8-11 mm image circle. That circle covers the 1/1.7-inch sensor's roughly 9.3 mm diagonal with margin. Six-megapixel optics will not resolve 1.85 µm pixels at their Nyquist limit, but gauging needs a symmetric, repeatable edge, not maximum contrast, and this class delivers that at 5 µm per pixel. For the strict 1.7 µm allocation, step up in resolution. The LS-FFL-0567 is a 16 mm, 1.1-inch, 20 MP C-mount lens with under 0.3% distortion. At 0.37x, 16 mm of focal length puts the working distance at 16 × 1.37 / 0.37 ≈ 59 mm, a compact-cell option.

How much depth of field does the hole surface need?

At 0.37x, an f/5.6 iris holds roughly 0.2 mm of object depth in sharp focus, and f/8 stretches that to about 0.3 mm — enough for a flat plate, not for a domed or tilted surface.

With the acceptable blur c set to one pixel, 1.85 µm: f/2.8 gives 0.10 mm, f/5.6 gives 0.21 mm and f/8 gives 0.30 mm. The f/5.6 line runs 2 × 5.6 × 1.37 × 0.00185 / 0.37² = 0.21 mm.

The (1 + m) factor is the working f-number: the iris mark refers to infinity conjugates, and at magnification the cone narrows — the same effect that doubles an f/1.4 mark near 1:1. At f/5.6 the working value is 7.7, and diffraction sets the blur floor: 2.44 × 0.62 µm × 7.7 = 11.6 µm at red 620 nm, or 8.4 µm at blue 450 nm. Four to six pixels of symmetric blur will not shift a centred edge fit, but it spends contrast, so stop down no further than f/8.

A domed or tilted surface that runs more than about 0.3 mm out of plane across the field is not an f-stop problem. Fixture it flatter, or move to a telecentric lens with working depth.

Backlight or coaxial light for the hole edge?

Put a through-hole on a diffuse backlight and it reads as a bright disc on a dark silhouette — a binary edge — with the strobe set between 100 µs and 1 ms; blind holes and surface recast need the coaxial path instead.

Backlight wins on diameter because the transition is symmetric and saturated: gradient interpolation lands the 50% crossing to 0.1-0.2 px, 0.5-1.0 µm of statistical noise at this sampling. Coaxial light, sent down the axis through a beamsplitter or a telecentric lens's built-in port, shows the entry hole and its recast ring. The ring is resolidified ejecta and it reads bright; fitting its outer halo reports the hole oversize, so fit the inner edge and qualify against a sectioned part. Both families are in the lights finder.

Motion sets the exposure. Blur equals speed × exposure: a stationary part is free, and 1 mm/s of indexing settle at 1 ms adds 1 µm, a fifth of a pixel. A 50 mm/s conveyor must drop to 50 µs to hold blur under 2.5 µm. Blue light at 450 nm cuts the diffraction spot 27% smaller than 620 nm red at the same stop.

When does hole gauging need a telecentric lens?

Go telecentric when standoff cannot be fixtured: at 130 mm the entocentric build shifts scale 1.05% per millimetre of standoff error — 5.3 µm on a 500 µm hole per millimetre, and the 50 µm tolerance is spent by ±10 mm.

The arithmetic: scale error = ΔWD / (WD − f) = 1 mm / 95 mm = 1.05%. Three fixes exist. Fixture the part within ±2 mm of the calibrated standoff and the error stays under 11 µm. Or place two fiducials of known spacing in every image and refit the scale each shot — standard practice, and it also absorbs thermal drift. Or buy magnification that cannot move: a telecentric lens fixes m by design, so standoff only has to stay inside the lens's stated depth range.

The LS-TCL-2194 is a 0.5x object-side telecentric C-mount lens for a 1-inch sensor, with a 110 mm working distance and a built-in coaxial light path. Pair it with the MV-CS200-10UM: 20 MP, 1-inch, C-mount, USB3.0, mono. Twenty megapixels over a 1-inch format works out near 5472 × 3648 pixels of about 2.4 µm; at 0.5x that is roughly 4.8 µm per pixel in object space and a field near 26 × 18 mm, with the hole still spanning about 104 pixels. For a single-hole close-up, take the 1x route instead: the LS-TCL-2118 is a 1x telecentric C-mount lens for a 2/3-inch sensor with a 108 mm working distance. At 1x magnification, the 2/3-inch sensor's roughly 8.8 × 6.6 mm active area is the field, pixel for pixel.

The trade-offs run deeper in when you need a telecentric lens for gauging and entocentric versus telecentric lenses; the shortlist is in telecentric lenses.

The telecentric pairing:

Which checks keep 5 µm accuracy honest in production?

Calibrate scale in every image from fiducials or a certified target, correct distortion before measuring, and demonstrate σ ≤ 1.7 µm hole-diameter repeatability over 30 images before the station ships.

• Scale. Put gauge blocks or a certified target across the field and fit pixels to millimetres. Any focus change invalidates the fit — the FAQ on refocus shows how much.
• Distortion. A 0.3% residual moves an edge point 10 mm off-axis by 30 µm, six pixels. Correct it with lens distortion correction for pixel-to-mm measurement, and read data sheets the geometric versus TV distortion way.
• Repeatability. Thirty images, ten refixtures, report the σ of the fitted diameter. Hold it at or under 1.7 µm — the band / 60 allocation — so six sigma sits inside a tenth of the 100 µm band.
• Thermal drift. Warm the camera and lens through their ramp before setting scale; why micron-level accuracy drifts quantifies the usual suspects.
• One trigger line. Camera and strobe fire together, after motion settles and after the laser shot.

When is this sizing the wrong answer?

This sizing assumes a through-hole in a flat, stationary part viewed square-on; blind holes, moving parts, curved surfaces and tighter tolerances each break one of those assumptions.

• Blind hole. Nothing comes through, so the backlight route is gone. Coaxial light shows the entry hole and recast; fit the ring's inner edge and qualify against a sectioned part before release.
• Moving part. A rolling shutter reads the circle row by row while it travels and reports an ellipse — false ovality, not blur. Stop the part, or move to a global-shutter sensor.
• Curved surface. A dome runs past the 0.2-0.3 mm depth budget within a few millimetres of its apex. Use a telecentric lens with working depth, or gauge at a flattened datum face.
• Tighter tolerance. The budget follows the tolerance: ±25 µm wants 2.5 µm pixels, and 20 mm of field at 2.5 µm needs 8000 pixels across — beyond a 1-inch 20 MP sensor. Trade field for sampling or plan a second station.

Take the numbers to the lens configurator — 20 mm field, 130 mm working distance, 1/1.7-inch sensor — and it holds the pairing together. If the cell fights those numbers, send the binding constraint, whether clearance, standoff wander or hole depth, through the contact page and we will size it against the catalog.