Telecentric lens selection: match magnification and image circle

Telecentric lenses are sold by magnification and image circle, not by focal length, so the sizing habit you use for ordinary lenses leads you astray. Two failures account for most reworked gauging stations: the part walks out of the frame when placement drifts, and the sensor corners vignette because the image circle never reached them. Work through the five-step routine below, follow the worked example with its arithmetic, and you can order a lens that frames the part on the first try.

The two numbers that decide the pick

A telecentric lens accepts only ray bundles parallel to its optical axis, so magnification holds constant as the part moves toward or away from the lens. That is what makes a measurement repeatable, and it is also why sizing works differently — the full argument is in When you need a telecentric lens for gauging. Two numbers decide the pick:

• Magnification sets the field of view: field = sensor width / magnification. The field must hold the part plus its placement tolerance, so magnification gets a maximum, not a minimum.
• Image circle sets how much of the sensor is illuminated. If the circle is smaller than the sensor diagonal, the corners vignette and the usable field becomes the circle itself, not the frame.

There is a mechanical consequence too: the front element must be at least as wide as the field of view, so big fields mean big barrels. Telecentric designs are strongest from a few millimetres to a few tens of millimetres of field; beyond that, hand the job to an ordinary lens or a line scan setup.

What you need before you size

Four inputs, all already on your desk:

• Camera datasheet: resolution in pixels and pixel pitch in µm — both printed on every listing in area scan cameras.
• Part drawing: the largest dimension that must sit inside the field, in mm.
• Fixture spec: how far the part can sit off the axis, as a ± mm placement tolerance.
• Mechanics: lens mount — C-mount on most industrial cameras — and the clearance the station needs around the part.

If the part is polished or shiny, note it now: you will want a lens with a built-in coaxial light port. Then browse telecentric lenses or the wider machine vision lenses range with the numbers in hand.

Size the lens in five steps

1. Compute the sensor width. Multiply horizontal pixels by pixel pitch, and keep the units: pixels × µm = µm, then 1,000 µm = 1 mm. Work from width, not the format name — a 1-inch sensor is nowhere near 25.4 mm across.
2. Fix the required field. Required field = part's largest dimension + (2 × placement tolerance). Add 10-20% spare on top for fixture wear and focus drift.
3. Cap the magnification. M_max = sensor width / required field. Any larger magnification shrinks the field until the part no longer always fits. Choose the highest catalog magnification at or below the cap — extra magnification means smaller object-space pixels, which is what a gauge buys; the object-space pixel size walkthrough converts pitch / magnification into µm per pixel at the object.
4. Check the image circle against the diagonal. Diagonal = √(width² + height²). Nominal diagonals run about 6 mm for 1/3", 8 mm for 1/2", 11 mm for 2/3" and 16 mm for 1" — the same bands as the shop's image-circle filters (up to 8 mm, 8-11 mm, 11-16 mm, 16-22 mm). A circle smaller than your diagonal vignettes the corners.

5. Match mount and working distance, then dry-run. Filter the telecentric lens finder by magnification band, sensor format and mount, pick a listed working distance that clears the fixture, and image a part at each extreme of the placement envelope before you order the second station. The lens configurator runs the same filters with your camera attached.

On 2/3" cameras this routine usually lands on a 1x lens with the 8-11 mm image circle: a 440 mm working distance clears guards and enclosures, a 108 mm one keeps the head compact:

Worked example: a 10 mm part with ±1 mm placement on a 2048 × 2048, 5.5 µm sensor

Inputs, with their sources:

• Sensor: 2048 × 2048 px at a 5.5 µm pitch — example values of the kind a camera datasheet prints; square, so a 1-inch-class format.
• Part: the largest feature inscribed in a 10 mm circle, from the drawing.
• Placement: the fixture holds the part within ±1 mm of the axis, from the fixture spec.

Rule: the field of view must contain the part circle plus both placement offsets, and the image circle must cover the sensor diagonal. The first sets the magnification cap; the second sets the format.

Arithmetic:

• Sensor width = 2048 px × 5.5 µm/px = 11,264 µm = 11.26 mm.
• Required field = 10 mm + (2 × 1 mm) = 12 mm.
• Magnification cap = 11.26 / 12 = 0.938x.
• Test the tempting 1x lens: field = 11.26 / 1.000 = 11.26 mm, so margin per side = (11.26 − 10) / 2 = 0.63 mm against a ±1 mm placement — the part edge leaves the frame by 0.37 mm at worst. The circle check fails too: diagonal = 11.26 × √2 = 15.93 mm, while the 1x models in this range list 8-11 mm circles on 2/3" formats — a 5.5 mm circle radius against corners sitting 7.96 mm from centre.
• The pass: 0.66x on a 1" lens. Field = 11.26 / 0.66 = 17.06 mm; margin per side = (17.06 − 10) / 2 = 3.53 mm; field margin = 17.06 / 12 = 1.42, roughly 42%. Pixel size at the object = 5.5 / 0.66 = 8.3 µm, so the 10 mm part spans 10,000 µm / 8.3 µm ≈ 1,200 px, and a tenth-pixel edge fit contributes about ±0.8 µm of sampling uncertainty — lighting quality and the algorithm add their own terms on top.

Decision: any magnification above 0.938x lets the part escape the frame, and the 15.93 mm diagonal pushes the choice to the 1" format class. The pick that clears both checks:

The LS-TCL-0651 is a 0.66x object-side telecentric lens for 1" sensors with an 11-16 mm image circle, a C-mount and a 110 mm working distance. For polished parts, the LS-TCL-2194 is a 0.5x, 1" lens with built-in coaxial light and the same 110 mm working distance. At 0.5x the field on this sensor grows to 11.26 / 0.5 = 22.5 mm, trading pixels for coverage and built-in illumination.

Two sizing routes: telecentric or fixed focal

If the part always sits at one distance and the tolerance budget survives perspective error, a calibrated fixed-focal lens covers a bigger field for less money. Size that route with the focal-length calculator below and correct the residual distortion in software; Lens distortion correction for accurate pixel-to-mm measurements walks the calibration. Choose the telecentric route when parts tilt, sit at varying heights, or the gauge must hold position without recalibration — Entocentric vs telecentric lenses: when to use each sets out the trade in full.

Picks from the catalog, by field size

The same two checks, run across the telecentric range, give a short list per format:

Reading the table: higher magnification pairs with smaller circles and smaller sensors; lower magnification opens the field. On the example sensor, any field past about 22 mm implies magnification at or below 0.5x.

Big fields need big front elements, so the catalog answers them with big-sensor, low-magnification designs:

The LS-TCL-1422 is a 0.166x bi-telecentric lens for 1" sensors with a 16-22 mm image circle and a 258 mm working distance. At 0.166x the example sensor's field reaches 11.26 / 0.166 = 67.8 mm — silhouette gauging of stamped and machined parts rather than micron work. The LS-TCL-0885 is a 0.287x bi-telecentric lens with an M58 mount, a 30-45 mm image circle, a resolution rating over 25 MP and a 288 mm working distance, sized for large sensors where a small circle would vignette.

Checks before you order

Run these on the bench, in this order:

• Corners: image a flat, diffuse target. Brightness must hold to the frame edges; gray corners mean the circle lost.
• Gauge: measure a calibrated pin or gauge block at the field centre and near a corner; both readings must sit inside tolerance.
• Depth: slide the part a few millimetres toward and away; the reading must hold. Where thick parts blur, Telecentric symmetric blur: why defocus keeps measurements repeatable explains why bi-telecentric optics keep edge contrast deeper into defocus.
• Distortion: read the geometric distortion line on the lens data and keep it inside your budget; Telecentric lens distortion and telecentricity explained decodes the terms.
• Edges on shiny parts: switch to the coaxial port or a collimated backlight; Collimated backlight or diffuse backlight for edge gauging compares the two.

When the usual answer is wrong

• "Buy the highest magnification." The worked example is the counter-case: past 0.938x the part leaves the frame, and the lens that looked most precise gauges nothing.
• "Telecentric means accurate." It removes perspective error, not distortion. Every telecentric lens still prints a geometric distortion figure — keep it inside the budget.
• "One lens fits the part family." A wider variant moves the cap. Rerun the arithmetic on the largest variant in the family, not the sample on the bench today.
• "Any format works if the image looks fine." A lens used beyond its circle still delivers a plausible-looking centre; the corners are where edges quietly vanish. Match the listed sensor format or the circle, and let the glossary of lens-choice terms keep the vocabulary straight.

Pre-order checklist

• Sensor pixels, pitch, part size and placement tolerance written down with units.
• Magnification at or below the cap; image circle at or above the diagonal; listed working distance clears the fixture; mount matches the camera.
• Bench pass at every placement extreme: corners bright, gauge block inside tolerance, reading stable through a few millimetres of depth.
• Distortion figure and the coaxial-light decision recorded for the build file.

With the cap and the diagonal in hand, the pick takes minutes: send the drawing and sensor sheet to expert support, or browse more sizing guides on the lenses topic page.