Object space vs image space telecentricity and why it matters

A gauge that drifts by tens of microns whenever the part sits a little higher in the fixture — or when a spare camera replaces the original — usually traces back to one design decision: where the lens puts its pupils. Object space and image space telecentricity are the two pupil conditions behind that decision, and doubly telecentric lenses simply satisfy both. The sections below define each condition through the entrance and exit pupils, put a number on the error each one removes, and work a 6 mm pin gauge on a 2/3" camera end to end, so you can choose the type your station needs from an error budget instead of a rule of thumb.

Pupils: the part of the lens telecentricity moves

Every imaging lens carries an aperture stop somewhere in its barrel. Viewed through the elements in front of it, that stop appears as the entrance pupil; viewed through the elements behind it, as the exit pupil. Both are images of the same stop, one formed out toward the object, one back toward the sensor. The chief ray, which crosses the optical axis at the centre of the stop, always passes through the middle of both pupils, and the chief rays define the field of view.

A conventional machine vision lens leaves both pupils a finite distance inside the barrel, so it views the world through an angle, like a pinhole. Move the part and the scale moves with it. Telecentric is the name for the cure: place a pupil at optical infinity so the chief rays on that side run parallel to the axis. Two pupils, two independent conditions, two different problems solved. Where the question is whether you need a telecentric lens at all, Entocentric vs telecentric lenses: when to use each works that comparison.

Object space telecentricity: the field of view stops being an angle

Object space telecentricity puts the entrance pupil at infinity, which designers achieve by placing the aperture stop at the focal point of the front group. Chief rays then run parallel to the optical axis in object space and the angular field of view is zero. The lens images a fixed slice of space: a 6 mm pin reads 6 mm whether its face sits at nominal working distance or a couple of millimetres proud in the fixture. Perspective error, the classic measurement fault of conventional lenses, is removed by construction.

The same constraint shapes the hardware. With only the object side pinned, the rear group stays free to carry moving elements, which is why object-side designs can be focusable and why the rare variable-magnification telecentrics are all this type. Because image-space rays are allowed to diverge, the barrel behind the mount need not out-size the sensor, so large formats fit in compact housings.

The shop's telecentric range splits this type out explicitly in the telecentric lenses category. The LS-TCL-1390 is a 0.179x object-side telecentric lens with a 260 mm working distance for 2/3" sensors, the long-stand-off style this construction permits. The LS-TCL-2118 is a 1x object-side telecentric lens with a 108 mm working distance, also for 2/3" sensors.

Image space telecentricity: magnification stops tracking the sensor

Image space telecentricity mirrors the idea on the sensor side: the exit pupil goes to infinity in image space, so chief rays land perpendicular to the sensor everywhere. Two production consequences follow.

First, magnification stops depending on sensor placement. Two cameras built to the same design still hold their sensors at slightly different depths; behind an object-side-only lens, each gets a slightly different pixel scale and needs its own calibration. Behind an image-space telecentric lens, shifting the sensor toward or away from its ideal plane leaves the image height unchanged, so identical lenses give identical scales and a camera swap no longer touches the measurement.

Second, corner brightness stops falling. A conventional lens strikes the corners at an angle θ, and off-axis illumination drops roughly with cos⁴θ:

On a 2/3" sensor with an 11 mm diagonal, a 12 mm wide-angle gives θ = atan(5.5 mm / 12 mm) = 24.6°, so cos⁴θ ≈ 0.68: corners about a third dimmer before any mechanical vignetting. A 50 mm lens on the same sensor gives θ = 6.3° and cos⁴θ ≈ 0.98, a 2% drop. Image-space telecentric designs run θ = 0 across the frame, so relative illumination stays flat unless vignetting is built into the design.

The cost is physical. To emit the cone perpendicular across a full image circle, the front group must be at least as wide as the sensor format, so barrel diameter tracks sensor size. That is why lens sensor format belongs in the shortlisting step, not after the purchase.

Doubly telecentric lenses: both pupils at infinity

A doubly telecentric lens, listed as bi-telecentric in the category filters, holds both conditions at once. The field of view is immune to part movement, the magnification is immune to sensor movement, and illumination stays flat corner to corner. It is the most accurate of the three types: published comparisons of the lens families show a doubly telecentric design holding dimensional error under about 0.2% across a 4 mm shift of working distance, while conventional and object-side-only lenses of similar magnification drift further over the same travel.

The double constraint has a price in flexibility. With both pupils pinned at infinity there is no free group to rack, so these designs are normally fixed-focus and the working distance is set mechanically at order time. Decide the stand-off before you buy, not after.

The LS-TCL-1422 is a 0.166x bi-telecentric lens with a 258 mm working distance for 1" sensors. For larger formats the same range steps up to APS-H:

The LS-TCL-0885 is a 0.287x bi-telecentric lens with a 288 mm working distance on an M58 mount, rated over 25 MP. If the open question is still whether you need a telecentric lens at all, When you need a telecentric lens for gauging works through that decision; what follows here picks among the telecentric types.

The three types side by side

Lining up two object-side and two bi-telecentric models from the shop's range:

Values as printed in each product's data sheet; open a part for its drawing and full specifications.

Read the Type row first: object-side only, or bi-telecentric. Then check magnification against your sensor, since FOV = sensor width ÷ magnification, and the working distance against the fixture and the lighting plan. Everything else in the table comes straight off the data sheets.

Worked example: a 6 mm pin gauge with a 2 mm fixture step

Inputs, with their sources:

• Camera: assume a common 5 MP 2/3" sensor of 2448 × 2048 pixels at a 3.45 µm pitch, so sensor width = 2448 × 3.45 µm = 8.45 mm (worked assumption, not a catalogued camera).
• Part: a 6 mm diameter pin, its top face 2 mm above the calibrated fixture plane, diameter toleranced at ±25 µm (typical gauging cell).
• Conventional option: the LS-FFL-0914 is a 0.3x machine vision lens with a 168 mm working distance for 2/3" sensors (data-sheet values).

The telecentric option is the LS-TCL-2118 from the object-side list above, 1x at a 108 mm working distance (data-sheet values).

The rule in words: a conventional lens views through a finite entrance pupil, so a feature closer to the lens than the calibration plane is magnified by WD ÷ (WD − h), with h the height of the feature toward the lens. A telecentric lens has chief rays parallel to the axis, so its scale does not depend on h at all.

Conventional arithmetic:

• Object pixel: 3.45 µm ÷ 0.3 = 11.5 µm. Field of view: 8.45 mm ÷ 0.3 ≈ 28 mm.
• Effective distance to the pin face: 168 mm − 2 mm = 166 mm.
• Magnification factor: 168 ÷ 166 = 1.0120.
• Apparent diameter: 6 mm × 1.0120 = 6.072 mm, an error of 72 µm — 1.2% of nominal, about 6 object pixels.

For conventional lenses the same coverage is picked by focal length rather than magnification; the calculator below runs that conversion:

Telecentric arithmetic:

• Object pixel: 3.45 µm ÷ 1 = 3.45 µm. Field of view: 8.45 mm, clearing the 6 mm pin by about 2.4 mm for placement margin.
• Perspective error: zero by design. Residual with a typical 0.1° telecentricity spec: 2 mm × tan 0.1° = 2 mm × 0.00175 = 3.5 µm, about one object pixel.

Decision, with the threshold spelled out. The conventional option spends 72 µm on perspective inside a ±25 µm tolerance before edge-finding error even exists, so it is out. A third of the tolerance band — about 8 µm — is the most perspective may take, leaving a third each for edge finding and calibration drift. That requires 6 mm × h ÷ 168 mm < 8 µm, which holds only while the height spread stays under 0.22 mm. Flush, coplanar parts can stay on a conventional lens; a 2 mm step cannot. The 1x object-side telecentric meets this gauge with about one pixel of total residual, and the pixel-scale arithmetic is the same relation worked in Calculate object space pixel size from magnification. Choose bi-telecentric instead when cameras are swapped or two cameras must agree on one part.

How to choose: the decision per case

• Parts judged only against their own plane — presence, OCR, surface defects, parts presented in a defined pocket: a conventional machine vision lens is the right tool. Telecentricity buys nothing when nothing is measured across depth, and it adds barrel diameter.
• Single-camera dimensional gauging, part height varying or stand-off long: object-side telecentric. Calibrate the pixel scale per camera and after any refocus.
• Gauging with interchangeable cameras, two cameras on one part, or tolerances that cannot absorb per-camera recalibration: doubly (bi-)telecentric, accepting fixed focus and the larger front group.
• Any type: depth of field is a separate specification, and a telecentric lens still has a finite depth over which the measurement holds — worked through in Telecentric depth of field: validate measurement accuracy.
• If the task is measuring from images in general rather than choosing a lens type, the chain from pixels to millimetres is laid out in Measure object size from a camera image.

Shortlist from the lens finder or step through the lens configurator.

When the usual answer is wrong

• Telecentric does not mean free of distortion. A perfectly telecentric lens still bends straight lines; distortion and telecentricity are separate specifications, as Telecentric lens distortion and telecentricity explained sets out, and the residual figure belongs in the same purchase decision — the two distortion numbers are compared in Geometric vs TV distortion: read lens datasheets for measurement, and the calibration that removes the residual is covered in Lens distortion correction for accurate pixel-to-mm measurements.
• Bi-telecentric does not scale to every field. Front aperture tracks image circle, and catalog designs thin out above the 60-90 mm image-circle bucket; at 0.3x magnification that is 90 mm ÷ 0.3 = 300 mm of field, and beyond it a calibrated conventional lens is often the honest answer rather than a custom barrel.
• Steep or shiny curved surfaces starve a telecentric lens: it accepts rays parallel to its axis, so sloped walls throw the illumination elsewhere and vanish from the image. Silhouettes and top faces suit it; flanks need different lighting geometry.

Checks before you order

• Image circle at or above the sensor diagonal: an 8-11 mm image circle serves a 2/3" sensor, not a 1" one.
• Telecentricity angle from the data sheet, budgeted at about 17.5 µm of shift per millimetre of part height per degree (tan 1° = 0.0175).
• Field of view with 5-10% margin for part placement, sized the same way as in Calibration target field of view and lens coverage margins.
• Working distance that includes lighting clearance: a collimated backlight behind the part needs its own stand-off, weighed up in Collimated backlight or diffuse backlight for edge gauging.
• Filter space in the parallel ray path, since where a filter sits changes what it does — Telecentric lens filters: where to place them and what they change.
• Fixed focus confirmed against the fixture: bi-telecentric working distance is set by spacing, so measure the mechanical stack before ordering.

Send your error budget through the lens configurator and read the shortlist back against it, or ask us to check it via the contact page. In-stock telecentric lenses ship within one business day, so the numbers above can be on your bench this week.