Entocentric vs telecentric lenses: when to use each

Every fixed-focal-length and zoom lens used in general vision work is entocentric: it obeys the same perspective as your eye, so an identical feature images larger when it sits nearer the camera. That is harmless when you check presence, read characters or decode a barcode. It is fatal when the output is a dimension. A telecentric lens images with chief rays parallel to the optical axis, so magnification belongs to the lens, not to where the part happens to sit. This comparison gives the two perspective-error formulas, the aperture-angle rule that bounds them, a fully worked bracket example, and a committed pick for each task.

The decision in one paragraph

Choose an entocentric machine vision lens for presence and position checks, robot guidance, print inspection, colour work, OCR and barcode reading — a few percent of size change with distance changes none of those verdicts. Choose a telecentric lens whenever the output is a number in millimetres: diameters, gaps, edge positions, anything with a tolerance. For very small fields, macro and fixed-magnification optics take over. If a project forces entocentric glass into a measuring station, go long: a long focal length at a long working distance, with the full aperture angle at or below about 10 degrees. Both families are in the lens finder, filterable by mount, sensor format and magnification.

What entocentric means in numbers

An entocentric lens views object space from one finite viewpoint, the entrance pupil, and three numbers follow from that geometry.

First, scale falls with distance. For a thin lens, m = f / (WD − f); double the working distance and you roughly halve the magnification.

Second, a normal lens matches the eye at about a 50-degree aperture angle — on a full-frame sensor, the diagonal roughly equals the focal length at that angle. On machine-vision formats the same angle belongs to short focal lengths: the LS-FFL-1582, an 8 mm design for 2/3-inch sensors, prints a 57.6° field of view. Focal lengths only compare once the sensor is named; lens sensor format: 1/1.8, 2/3 and 1 inch lenses covers the mapping.

Third, the view is square-on at field centre and oblique at the edge. A wider angle means stronger obliquity, more geometric distortion and more field curvature — a curved object space pressed onto a flat sensor. Aspherical elements push back: the LS-FFL-0567, a 16 mm 20 MP lens for 1.1-inch sensors, prints <0.3% distortion, while a fisheye at the far end of the scale reaches tens of percent.

Working distance is elastic down to the lens's minimum object distance, and extension rings reach closer at the price of aberrations; the ring and adapter arithmetic is in C mount vs CS mount: adapters, focus and clearance. Two rings set everything else: the iris for brightness, depth of field and aberration balance, the focus ring for the image plane. For the focal length itself, start at how to choose a machine vision lens focal length. Wide-angle designs also deliver chief rays to the sensor edge at steep angles; each pixel sits under a microlens, so the corners can fall off in brightness on small-pixel sensors — a lens-sensor mismatch, not a lighting problem.

What a telecentric lens changes

An object-side telecentric lens puts its aperture stop where chief rays in object space travel parallel to the optical axis: the entrance pupil sits at infinity, and the size-versus-distance coupling disappears. Magnification becomes a design constant, and the part can move along the axis inside the telecentric depth of field without changing scale. The physics has a price: the front aperture must be larger than the field of view, because the lens must face every point of the part squarely, and each model is built around one working distance — you shop by magnification and WD. Checking that the depth of field really covers your part is its own procedure: telecentric depth of field: validate measurement accuracy.

Distortion and telecentricity turn from incidental traits into headline specs, measured and printed per model — telecentric lens distortion and telecentricity explained shows how to read those numbers. A bi-telecentric lens adds the same condition on the sensor side, evening out brightness and depth of field symmetrically, which is why reproduction and photolithography use the design (Wikipedia: telecentric lens). Many models also carry a built-in coaxial port for flat, shiny parts; filter placement around that port has its own rules in telecentric lens filters: where to place them and what they change.

Entocentric vs telecentric at a glance

The two perspective errors, and the 10-degree rule

Error one is axial scatter. The part never seats at exactly the same height, and every millimetre of that scatter rescales the whole image. Take a 40 mm dimension with ±1 mm of seating scatter at a 200 mm working distance: e_scale = 40 × 1 / 200 = 0.2 mm, twice a ±0.1 mm tolerance, at a sixth of the working distance the formula demands. No iris setting touches this error; only working distance does.

Error two is height parallax. Toward the field edge the lens looks at the part obliquely, so a feature standing h above its neighbour appears shifted sideways by h × tan(α/2). On a stepped part this reads as a diameter or edge-position error that no flat-field correction repairs.

Hence the rule: when an entocentric lens must measure, hold the full aperture angle at or below about 10 degrees. Since FOV = 2 × WD × tan(α/2) and tan 5° ≈ 0.0875, a 10-degree view means FOV ≈ 0.175 × WD, so a 45 mm field needs roughly 260 mm of working distance. The angle rule fixes parallax and edge obliquity; it does not fix axial scatter, which sets the working distance on its own. Run both tests.

Worked example: gauging a 45 mm bracket to ±0.1 mm

The case: a stamped bracket, 45 mm wide, with a critical dimension of 40.0 mm at ±0.1 mm on the drawing. The nest allows ±1 mm of axial scatter — stampings bow, and nests are that loose. The camera is a 2/3-inch sensor, 8.8 mm wide, with 3.45 µm pixels (a 5 MP class format). The error budget gives perspective a third of the tolerance at most: 0.033 mm.

Entocentric attempt. The scale rule demands WD ≥ L × Δz / e = 40 × 1 / 0.033 ≈ 1,200 mm. Spending the whole tolerance still needs 40 / 0.1 = 400 mm. At 400 mm, a field covering the bracket with margin is 49.2 mm wide, so m = 8.8 / 49.2 = 0.179 and f = WD × m / (1 + m) = 400 × 0.179 / 1.179 = 60.7 mm. That is a 60 mm lens at 400 mm with perspective alone eating the entire tolerance: rejected. The angle cross-check even passes — 2 × atan(24.6 / 400) = 7.0 degrees, inside the 10-degree rule — which is exactly why both formulas must be run.

Telecentric arithmetic. At 0.179x on an 8.8 mm sensor, FOV = 8.8 / 0.179 = 49.2 mm, so the 45 mm bracket fits with about 2 mm of clearance per side. The object-space pixel is 3.45 µm / 0.179 = 19.3 µm, and the 0.1 mm tolerance spans 0.1 / 0.0193 ≈ 5 pixels — comfortable for sub-pixel edge finding; the conversion is spelled out in object space pixel size from magnification. The ±1 mm of scatter now costs no scale at all; only the depth of field matters.

The pick from the catalog:

The LS-TCL-1390 is a 0.179x object-side telecentric for 2/3-inch sensors, with a 260 mm working distance and no coaxial port. Smaller flat parts that need coaxial light move to the LS-TCL-2194, a 0.5x model with a 110 mm working distance for 1-inch sensors and a built-in coaxial port. On a 1-inch camera the family also widens the field: the LS-TCL-1422 is a 0.166x bi-telecentric with a 258 mm working distance. At that magnification a 12.8 mm-wide sensor spans 12.8 / 0.166 = 77 mm of part.

Decision. Order the telecentric: it holds the tolerance with the fixture scatter present. Keep the 60 mm entocentric layout only if the nest is hardened to ±0.1 mm of axial position — then e_scale = 40 × 0.1 / 400 = 0.01 mm — and residual distortion is corrected in software.

How to choose, task by task

• Presence, print, colour, OCR and barcode: entocentric, sized by field of view and pixel size, with the method in machine vision lens selection for reliable inspection. The LS-FFL-0679, a 35 mm 6 MP lens for 2/3-inch sensors, is the workhorse class for mid-size fields.

A standard mid-field pick:

• Robot guidance and pick and place: entocentric, because coverage beats metric scale; see 2D vision pick and place: selecting a planar guidance system.
• Gauging and dimensional checks: telecentric, magnification first, m = sensor width / FOV. The borderline-call test is in when you need a telecentric lens for gauging.
• Very small fields: macro and fixed-magnification optics; measuring points on a 5 mm part in under one second shows that end of the scale.
• Inside holes and along side walls: fisheye at very short working distance, where the oblique view is the goal rather than a defect. The LS-CTV-0028, a 1.5 mm M12-mount fisheye for 1/2-inch sensors, is that class among CCTV lenses.

To size an entocentric pick yourself:

Run your numbers through the lens focal length calculator, then bring the shortlist into the lens configurator. Three telecentric magnifications side by side:

All 3 share: Mount C-mount. Values as printed in each product's data sheet; open a part for its drawing and full specifications.

Match the printed working distance to the station before the magnification: a telecentric model is not refocused to a new distance, and a move means a different model.

Checks before you order

• Image circle at least the sensor diagonal; a 2/3-inch lens on a 1-inch sensor vignettes the corners.
• Lens resolution band at or above the camera's pixel count — a 5 MP lens is the floor for a 5 MP sensor.
• Entocentric: minimum object distance versus your closest pass, and extension rings add aberrations.
• Telecentric: printed working distance versus the fixture, depth of field versus part scatter.
• Telecentric: coaxial port or not, decided with the lighting plan before the order.
• Distortion spec against the tolerance; the residual is removed in software by lens distortion correction for accurate pixel-to-mm measurements.
• Locking screws on focus and iris for anything mounted on a machine — lens locking screws: focus, aperture and enclosure clearance covers clearance too.
• A front filter thread, if polarizing or colour filters are in the plan.

When the usual answer is wrong

Telecentric-for-measurement fails on size. The front element must outsize the field of view, and past a few hundred millimetres of field the lens becomes a piece of process equipment in its own right. There the long entocentric route wins: aperture angle near 10 degrees, distortion corrected in software, fixture controlling part height.

Telecentric also fails when the working distance must move, because each model is built around one value. A varying target wants an entocentric lens with autofocus — liquid lens autofocus for changing working distances covers that path.

Entocentric-never-measures is wrong twice. Loose tolerances pass the scale test outright when the allowed error sits comfortably above L × Δz / WD, and a hardened fixture that pins part height makes the error computable instead of dominant.

The fisheye, the worst lens for flat measurement, is the right lens for seeing inside a hole or along a wall: extreme focal length, very short working distance, obliquity on purpose.

The next step is mechanical as much as optical: lock camera, lens, light and controller in one pass in the system configurator. If the station is borderline — a tolerance near the perspective limit, a part that will not sit flat — send the numbers and the applications desk will run both formulas with you.