Telecentric symmetric blur: why defocus keeps measurements repeatable

Parts move. A conveyor bounces, a fixture releases a millimetre high, a tray sits deeper than the last one. On a fixed focal length lens every one of those depth shifts changes the magnification, and the gauge reads a different size. On a telecentric lens the part simply blurs, symmetrically on both sides of best focus, and the measurement holds. This explainer shows why that symmetry keeps edges and centroids where best focus put them, prices the parallax error you avoid, and covers the trick gauging engineers use on purpose: slight defocus to spread an edge over 3 to 6 pixels for more repeatable sub-pixel location. You leave with the f-number that gets you there, the depth range you can trust, and the bench checks that prove both.

Why does a telecentric lens measure the same size when the part moves?

Because its angular field of view is zero, with every chief ray leaving the part parallel to the optical axis, image height depends on object height alone, and a ±2 mm depth shift changes a telecentric reading by essentially nothing while costing a 25 mm lens at 200 mm over 1%.

A conventional lens images the way your eye does: rays from the edges of the field converge at an angle, so the farther the part sits from the lens, the smaller it appears. That angle is what makes depth perception possible, and it is also what makes gauging unreliable: magnification becomes a function of distance, and distance is the one thing a production line does not hold still. Photograph two identical parts at different distances through a telecentric lens and you cannot tell from the image which one is nearer. The size information carries no depth cue at all.

That constant magnification is the headline reason to reach for telecentric lenses when a measurement must not drift, and when you need a telecentric lens for gauging walks that decision in detail. The specification that quantifies the effect is telecentricity, covered in telecentric lens distortion and telecentricity explained.

How much does a fixed focal length lens's reading change with depth?

Carry this rule to any bench: the relative size error of a conventional lens is about 1/(WD - f) per millimetre of depth shift, so a 25 mm lens working at 200 mm loses close to 0.6% of its reading for every millimetre the part drifts away.

Work it through. A 25 mm lens focused at a 200 mm working distance gives m = 25 / (200 - 25) = 25 / 175 = 0.143x, and a 10.00 mm part images at 1.43 mm. Let the conveyor lift the part 3 mm farther out: m = 25 / 178 = 0.140x, and the same part now measures 10.00 × (0.140 / 0.143) = 9.83 mm. Three millimetres of bounce cost 170 µm, roughly eighty times a 2 µm repeatability target, from part position alone.

Now the telecentric comparison. A lens with a 0.1° telecentricity specification, a common datasheet figure, limits the edge displacement from that same 3 mm shift to tan(0.1°) × 3 mm ≈ 5 µm. One hundred seventy µm versus five: that is the whole decision, made before any algorithm runs.

What does symmetric blur do that asymmetric blur does not?

Defocus through a telecentric lens spreads an edge equally to both sides, so the 50% contrast crossing and the intensity centroid stay on the pixel they occupied at best focus; defocus through a conventional lens shifts them, because each edge physically expands or contracts as magnification changes.

Defocus is a blur disc folded into the image. Centre that disc on the chief ray of each object point, which is the telecentric case, and folding any shape with a symmetric disc leaves its centre of mass and its edge midpoints unchanged: width grows, position does not. Under a conventional lens the disc sits off-centre on every edge, because magnification moves with depth. A nearer out-of-focus part shows its edges migrated outward, a farther part pinches them inward, and the 50% crossing travels with them.

The practical consequence is graceful degradation. Past best focus a telecentric image softens and loses contrast, but every position-based measurement keeps its calibration; the limit is the point where the edge finder runs out of contrast, not a shift in geometry. The invariance does assume the blur stays symmetric over the feature. At the far edges of the field, or with dirt or stray light shading one side of an edge, symmetry breaks and the centroid drifts, so keep gauging inside the field the lens is specified for.

Do telecentric lenses actually have more depth of field?

No. Depth of field is set by wavelength and f-number exactly as for any other lens; a telecentric lens instead has more usable depth, because measurements stay valid after the image softens, so long as contrast remains high enough for the edge finder to lock.

The diffraction disc at 550 nm grows as 2.44 · λ · N: about 5 µm at f/4, 10.7 µm at f/8, 14.8 µm at f/11 and 21.5 µm at f/16. Depth range scales with f-number the same way. To size the usable travel, convert an allowed sensor-side blur into object-side defocus:

For the 0.166x example at f/8, allowing a 6-pixel (14.4 µm) blur disc: Δz = 0.0144 × 8 × 1.166 / 0.166² ≈ 4.9 mm on each side of best focus. About ±5 mm of part travel before the edge spread leaves the band, and because the blur is symmetric, the gauge holds calibration through all of it. Before trusting that range on your own part, run the sweep described in telecentric depth of field validation.

Why would you defocus a gauging lens on purpose?

Because a sub-pixel edge locator works from a ramp, not a cliff: an edge spread over roughly 3 to 6 pixels gives the interpolation kernel real samples to fit, which buys more repeatability than switching interpolation method, and telecentric symmetry guarantees the fitted position stays on the true edge.

A well-focused telecentric lens can put a black-to-white transition into one or two pixels. Two samples barely define a crossing: a single noisy pixel, and sensor noise is 1 to 2 gray levels on a clean signal, can move the fitted position by a large fraction of a pixel. Published sub-pixel interpolation benchmarks keep finding the same result: cubic kernels improve accuracy, but precision depends on how many pixels the edge spans, and sharply sampled edges locate far less precisely than ramps a few pixels wide.

The classic case is the centre of a pin or a shaft. In sharp focus the silhouette transition takes a pixel or two and the centre estimate flickers with every gray-level wiggle. Slightly defocused, the transition takes five or six pixels, the centroid of the whole silhouette integrates a smooth ramp, and the centre repeats to a small fraction of a pixel, with no bias, because the symmetric blur has not moved it. How small you can push that scatter is the subject of estimating edge position accuracy from image sampling.

You often reach the band without touching focus. With 2.4 µm sensor pixels, the common 20 MP 1" format, an f/8 aperture gives a 10.7 µm diffraction spread, which is 4.5 pixels of edge transition: mid-band, with the focus ring untouched.

How far can you defocus before accuracy breaks?

Stop when the transition either falls below about 30 gray levels of total contrast or spans more than about 8 pixels: inside the 3 to 6 pixel band repeatability improves, and beyond roughly 8 pixels the slope flattens to a few gray levels per pixel, so repeatability and bias worsen together.

Put numbers on the slope. A 120 gray-level transition across 4 pixels is 30 gray levels per pixel, and 1 to 2 gray levels of noise barely moves a line fit through that. The same 120 levels across 12 pixels is 10 gray levels per pixel, and noise starts to dominate the fit. Push further and second-order effects join in: surface texture and stray light weight one side of the ramp, and toward the field edge the blur disc stops being symmetric.

The failure mode of a defocused telecentric gauge is always lost contrast, never lost calibration. If a dark alloy under flat lighting only gives you a 60 gray-level transition at best focus, there is no contrast budget for deliberate blur. Fix the lighting first; for silhouette gauging, a collimated backlight is the strongest lever you have.

How do you set up and verify a defocused gauge on the bench?

Fix the optics at nominal depth, stop down until the edge spans 3 to 6 pixels, then calibrate and sweep a master part through its travel: top, middle and bottom must hold one reading to about a tenth of a pixel.

1. Mount the lens and camera, and set best focus on a master part at the nominal depth.
2. Stop down to around f/8 and profile the edge; adjust the aperture, not the focus, until the transition spans 3 to 6 pixels.
3. Calibrate the scale with a certified gauge block. Object pixel size = sensor pixel ÷ magnification: 2.4 µm ÷ 0.166 = 14.5 µm, so a 10.00 mm part spans about 690 pixels. The arithmetic is in calculating object space pixel size from magnification.
4. Sweep the master through its travel in 1 mm steps over about ±5 mm; readings should stay within one object-side pixel, ±15 µm here.
5. Hold position and log 100 frames; the standard deviation of each dimension should sit at or under 0.1 pixel, about 1.5 µm object-side in this example.
6. Repeat steps 4 and 5 at the corners of the field of view, where telecentricity and blur symmetry are weakest.

The numbers through this article assume a 1" sensor with 2.4 µm pixels at 0.166x. That pairing suits the LS-TCL-1422, a bi-telecentric 0.166x lens with a 258 mm working distance for 1" sensors.

Pair it with the MV-CS200-10UM, a 20 MP USB3 camera with a 1" sensor and C-mount.

For pin and shaft work at unit magnification, the LS-TCL-1972 is a 1x telecentric lens with a 440 mm working distance for 2/3" sensors. At that magnification one sensor pixel maps to one object-side pixel, so the 3 to 6 pixel edge band applies directly.

All 2 share: Mount C-mount. Values as printed in each product's data sheet; open a part for its drawing and full specifications.

When is deliberate defocus the wrong choice?

Skip it when the station must read surface detail, such as print, laser marks, scratches or codes, because the blur that sharpens silhouette repeatability erases the gradients those tools need; and skip it when best-focus contrast is already weak, since there is no contrast budget left to spend.

• Surface inspection: run a second, focused camera. One lens split between gauging and reading will do neither job well.
• Low-contrast parts: if the best-focus transition is 40 to 60 gray levels, blur pushes the edge under the finder's floor. Improve the lighting before you touch the aperture.
• Travel beyond the printed depth of field: symmetric blur keeps the centroid, but contrast falls and field-edge symmetry degrades. No defocus trick extends a lens past its range; pick the next magnification or working distance instead.
• Tasks that need depth information: telecentric imaging deliberately discards it, which is its virtue in gauging and its absence anywhere else.

To buy against this: fix the field of view, divide the sensor width by it for magnification, then choose the aperture that puts your edge at 4 pixels. The lens finder filters telecentric lenses by magnification, working distance and mount; the configurator walks camera, lens and light in one pass; the lenses topic page gathers the related guides. If the trade-offs are tight, bring the part drawing to our contact page and we will run the numbers with you.