Telecentric lens image stitching: why tiles line up without rescaling

A part is wider than one field of view, but the drawing still calls for true millimetres at every edge. Put an object-side telecentric lens on an XY stage, capture a grid of tiles, and the mosaic measures like a single photograph: one scale, no perspective, no per-tile rescaling. This guide sizes the tile, counts the grid for a 100 × 60 mm plate, sets an overlap that registration can live with, and shows why an M12 board lens cannot produce the same seams. It assumes a flat part square to the optical axis, a fixed working distance and a fixed exposure — break those and the arithmetic changes.

Why do telecentric tiles stitch without rescaling?

Tiles line up by pure translation because an object-side telecentric lens is an orthographic projector: its chief rays run parallel to the optical axis, so magnification stays constant across the depth of field and every tile shares one pixels-per-millimetre scale.

An ordinary lens views the centre of its field from a different angle than the corners, so each tile carries an internal scale gradient and neighbouring tiles disagree about the same feature. Telecentric optics remove that disagreement at the source. Because magnification does not change with depth — the property telecentric datasheets are built around — a surface wandering inside the depth of field neither scales nor skews between rows. Distortion does not vanish; it is fixed to field position, repeats tile to tile, and shows up as a small, consistent seam shift that the verification pass measures.

Object-side telecentricity is the one that matters here; object space vs image space telecentricity separates the two.

What field of view does each tile cover?

Multiply the sensor format by one over the magnification: a 1-inch sensor at 12.7 × 9.6 mm behind a 0.5x telecentric lens images a 25.4 × 19.2 mm tile, and that tile stays 25.4 mm wide whether the surface sits at focus or a few tenths of a millimetre away.

The common formats are 2/3 inch at 8.8 × 6.6 mm and 1 inch at 12.7 × 9.6 mm. At 0.5x the 1-inch format gives 25.4 × 19.2 mm tiles; at 0.166x it gives 76.5 × 57.8 mm; at 1x on a 2/3-inch sensor the tile is 8.8 × 6.6 mm. The telecentric field of view calculation works this arithmetic in detail, and the object space pixel size guide covers the last line: 3.45 µm sensor pixels become 6.9 µm in the part at 0.5x.

For the worked example, the pairing is a 0.5x object-side telecentric with a 110 mm working distance, a built-in coaxial port and a 1-inch sensor format:

How many tiles does a 100 mm by 60 mm plate need?

For a 100 × 60 mm plate with 20 percent overlap, the 0.5x tile steps 20.32 mm in X and 15.36 mm in Y, so the grid is five columns by four rows — 20 tiles.

The arithmetic: step = 25.4 × 0.8 = 20.32 mm and 19.2 × 0.8 = 15.36 mm. Columns: (100 − 25.4) / 20.32 = 3.67, round up, add the starting tile → 5. Rows: (60 − 19.2) / 15.36 = 2.66, round up, add one → 4. Stage travel is 4 × 20.32 = 81.3 mm in X and 3 × 15.36 = 46.1 mm in Y. Run a serpentine path so every seam is approached from the same direction and backlash lands in the overlap, where correlation absorbs it.

The 1x row is the reality check: fine pixels cost tiles. Reserve that tier for parts of about 25 × 20 mm or smaller, where the same arithmetic gives 4 × 4 = 16 tiles.

How much depth error can the overlap tolerate?

Budget depth and stage separately: 0.1° telecentricity moves an edge about 1.7 µm per millimetre of height error — a quarter pixel at 6.9 µm — while a ±0.1 mm stage error spends only 14 of the 736 overlap pixels.

Depth first. Constant magnification holds only inside the depth of field, so keep the surface inside it. A working estimate is DOF ≈ 2 × F# × c × (1 + M) / M², with c the permissible blur on the sensor. At F4, c = 2 pixels = 6.9 µm and M = 0.5, that is 2 × 4 × 6.9 µm × 1.5 / 0.25 ≈ 0.33 mm. Treat it as an estimate; the printed depth of field for the exact lens governs. The telecentric depth of field guide shows the validation method.

Height inside that depth does not rescale a tile, but telecentricity is finite. At a typical datasheet figure of 0.1°, tan 0.1° ≈ 1.75 mrad, so a feature 1 mm above focus shifts about 1.7 µm in the part — a quarter pixel. In-plane error is where the overlap earns its keep: 20 percent of a 25.4 mm tile is a 5.08 mm corridor, or 5.08 mm / 6.9 µm ≈ 736 pixels. A ±0.1 mm stage repeatability spends 14 of them and a ±30-pixel correlation search still leaves margin. Below roughly 10 percent overlap the corridor thins faster than the tile count falls.

Why won't an M12 board lens stitch the same way?

An M12 board lens is entocentric even when its distortion is low: magnification falls as depth increases, so a tile of a part with 3 mm of height relief changes scale between rows and every pair needs its own rescale and warp before it blends.

Board lenses are built for small size, not orthography. Low-distortion M12 types typically sit near 1 percent distortion, against the sub-0.1 percent figures telecentric datasheets commonly print, and no flat correction undoes perspective scale change with height. There is a hard optical limit too: an object-side telecentric front group must span the whole field, so a 25.4 mm tile needs a front aperture wider than the M12 thread itself — true telecentric fields start at C-mount barrels and up. For board-camera work that stays entocentric, pick with working distance and field of view among the M12 board lenses.

Which lens matches your tile size?

Pick magnification from tile size, then confirm the image circle covers your sensor: 0.166x tiles 76.5 mm, 0.5x tiles 25.4 mm and 1x tiles 8.8 mm on the sensors these catalog lenses serve.

Large parts: the LS-TCL-1422 is a bi-telecentric 0.166x lens with a 258 mm working distance and a 16-22 mm image circle for 1-inch sensors. At 0.166x each tile spans 76.5 × 57.8 mm, so the plate collapses from 20 tiles to 2 × 2, and the long working distance clears clamps and rotary fixtures.

Fine detail: the LS-TCL-2118 is an object-side telecentric 1x lens with a 108 mm working distance and an 8-11 mm image circle for 2/3-inch sensors. At 1x the tile is 8.8 × 6.6 mm and the object pixel 3.45 µm with a 3.45 µm sensor — the tier for hole patterns and pitch checks inside a 25 × 20 mm block.

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

Confirm the image circle covers the sensor diagonal: 16-22 mm covers a 16 mm 1-inch diagonal and 8-11 mm covers an 11 mm 2/3-inch diagonal. Filter the telecentric lenses by magnification and working distance in the lens finder.

How do you verify the mosaic before you measure it?

Stitch two tiles first: correlate the overlap, check the residual offset is under one pixel after translation-only registration, then re-image one tile at the four corners of the stage travel — any scale change between them means depth or perspective crept in.

Then run the full pass in this order:

1. Scale. Image a step gauge, or command a 10 mm stage move and measure the same edge twice: 10 mm must read 1449 pixels at 6.9 µm per pixel, and the percentage error becomes your one scale factor.
2. Registration. Register two tiles with translation-only correlation. A residual rotation or scale term above about one pixel means depth or focus moved between exposures — find the mechanical cause, since spacers and focus changes shift the geometry.
3. Seams. Inspect each seam at high zoom. A consistent one-to-two-pixel shift on every seam is lens distortion — apply the correction profile from the lens distortion correction guide. A random shift is stage error; tighten the mechanics.
4. Illumination. Keep exposure and strobe pulse fixed and hold mean grey level per tile within a few grey levels of its neighbours, or edge thresholds walk between tiles.

When is stitching the wrong tool?

Skip stitching when one tile covers the part: a single 0.166x view spans 76.5 × 57.8 mm at 258 mm working distance, and one exposure carries no overlap, no stage error and no registration step at all.

One view beats twenty whenever it fits. If the part is 75 × 55 mm or smaller, the 0.166x tier covers it in a single exposure with no registration code to maintain. Stitching also assumes flatness: height variation beyond the depth of field breaks the orthographic assumption, so a part with tall features needs one pass per height band or a different sensor. If the real problem is just a field that feels small, check template matching a part larger than the field of view first; if plain gauging would do, start from when you need a telecentric lens for gauging.

Ready to spec it: size the tile, count the grid, then let the lens configurator pair magnification, camera and light. The lenses topic page collects the related guides, and the applications team will turn your part size and smallest feature into a tile count.