Telecentric lens distortion and telecentricity explained

A lens can hold magnification nearly constant with object depth and still place an edge incorrectly within the image. Conversely, a distortion correction that works on a flat target can leave depth-dependent measurement errors untouched. These are different problems, and buying against one percentage will not resolve both.

For dimensional inspection, you need to translate the lens specifications into errors at your actual field positions, part heights, and illumination wavelength. The method below separates those contributions, shows the arithmetic, and identifies the evidence to request before choosing a lens.

Separate field errors from depth errors

Telecentric lens distortion and telecentricity describe different departures from ideal imaging. Distortion concerns the mapping of object coordinates into image coordinates at a specified object plane. Residual object-side telecentricity concerns the angle of the object-space chief rays, which can produce position changes as object depth changes.

Object-side telecentricity addresses object-depth sensitivity. Image-side telecentricity describes rays on the sensor side; it is not a substitute for object-side telecentricity in this task. A bi-telecentric design addresses both sides, but its architecture alone does not establish measurement accuracy.

Start with the telecentric gauging decision if you have not yet established whether height variation makes telecentric imaging necessary.

Convert distortion into dimensional error

Geometric distortion compares an actual image position with the position predicted by a reference magnification. For a radial description away from the image center:

Here, m is the magnitude of the reference magnification. The object-space error describes displacement of a point, not automatically the error of a complete dimension. The reference magnification and coordinate origin must match the specification's definition.

Consider an illustrative distortion value of 0.02% at an object-space radius of 20 mm:

That is the displacement of one point. For two measured edges, the dimension error is the difference between their signed coordinate errors:

If symmetric outward distortion moves opposite edges by 4 µm each, the measured width increases by 8 µm. Two nearby edges with similar coordinate errors might instead show much less dimensional error.

This distinction matters when inspecting short features near the field edge. Their error depends on the local change in the distortion map, not simply the largest displacement anywhere in the image.

A calibrated map can correct stable coordinate errors. It cannot automatically correct unmeasured depth changes. The methods in distortion-correction verification help distinguish a fitted correction from independently demonstrated accuracy.

Read the definition and the whole distortion plot

TV distortion and geometric distortion are not interchangeable percentages. TV distortion commonly characterizes deformation of a rectangular image boundary or line pattern. Geometric distortion compares image coordinates against an ideal mapping. Their reference geometry and normalization can differ.

Do not convert between them using an assumed constant. Request the definition, calculation diagram, reference magnification, and field location associated with each quoted value.

Check the distortion plot for these details:

• Horizontal axis: establish whether it represents image height, object height, or normalized field position.
• Vertical axis: distinguish percentage distortion from displacement expressed in length units.
• Reference scale: identify how the ideal magnification was selected or fitted.
• Field coverage: compare the plotted range with your actual sensor and inspection region.
• Operating conditions: look for working distance, wavelength, aperture, and focus conditions.

A curve can cross zero at the outer field while reaching a larger positive or negative value inside it. An edge-only number therefore cannot bound every interior point when distortion is non-monotonic.

A radial curve also may not describe decentering, assembly asymmetry, or the complete two-dimensional mapping. For tight tolerances, request field data or validate a grid across the assembled system. The calibration target coverage guide explains why sparse central coverage leaves edge behavior unverified.

Translate telecentricity into a depth allowance

Residual object-side telecentricity is often described using an angular deviation from the optical axis. Confirm whether the specification is a maximum magnitude, a signed field curve, or another summary.

For small departures from a reference object plane, a useful geometric estimate is:

Here, Δz is object displacement along the optical axis. The angles are signed object-space chief-ray deviations in the measurement direction. This estimate does not include defocus-related edge bias or changes in the distortion map.

Suppose an illustrative maximum angular magnitude is 0.01°, and the part can move 5 mm from the calibration plane:

If the two edge angles have opposite signs, a conservative width-error estimate is twice that displacement, approximately 1.75 µm. If their angular deviations match, they may primarily cause translation rather than width change.

Be precise about the reference. A ±5 mm depth range has a 10 mm end-to-end span. Under the same assumptions, width variation between its endpoints could approach 3.5 µm, even though the deviation from a central calibration plane is approximately 1.75 µm.

A telecentricity specification does not establish usable depth of field. You must also verify that edge localization remains acceptable throughout that depth range.

Build an error budget before comparing lenses

Begin with the allowable measurement error, not the smallest advertised distortion percentage. For an illustrative maximum absolute error of 10 µm, a preliminary conservative allocation could be:

These are planning allowances, not claims about achievable performance. The calibration-reference allowance, for example, must include the target's documented uncertainty and the conditions of use.

The earlier uncorrected width error of 8 µm would exceed the 3 µm field-error allowance. You would need better native mapping, a validated correction, a smaller used field, or a revised measurement requirement.

Check sampling separately. Suppose a 40 mm field spans 4,000 pixels:

An edge-position variation of 0.1 pixel corresponds to 1 µm at each edge. If both edge errors reach their opposite signed limits, width error reaches 2 µm. Subpixel reporting alone does not prove this performance; verify it with repeated measurements.

Add bounded errors conservatively when their signs or relationships are unknown. Root-sum-square combination needs a justified uncertainty model; it should not hide systematic distortion or scale bias.

Match illumination and calibration conditions

Distortion, best focus, and telecentricity can depend on wavelength. A specification measured under one illumination band does not establish the same behavior under another. Ask which wavelength or spectral band applies to the published curves.

For demanding gauging, a stable narrowband source can simplify qualification by reducing spectral variation. However, there is no universally best color. Select the band using lens data, part contrast, camera response, and the complete optical path.

If the application alternates illumination colors, verify each measurement channel. Do not assume that one calibration remains valid merely because the camera and lens have not moved.

Filters also belong in the qualified configuration. Their placement and optical properties can affect the imaging path, especially when installed in converging light. Review filter placement around telecentric optics before adding or relocating one after calibration.

Keep exposure, aperture, edge polarity, and the edge-detection method consistent during comparison tests. Changing illumination geometry can move the apparent edge of a reflective or translucent part without changing the lens's geometric mapping.

Shortlist catalog parts without assuming accuracy

Use the telecentric lenses category and the lens finder to establish magnification, sensor coverage, working distance, mount, and illumination compatibility. Then evaluate the remaining candidates against your error budget.

The LS-TCL-2194 is an object-side telecentric lens with built-in coaxial light. It is a relevant starting point when that illumination arrangement fits the inspection task.

The LS-TCL-0648 is another object-side telecentric candidate. Compare its catalog configuration with the mechanical and imaging requirements before requesting metrology data.

The supplied catalog descriptions do not establish distortion or telecentricity tolerances for these candidates. Do not treat either card as evidence of a particular dimensional accuracy.

For each shortlisted part, request:

• Geometric distortion curves across the required field, with the reference mapping defined.
• Object-side telecentricity curves or documented magnification stability across depth.
• Conditions covering wavelength, working distance, aperture, and sensor format.
• An explanation of whether values are nominal design data, typical measurements, or guaranteed limits.
• Any available unit-specific verification appropriate to the required tolerance.

The broader lens-selection workflow covers compatibility choices that must be settled alongside these metrology questions.

Verify the assembled measurement system

Use a traceable dimensional reference with uncertainty suitable for your budget. The target must cover the measurement field and remain correctly aligned during depth testing.

1. Establish the reference plane. Record its position relative to the lens and the intended part-measurement plane.
2. Map the full used field. Include corners, central regions, and the actual locations of measurement edges.
3. Separate fitting from verification. Reserve independent positions or reference dimensions that were not used to fit the correction.
4. Test depth explicitly. Measure at the minimum, nominal, and maximum required depths. Add intermediate planes if behavior is nonlinear or tolerances are tight.
5. Repeat under operating illumination. Test each wavelength or illumination configuration used for measurement.
6. Check repeatability and bias separately. Repeated captures reveal variation; comparison with the reference reveals systematic error.
7. Repeat after thermal stabilization. Include expected operating states if temperature changes can affect mounting or scale.

Do not refit the scale independently at every depth when testing a system intended to use one fixed calibration. That procedure can conceal the magnification instability you need to measure.

Likewise, choose a calibration model appropriate to telecentric imaging. A conventional perspective model should not be adopted solely because the software offers it. The guide to interpreting distortion coefficients explains why coefficients require their associated model and coordinate conventions.

Recognize the limits and choose the next step

Telecentric imaging does not remove every geometric error. A tilted flat part is still projected into the image plane. For ideal orthographic projection, a length tilted out of that plane appears as L × cos(α) along the affected direction. At 5°, a 20 mm length appears approximately 19.924 mm, a shortening of about 76 µm.

Low distortion cannot compensate for that alignment error. Nor does a sharp image guarantee accurate scale, correct edge interpretation, or valid calibration.

Before ordering, confirm the used field, depth range, illumination band, allowable dimensional error, and verification method. Then start a lens configuration or request application support with those requirements and ask for the missing specification evidence.