Chromatic confocal displacement sensors routinely deliver linearity error between ±0.05% and ±0.3% of full scale in commercial form, while research-grade compact optics have demonstrated a maximum linear error of ±0.7 μm over a 12 mm dispersion range at 0.15 μm resolution [S1]. Across the OEM catalog, Micro-Epsilon specifies its confocalDT line at linearity (displacement and distance) under ±0.6 μm, which converts to roughly ±0.02% to ±0.06% F.S. on a 1 mm to 3 mm measuring range [S3].
Linearity error is the deviation of the actual output from the best-fit straight line, expressed as a ± percentage of the full-scale output (F.S.) and treated as a non-additive contributor to total measurement uncertainty [S4][S6]. In practice, the %F.S. figure is what procurement and metrology engineers compare when stacking confocal against triangulation, eddy-current, or laser displacement sensor candidates for a given stand-off and target reflectivity range.
What linearity error %F.S. actually means on a confocal head
A confocal head reports displacement by mapping the peak wavelength of the back-scattered spectrum to a calibrated axial focus position, so any residual non-linearity in that wavelength-to-distance law becomes the dominant %F.S. term in the spec sheet [S5]. Omron's measurement-sensor glossary defines linearity error as "the error with respect to ideal straight line of linear output," normally quoted as a percentage of the measurement range (full scale: F.S.) [S6].
For a sensor with a 10 mm range, ±0.1% F.S. equals ±10 μm of end-to-end deviation across the entire stroke, a useful sanity check when reading OEM datasheets. Longvista's product brief notes that chromatic confocal sensors use wavelength-based focusing to measure displacement, distance, and thickness independent of surface finish, which is why their linearity spec is usually tighter than triangulation heads of comparable range [S7]. The same physical principle, axial chromatic dispersion through a multi-element objective, is described in the Sentech / University of Southampton teaching deck, where the focus position of any given point depends on the wavelength of the incident light [S8].
How range, NA, and lens count push linearity numbers around
Compact 6-element dispersive objectives with NA 0.22 and a 12 mm dispersion range over 450-656 nm reach ±0.7 μm maximum linear error, roughly ±0.006% F.S. on that 12 mm range, by trading absolute stroke for tight chromatic correction [S1]. The four-piece spherical-lens design with axial chromatic aberration near 10 mm in the working band is tuned in Zemax for spot size and spherical aberration, with linearity deliberately de-weighted to widen the measurement range, illustrating the classic range-versus-linearity lever [S2].
Wang et al. (2025) used line-spectrum anti-interference encoding to suppress ambient-light drift on spectral confocal displacement sensors, directly attacking a secondary source of %F.S. error on shop-floor installations [S9]. Micro-Epsilon's confocalDT datasheet quantifies the end result: linearity under ±0.6 μm on the high-precision sub-ranges, with resolution down to sub-nanometer class depending on controller and averaging settings [S3]. For engineers comparing spec sheets across displacement sensor families, the rule of thumb is: shorter measuring range plus higher NA plus more correction elements yields a tighter %F.S. linearity number at higher unit cost.
Commercial %F.S. figures: how the major families compare
Triangulation sensors typically spec linearity around ±0.1% to ±0.3% F.S. and degrade further on shiny or steeply tilted targets, while capacitive and eddy-current displacement sensor families sit in a similar ±0.2% to ±0.5% F.S. window but require conductive or ferrous targets. Chromatic confocal heads undercut both on polished metal, glass, and mirror-finish surfaces because the wavelength-encoded focus is largely independent of surface reflectivity and tilt [S7].
The caveat is range: a typical confocal probe covers 0.5 mm to 12 mm, whereas triangulation commonly reaches 25 mm to 500 mm and eddy-current up to 50 mm, so the %F.S. comparison only holds when the same stand-off is in play [S3][S8]. Specifying a confocal displacement sensor for a shaft runout or wafer-thickness application, the published ±0.05% to ±0.3% F.S. line is what shows up on most datasheets, with sub-±0.06% F.S. achievable on the short, well-corrected OEM heads [S3].
Selection criteria: matching %F.S. to the metrology task
Engineers should pin the required %F.S. linearity against the application's allowable measurement uncertainty, not against the headline spec, then back out the matching range and stand-off. A precision bearing race OD check at ±2 μm on a 6 mm diameter needs roughly ±0.03% F.S. over the scan, which rules out mid-range triangulation and forces a confocal head with calibrated linearity below ±0.05% F.S. [S1][S3].
For transparent-layer thickness or multi-peak spectral work, the confocal architecture is preferred because the same probe decodes two surface returns and reports thickness from the same wavelength-to-distance law, and the same %F.S. linearity figure applies to each peak [S7][S9]. When the target is hot, vibrating, or sitting in stray light, anti-interference line-spectrum encoding has been demonstrated in 2025 work to hold the linearity budget on production lines where ambient spectra would otherwise shift the peak-detection algorithm [S9].
Limitations and failure modes that inflate real-world %F.S.
Field %F.S. numbers almost always exceed the datasheet because of three practical effects: temperature-induced shift of the dispersive objective's focal mapping, surface-roughness broadening of the spectral peak, and fiber-bend-induced wavelength-dependent attenuation [S2][S9]. The 2024 Liu et al. precision-measurement-accuracy study makes the point that the chromatic confocal sensor determines actual distance by analyzing the wavelength with maximum light intensity in the reflected bandwidth, so any change in spectral shape translates directly into a peak-shift error and a hidden linearity degradation [S5].
Most published OEM linearity specs are taken on a near-perfect diffuse or mirror target at 20°C ± 2°C, so users on warm shop floors, oil-coated parts, or curved specular surfaces should expect to add 30% to 100% margin to the published %F.S. when budgeting total measurement uncertainty [S3][S6]. Calibration is the second-line defense: re-running the wavelength-to-distance polynomial against a known artefact, exactly as the spectral-characteristic normalising method in the four-piece objective paper does to strip fiber attenuation, source spectrum, and detector response artifacts, recovers a large share of the lost %F.S. budget [S2].
Standards, sourcing, and what to track next
No single ISO or IEC standard fixes a numerical %F.S. linearity budget for chromatic confocal displacement sensors; the practice is to apply the generic sensor-linearity definitions used in fluid-power and industrial-sensor guidance, where the maximum linearity error is expressed as a ± percentage of full-scale output referenced to a best-fit straight line [S4]. VDI/VDE 2617 and ISO 10360 family documents are the closest widely cited metrology references for evaluating displacement-probe linearity, though they are not sensor-class-specific.
On the sourcing side, expect the 2026 commercial benchmark to remain a sub-±0.1% F.S. figure for mid-range confocal probes, with OEM high-precision controllers pushing the headline number toward ±0.02% to ±0.06% F.S. on short ranges, and research demonstrators continuing to print ±0.7 μm maximum linear error on compact 6-element objectives [S1][S3]. Track two signals: (1) line-spectrum anti-interference encoding products reaching general release from the 2025 MDPI line-scan sensor work, and (2) multi-peak decoders for transparent layer and film-thickness probes that extend the same %F.S. envelope to two simultaneous measurements [S9]. For a deeper primer on how these heads differ from triangulation and eddy-current alternatives, the displacement sensor encyclopedia entry maps the families side by side, and the chromatic confocal principles page walks through the wavelength-to-distance mapping that defines the linearity error in the first place.
See also our earlier report, How an Arc Welding Machine Strikes and Holds the Arc.