Machine Vision Optical Imaging Systems — Performance Test Methods

Document identity statement

This document is a technical reference developed by POMEAS based on optical engineering principles, laboratory testing practices and machine vision application experience. It is intended to support optical system specification, testing, comparison and integration. It is not an official national, international or industry standard.

Where this document cites an external standard, the standard is identified by number, title and edition. Only the standards listed in Section 3 have been verified against their issuing body's catalogue at the release date of this document. Nothing in this document claims conformance to, or approval by, ISO, IEC, GB, DIN, ANSI, IEEE, EMVA or any other standards body.

1. Scope

This document specifies test methods, calculation methods and interpretation guidance for the performance parameters of machine vision optical imaging systems.

It covers the following parameters:

1. Field of View (FOV)
2. Working Distance (WD)
3. Magnification (β)
4. Optical Resolution and Modulation Transfer Function (MTF)
5. Pixel Resolution and System Resolution
6. TV Distortion
7. Full-field Geometric Distortion
8. Depth of Field (DOF)
9. Telecentricity
10. Numerical Aperture (NA) and Aperture Setting
11. Parfocality (motorized zoom lenses)
12. Zoom Repeatability and Backlash
13. Focus Repeatability
14. Sensor Compatibility and Image Circle
15. Illumination Conditions
16. Calibration and Measurement Uncertainty

The methods are written to be executable with equipment normally available to a machine vision integrator: a rigid bench, a calibrated target, a translation stage, an industrial camera able to output unprocessed images, and a focus/edge evaluation software tool. Where a method needs equipment that is normally found only in a metrology laboratory or a lens manufacturer's facility, this is stated explicitly.

Out of scope. Surface form and surface imperfection of optical elements; environmental and durability testing; chromatic aberration and colour reproduction; stray light and veiling glare; laser and non-imaging optical systems; and the internal design or production tolerances of the lens. This document evaluates systems as they are used, not optical designs in isolation.

Application. The results of these methods support three decisions: (a) whether a candidate lens meets a stated requirement before purchase; (b) whether an incoming or in-service lens is fit for a measurement task; (c) whether an existing measurement station is still within its calibration interval. They are not a substitute for a type test performed by the manufacturer against its own specification.

2. Purpose

Most lens data published by machine vision suppliers answers the question "what are the numbers?". This document answers a different question:

How do you test it?

For each parameter, this document provides, in a fixed structure:

Definition → Test Equipment → Test Setup → Test Procedure → Calculation → Result Recording → Common Errors → Engineering Interpretation

The structure is deliberate. A number without a test condition is not a specification: "FOV 100 mm" is meaningless unless the magnification, the working distance, the sensor format and the measurement plane are also stated. Section 12 catalogs the errors that most often make a reported value unreproducible, and Section 11 provides a report template that forces the test conditions to be recorded alongside the result.

Measured values versus theoretical values. Through this document, values are labelled as one of:

• [T] — Theoretical / calculated from geometry and the datasheet parameters of the components. Exact within its model, but the model is an approximation of the real system.
• [M] — Measured on a specific physical assembly under the stated test conditions. Applies to that assembly only, within the stated uncertainty.
• [POMEAS LAB TEST DATA REQUIRED] — A value that this document's method defines, but for which POMEAS does not yet have published laboratory data. Appendix B is the register of every such value, and the companion deliverable TR-001 Laboratory Test Data Plan defines the experiment, the equipment, the photographs and the data records required to fill it in.

No value in this document is presented as a POMEAS product specification unless it appears in a POMEAS datasheet. Engineering examples used for illustration are labelled as such.

3. Normative references

The following documents were verified against the issuing body's catalogue at the release date of this document. Where a later edition exists, the later edition applies.

Not referenced. This document deliberately does not reference GB, DIN, ANSI or IEEE documents for the parameters it covers, because no verified edition of such a document was identified that is directly applicable to machine vision lens system characterisation. Their absence is a statement about applicability, not a claim about their quality.

4. Terminology and symbols

4.1 Symbols

4.2 Key definitions

Active area. The part of the sensor that produces valid image data over the full exposure. Determined from the camera's own documentation, not from the marketing pixel count.

Best focus. The axial position of the object (or of the image plane) at which the chosen focus metric is maximal. Because different metrics peak at slightly different positions, best focus is only defined together with the focus metric. This document uses the MTF50 of a slanted edge at the centre of the field unless stated otherwise (Section 6.4).

Measurement plane. The object plane at which the measurement is taken. For a system with a depth of field, the object may be anywhere within the DOF, and the measurement result validly applies to that plane. A measurement is not valid for objects outside the measurement plane unless the system is object-side telecentric (Section 8.9).

Optical resolution. The ability of the lens to transfer contrast at a given spatial frequency. A property of the lens, evaluated at the image plane.

Pixel resolution. The spatial frequency limit imposed by the sensor's sampling: the Nyquist frequency. A property of the camera.

System resolution. The combined imaging capability of lens + sensor + illumination + relative motion + algorithm. Always lower than either the optical or the pixel resolution taken alone.

Telecentricity (object side). The degree to which the chief rays of the imaging bundle are parallel to the optical axis in object space, expressed as the maximum chief-ray angle over the specified object field.

Parfocality. The property of a zoom lens that the image remains at the same axial position (the object stays in focus at the same WD) as the magnification is changed.

Repeatability. The closeness of agreement between the results of successive measurements of the same measurand carried out under the same conditions (same procedure, same operator, same instrument, same location, over a short period). Reported as a standard deviation and a range.

Distortion. The variation of magnification over the field, i.e. the departure of the image from a geometrically similar mapping of the object. Distortion does not blur an image; it displaces it, which is why it matters for measurement and does not matter for presence/absence inspection (Section 8.7.8).

5. General test conditions

Unless a procedure states otherwise, all tests are performed under the following conditions. The actual values must be recorded in the test report (Section 11). A result without its test conditions is not a result.

5.1 Environment

5.2 Illumination

5.3 Camera settings

The camera is a measuring instrument in this document's methods. Its processing must be neutralised.

5.4 Alignment

5.5 Data handling

• Repeat count. Minimum 5 repeats for any reported value. Where the parameter is the subject of an acceptance decision, minimum 10.
• Report format. Report the mean, the standard deviation s, and the range (max − min). Do not report only the mean.
• Outliers. Reject a value only on an identified cause (a bumped bench, a lost frame, an illumination change). Record every rejection and its cause. Never remove a point only because it is far from the mean.
• Rounding. Round only the reported value, never an intermediate result. Report to the resolution of the reference standard used: for a typical chrome-on-glass scale with a certificate uncertainty of 1 µm, reporting more than 0.1 µm is not justified.
• Traceability. Record the certificate number and the calibration due date of every certified reference used.

6. Required equipment

Equipment that is normally available only to a lens manufacturer or a metrology laboratory — and that this document therefore does not require: an interferometer for transmitted wavefront, a collimator of known focal length for infinite-conjugate measurement, a nodal-slide bench, or a goniometric spectrophotometer. Where a lens must be characterised at an infinite conjugate, the manufacturer's own data should be used.

7. Performance parameters — master table

8. Test methods

Each subsection has the same eight parts. Section 8.1 is written in full as the pattern; later subsections refer back to it rather than repeating general conditions.

8.1 Field of View (FOV)

8.1.1 Definition. The extent of the object plane that is imaged onto the active area of the sensor, at a stated working distance and zoom position.

For a system that is distortion-free and paraxial:

FOV_H = (N_H × p) / β        [T]        (8.1a)
FOV_V = (N_V × p) / β        [T]        (8.1b)

with N in pixels and p in µm (giving FOV in µm; divide by 1000 for mm).

Two warnings that invalidate most published FOV figures:

• Use N_H, not the total pixel count. A 2448 × 2048 sensor with 16 optical-black and 8 dummy columns per line does not have 2448 active columns. The error is typically 0.5–2 %, which is larger than the tolerance on many measurement tasks.
• Use the diagonal only when the sensor is used diagonally. The frequently seen formula FOV = sensor diagonal / β is a field coverage statement (does the image circle cover the sensor?), not a field-of-view statement. Reporting a diagonal FOV as "the FOV" overstates the usable field by 20–30 % and causes integrators to specify a lens that does not cover the part.

8.1.2 Test equipment. E1, E2, E3, E4, E9, E11, E13, E14.

The scale (E4) must be long enough that the full FOV falls inside the certified region, with at least two graduations inside each edge of the frame. A scale that only just covers the FOV forces the operator to use the physical end of the scale, whose position is not certified.

8.1.3 Test setup.

1. Mount the lens and camera on the bench (E1); the camera sensor plane parallel to the lens mounting flange within the mechanical tolerance of the mount.
2. Set the target plane at the nominal WD using the z-stage (E2), referenced to the stated datum of the lens.
3. Place the calibrated scale (E4) at the target plane, centred, with its graduations horizontal for the measurement of FOV_H. Backlight it (E9) if it is a negative chrome-on-glass scale.
4. Verify perpendicularity per Section 5.4 before taking data.

8.1.4 Test procedure.

1. Set the lens to the zoom or focus setting under test. If the setting is reached by a motor, always approach it from the same direction (Section 8.12).
2. Adjust the exposure so that the graduations are in the linear part of the sensor response and neither the clear nor the chrome regions are clipped.
3. Identify two graduations whose object coordinates x₁ and x₂ are known from the certificate, separated by at least 60 % of the frame width, and both clearly inside the frame. The lines must be imaged, not synthesised, and their pixel positions u₁, u₂ determined by sub-pixel centroid of the line profile (fit the line with a first moment or a Gaussian; a threshold-based measurement introduces a half-pixel bias that depends on the illumination).
4. Compute the local scale factor:

s = (x₂ − x₁) / (u₂ − u₁)        [M]        (8.1c)

in mm per pixel. Take the reciprocal for the pixel size in object space, in µm: L_obj,meas = 1000 / s.

5. Compute the measured FOV from the active pixel count:

FOV_H,meas = s × N_H        [M]        (8.1d)

6. Repeat at four positions across the field (left, centre, right, and the two diagonals if the target allows), so that the variation of the local scale factor across the field becomes visible. That variation is the distortion (Section 8.7) and it is the reason a single scale factor is not sufficient for a measurement system.
7. Repeat the whole procedure 5 times, refocusing between repeats, and report the mean and standard deviation.

8.1.5 Calculation.

• Object-space pixel size: L_obj = 1000 / s, in µm.
• FOV for an arbitrary region of interest: FOV = s × N_roi.
• FOV sensitivity to working distance (important for non-telecentric lenses): repeat the measurement at WD_nom ± ΔWD (e.g. ±0.5 mm) and report

d(FOV)/d(WD) = ΔFOV / ΔWD        [M]        (8.1e)

For an ideal object-side telecentric lens this slope is zero up to the measurement uncertainty. A non-zero slope means the system is not object-side telecentric, and every measurement result carries a FOV error proportional to how well the WD is reproduced.

• Magnification from the scale: β = (u₂ − u₁) × p / (1000 × (x₂ − x₁)), with p in µm and x in mm. This is the same quantity as Section 8.3 and must agree with it within the stated uncertainty.

8.1.6 Result recording.

8.1.7 Common errors.

8.1.8 Engineering interpretation.

• A FOV specification is only comparable if the sensor format, the active pixel count, the WD and the measurement plane are the same. Require all four when comparing two suppliers' data.
• Use the inscribed circle, not the corners, when specifying the field for a circular part: FOV_circle = min(FOV_H, FOV_V). For a 2/3" sensor at 1× the inscribed circle is 8.4 mm, not 11.0 mm.
• Add a working margin: a part that exactly fills the FOV cannot be measured at its edges, because distortion, vignetting and edge MTF are all worst there. A practical target is that the part occupies ≤80 % of the FOV_H and is fully inside the 0.9-field radius.
• If the required FOV cannot be achieved with an object-side telecentric lens at the required magnification, this is a design conflict, not a lens selection problem: FOV and β are linked by equation 8.1a. The available responses are (i) a larger sensor, (ii) a different β, or (iii) accepting a non-telecentric system with the height-variation error quantified per Section 10.3.
• [POMEAS LAB TEST DATA REQUIRED — FOV-01] Measured FOV and d(FOV)/d(WD) for each POMEAS telecentric and motorized zoom model at its specified WD, with the actual active pixel counts of the standard POMEAS test cameras. See Appendix B for the register of all such values, and the companion deliverable TR-001 Laboratory Test Data Plan for the experiment design.

8.2 Working Distance (WD)

8.2.1 Definition. The distance from the manufacturer's reference plane to the object plane at which the system is in best focus.

Three different quantities are commonly called "working distance" and must not be confused:

8.2.2 Test equipment. E1, E2, E4 or E6, E9, E11, E13, E14.

8.2.3 Test setup. Mount a slanted-edge target (E6) or a scale (E4) on the z-stage. Ensure the stage travel covers WD_nom ± (2 × the expected focus band). Align per Section 5.4. Set the illumination and the camera once and do not touch them for the rest of the series.

8.2.4 Test procedure.

1. Approach WD_nom from below (from the lens side) to eliminate backlash.
2. Step the stage in increments of Δz = band_expected / 10 along z. At each step, capture one frame and compute the focus metric M(z) — this document uses MTF50 of the central slanted edge (E14), or, if MTF analysis is unavailable, the normalised gradient energy of a high-contrast region. Do not change exposure between steps; a metric computed on differently exposed frames is not comparable.
3. Continue until M(z) has decreased to 50 % of its peak on both sides.
4. Fit a parabola to the 5–7 points around the peak (or a Gaussian, which is often a better model for the through-focus MTF of a real lens):

M(z) ≈ M_max − a (z − z₀)²        [M]        (8.2a)

and solve for the vertex z₀.

5. Best-focus WD = z₀ (referenced to the datum).
6. Focus band. Find the two axial positions at which M(z) falls to the acceptance threshold M_thresh, and report the band as z₊ − z₋. The threshold must be tied to the application: a common choice is M_thresh = 0.8 × M_max for a measurement task, and 0.5 × M_max for a detection task.
7. Repeat 5 times, approaching from below each time; report the mean and standard deviation of z₀.

8.2.5 Calculation.

• Object-space focus band from the geometric DOF formula (8.8a), for comparison with the measured band.
• WD error sensitivity: for a non-telecentric lens, the magnification error caused by a WD error Δz is Δβ/β ≈ Δz × (dβ/dz)/β, measured per Section 8.3.5. For a typical 0.5× FA lens, a 1 mm WD error changes β by roughly 0.5–1 %, i.e. a 100 mm measurement changes by 0.5–1 mm. For an object-side telecentric lens the same WD error changes β by ≈0, which is exactly what the user is buying.

8.2.6 Result recording. Datum definition; stage readout value at best focus; measured WD; focus band with its threshold; number of repeats with mean and s; temperature; and the target and camera used.

8.2.7 Common errors.

8.2.8 Engineering interpretation. The nominal WD is a design number; the mounting of the station should reproduce the measured best-focus WD, not the nominal one. The difference between the two is a useful incoming-inspection item: if it exceeds the focus band, the mechanical interface of the station will need adjustment. For a motorized zoom lens, the WD at which focus is set must be the WD at maximum zoom (Section 8.11), because the DOF is smallest there and a focus error is most visible.

8.3 Magnification (β)

8.3.1 Definition. The ratio of image size to object size:

β = (n_px × p) / L_obj        [M]        (8.3a)

where n_px is the number of pixels between two features, p the pixel pitch in µm and L_obj the corresponding object distance in µm.

Note that for a lens with a specified magnification, β is defined at the design working distance. Reporting β without WD is incomplete: for a non-telecentric lens the two are coupled, and for a telecentric lens β is nominally independent of WD — the residual dependence is a direct measure of the telecentricity error (Section 8.9).

8.3.2 Test equipment. E1, E2, E4, E9, E11, E14.

8.3.3 Test setup. Calibrated scale (E4) at the target plane, centred and perpendicular. Prefer a line scale with lines of 3–10 µm width, whose centroid can be determined to better than 0.1 pixel.

8.3.4 Test procedure.

1. Choose two graduations separated by at least 60 % of FOV_H. The relative error of β is dominated by the relative error of the measured pixel count; a short baseline wastes the available accuracy. With a 2448-pixel sensor and sub-pixel centroids of 0.05 px, a 60 % baseline gives a relative uncertainty of about 0.007 %; a 10 % baseline gives about 0.04 %.
2. Compute the pixel positions u₁, u₂ by sub-pixel centroid.
3. β_centre = (u₂ − u₁) × p / L_certified.
4. Move the scale so that the same two graduations now straddle a field position at 0.7 × FOV_H/2, and repeat → β_edge.
5. Repeat at 0.7 field in four directions (up, down, left, right).
6. Repeat the whole set 5 times at fixed WD; report the mean and s for each position.
7. WD dependence. Repeat steps 3–5 at WD_nom ± 0.5 mm and ±1.0 mm. Fit β(z) and report dβ/dz in %/mm and the corresponding Δβ for a 1 mm WD error.

8.3.5 Calculation.

• Object-space pixel size: L_obj = p / β.
• Magnification error from a WD error:

Δβ/β = (1/β) × (dβ/dz) × Δz        [M]        (8.3b)

• Field-dependent magnification (this is the distortion):

D(x) = (β(x) − β_centre) / β_centre × 100 %        [M]        (8.3c)

• Perspective magnification for a non-telecentric lens [T]: for a chief-ray angle θ at the field point, an object at height h above the nominal measurement plane is imaged with an apparent lateral shift of h·tanθ and an apparent magnification change of approximately (h·tanθ)/x, where x is the distance of the feature from the axis. This is the single most common source of gross measurement error in machine vision, and Section 10.3 gives the decision threshold.

8.3.6 Result recording. β at centre and at four 0.7-field positions; the certified distance used and the certificate number; WD; zoom position; dβ/dz; repeat count and s; temperature.

8.3.7 Common errors.

8.3.8 Engineering interpretation. For a measurement system, what matters is not β itself but the measured scale factor s (mm/pixel) and its stability. β is a useful cross-check against the datasheet and a useful diagnostic: a β that differs from nominal by more than the combined uncertainty indicates that the WD is wrong, the sensor pixel pitch assumption is wrong, or the lens is not the model it is claimed to be. Report β and s together, and state the field position for both.

8.4 Optical Resolution and MTF

8.4.1 Definition. The ability of the lens to transfer contrast from the object to the image as a function of spatial frequency. The modulation transfer function MTF(f) is the modulus of the optical transfer function; it is dimensionless, from 1 at zero frequency to 0 at the cutoff. Three ways of reducing MTF to a single number are in common use:

The diffraction limit for incoherent illumination is:

f_cut = 2 × NA / λ        [T]        (8.4a)

with NA on the same side as f_cut and λ in mm. With NA_obj = 0.1 and λ = 0.55 µm, f_cut,object = 364 lp/mm; the image-side cutoff is f_cut,obj / β.

8.4.2 Test equipment. E6 (ISO 12233 slanted edge or certified Siemens star), E1, E2, E11, E9, E13, E14.

8.4.3 Test setup.

1. Mount the slanted-edge target at the target plane, at the exact WD, perpendicular to within 0.1° (an edge that is imaged with tilt is imaged at a different magnification across its length, which biases the SFR).
2. Use a narrow-band source (λ = 0.55 µm ±20 nm) for the reported measurement. If the application is white light, additionally report a white-light measurement and label it as such; expect a lower MTF50 due to chromatic aberration.
3. Set the edge angle between 2° and 7° from vertical. Outside this range the ISO 12233 algorithm's phase averaging loses accuracy; near 0° the edge aliases.
4. Position the edge so that its analysed length covers at least 10 pixels and it does not run into a corner region where perspective or vignetting changes the local magnification.
5. Focus at the centre of the field using the same slanted edge before moving to other field points. Record the focus position.

8.4.4 Test procedure.

1. Capture the edge. Confirm: no clipping, peak signal 70–80 % of full scale, background above black level but below 10 % of the peak. Confirm the camera settings of Section 5.3 are in force.
2. Apply the ISO 12233 e-SFR algorithm: locate the edge, project the pixels onto the edge normal direction, bin them into the oversampled edge profile, differentiate to obtain the line spread function (LSF), and take the modulus of the Fourier transform of the LSF to obtain the SFR. The phase averaging over the edge length is what makes the method robust to noise.
3. Apply the correction for the finite pixel aperture if the standard's method requires it (the pixel's own integration over its area acts as a low-pass filter with a sinc response). Report whether this correction was applied.
4. Read off MTF50, and MTF at the target working frequency.
5. Repeat at: field centre; the four 0.7-field positions (up, down, left, right); and the four corners. Report a table, not a single number, plus the ratio of the worst field point to the centre.
6. Where the lens is astigmatic, measure MTF50 separately for the sagittal and tangential orientations at each field point and report both.
7. Repeat the centre measurement 5 times, refocusing between repeats. The spread of MTF50 across repeats with refocusing is the focus-related reproducibility of the measurement and is normally larger than the within-focus repeatability.
8. Convert to object space for the application:

f_obj = β × f_img        [T]        (8.4b)
w_obj = 1000 / (2 × f_obj)   µm     [T]        (8.4c)

where w_obj is the width of one line pair (line + space) that the lens resolves at that frequency. If the application's smallest feature is w_obj or smaller, the lens is marginal; a factor of 2–3 in hand is normal engineering practice.

8.4.5 Calculation.

• Object-side MTF50: f50,obj = β × f50,img.
• Object-side limiting resolution from equation 8.4a.
• Consistency check: f50,obj must not exceed f_cut,obj. A value above the diffraction limit is a measurement artefact (usually sharpening left on, or a stale focus position).
• Field uniformity metric: MTF50_min across the measured field points, divided by MTF50_centre. Report as a percentage. A lens with a uniform 70 % across the field is often a better choice for a vision system than one with 100 % at the centre and 30 % at the corner.

8.4.6 Result recording. Table of MTF50 (and MTF at the stated frequency) for each field position and orientation; λ; f-number; WD; zoom position; whether the pixel-aperture correction was applied; objective and camera; focus metric used; repeat statistics for the centre; and the diffraction limit for comparison.

8.4.7 Common errors.

8.4.8 Engineering interpretation. Resolution is a system property, not a lens property (Section 8.5). The lens MTF sets the ceiling; the sensor's pixel aperture and sampling set a second ceiling; motion blur and the algorithm set a third. When a system fails to resolve a feature, the useful diagnostic sequence is: (1) confirm the focus at the feature's plane; (2) compare the feature's image-side frequency with the sensor's Nyquist — if it is above Nyquist, the sensor is the limit, and adding optical resolution will not help; (3) if it is well below Nyquist, measure MTF50 and check it against the diffraction limit; (4) only then consider the lens. A lens whose MTF50 is within 30 % of the diffraction limit for its aperture is performing as designed, and no amount of lens replacement will produce a large gain.

8.5 Pixel Resolution and System Resolution

8.5.1 Definition.

• Pixel (sampling) resolution, image side, is the Nyquist frequency of the sensor:

f_Nyq,img = 1000 / (2 p)        [T]        (8.5a)

with p in µm. For p = 3.45 µm, f_Nyq = 145 lp/mm. For p = 5.5 µm, 91 lp/mm. For p = 2.4 µm, 208 lp/mm. - Pixel resolution, object side:

f_Nyq,obj = β × 1000 / (2 p) = 1000 / (2 L_obj)        [T]        (8.5b)

• Smallest object detail that can be sampled: one line pair occupies 1000/f_Nyq,obj µm = 2·L_obj. A practical design rule is to place ≥3 pixels across the smallest feature to be detected, and ≥5 pixels across the smallest feature to be measured, i.e. L_obj ≤ d/3 and L_obj ≤ d/5 respectively.
• System resolution is the combined capability of lens + sensor. Because the two transfer functions multiply, and because a Gaussian MTF is a good approximation for both over the range of interest, the reciprocals of the squared MTF50 values add:

1 / f50,sys² ≈ 1 / f50,lens² + 1 / f50,sensor²        [T]        (8.5c)

Equation 8.5c is exact for Gaussian MTFs and a good engineering approximation in general. Its practical message: the weaker of the two dominates, and making the stronger one better buys very little. A lens at 200 lp/mm with a sensor at 90 lp/mm gives 82 lp/mm — better than the sensor alone by 9 %, but nowhere near 200.

Motion blur, illumination and the algorithm each multiply in the same way. For a system with an exposure time t and an object-space velocity v, the blur is v·t; if this exceeds L_obj, it will dominate everything else and must be fixed mechanically before any optics work is done.

8.5.2 Test equipment. E1, E2, E6, E11, E14, plus a way to induce a known motion (a conveyor or a rotating target) if the motion-blur term is to be measured.

8.5.3 Test setup. As Section 8.4, with the sensor at its working format and binning off.

8.5.4 Test procedure.

1. Measure f50,lens per Section 8.4 with the lens at the setting under test.
2. Determine f50,sensor. Two acceptable routes: (a) take it from the camera supplier's EMVA 1288-based characterisation, if the sensor MTF is reported; (b) measure it directly by imaging the same slanted edge onto the sensor with a better lens — a diffraction-limited macro lens at a small aperture, whose f50 exceeds the sensor's Nyquist — and computing the SFR of the sensor + reference lens.
3. Compute f50,sys from equation 8.5c and compare with a direct measurement of the whole chain. The difference is the model error, typically 5–15 %.
4. Compute the working margins: - Detection margin: M_det = f_Nyq,obj / f_required, where f_required = 1000/(3 × d) for a feature size d. M_det should be ≥1.3. - Measurement margin: M_meas = f_Nyq,obj / (1000/(5 × d)) for a measured feature. M_meas should be ≥1.3.
5. Where the object moves, add the motion term: f_motion ≈ 1000/(2 × v × t) and combine per equation 8.5c.
6. [POMEAS LAB TEST DATA REQUIRED — RES-02] A measured lens + sensor matrix for the standard POMEAS camera/lens pairings (for example: a 5 MP 2/3" sensor at 3.45 µm with each POMEAS telecentric model, and a 16 K line-scan sensor with the line-scan and large-format lens families), giving f50,lens, f50,sensor, f50,sys and the model error of equation 8.5c. This is the single most reusable dataset POMEAS can produce, because it answers "which lens for which camera" with evidence rather than with a rule of thumb.

8.5.5 Calculation. Equations 8.5a–8.5c, plus the conversion L_obj = p/β, plus the standard "N pixels per feature" rules.

8.5.6 Result recording. p and its source; active format; binning state; f50 for lens, sensor and system (measured and modelled); the field position; motion parameters if applicable; and the margins.

8.5.7 Common errors.

8.5.8 Engineering interpretation. The design sequence is: (1) smallest feature to be detected or measured; (2) required object-space pixel size from the 3-pixel / 5-pixel rules; (3) β = p / L_obj; (4) FOV = sensor size / β, checked against the part; (5) if FOV and L_obj cannot both be satisfied, the sensor must be changed — not the lens alone, because equations 8.1a and 8.5b are both set by the same pair of numbers. Step 5 is where most machine vision selection errors occur, and it is the reason a lens selection cannot be done without the camera.

8.6 TV Distortion

8.6.1 Definition. TV distortion is a shape descriptor inherited from television-optics testing and is still quoted by most machine-vision lens suppliers. In its most common form, a nominally straight line at the edge of the field is imaged; the imaged line bows; and the sagitta of the bow is normalised to the image height:

TV = (Δy / H) × 100 %        [convention]        (8.6a)

where Δy is the maximum deviation of the imaged line from a least-squares straight line fitted to the same imaged line, and H is the full image height (greater dimension of the active area, usually the vertical).

The convention is not standardised, and this matters. Three variants are in simultaneous use:

Two suppliers can therefore quote 1.0 % and 0.5 % for the same lens. Never compare TV distortion values across suppliers unless the variant is stated, and never use TV distortion as the specification for a dimensional measurement system.

8.6.2 Test equipment. E1, E3, E5 (or a square grid / a bar target), E9, E11, E12, E14.

8.6.3 Test setup.

1. Mount a square grid or a target with straight lines at the field edges at the exact WD.
2. Verify perpendicularity to 0.2° per Section 5.4. A tilt is indistinguishable from distortion in this test — it produces a linear magnification gradient that the line-fit will convert into an apparent bow.
3. Align the grid axes to the sensor axes to within 0.5°.
4. Keep the peak signal at 60–80 % of full scale; a saturated line has a flattened profile and a biased centroid.

8.6.4 Test procedure.

1. Capture the target.
2. Extract the centre-line of the chosen horizontal line across at least 80 % of the image width, at sub-pixel resolution. Fit a least-squares straight line to the extracted centre-line.
3. Compute the maximum deviation Δy from the fitted line, and its position along the line (the position matters: a bow whose maximum is not near the centre of the line indicates non-symmetric handling or a tilted target).
4. TV = Δy / H × 100 %. State which variant and which line.
5. Repeat for a vertical line at the field edge and for the symmetric lines on the opposite side. A symmetric pair should give the same magnitude with opposite sign; an asymmetric result indicates decentring.
6. Repeat 5 times with refocusing; report the mean and s.

8.6.5 Calculation. Equation 8.6a. If the supplier's convention is unknown, report the raw sagitta Δy in pixels and in µm, alongside H — that data can be converted to any convention.

8.6.6 Result recording. Which line (position, orientation, which edge); Δy in µm and px; H in px and mm; the convention used; WD; zoom position; the fit residuals; temperature.

8.6.7 Common errors.

8.6.8 Engineering interpretation. TV distortion answers the question "will a straight edge look bent in my image?". It is the right metric for cosmetic inspection and for image-comparison algorithms. It does not answer the question "how large is my measurement error at the edge of the field?" — that requires the full-field local-magnification map of Section 8.7. The two correlate loosely, and a lens can be acceptable by one and unacceptable by the other. Report both when a measurement application is being specified.

8.7 Full-field Geometric Distortion

This subsection provides the metric that should be used for measurement applications. Its principle follows the distortion determination described in ISO 9039:2008 for rotationally symmetric imaging systems; the procedure below is adapted to a machine-vision camera and lens and is not a claim of conformance to that document.

8.7.1 Definition. Distortion is the variation of magnification over the field. The metrologically useful expression is the relative local-magnification error, referenced to the magnification at the field centre:

D(x, y) = [ β(x, y) − β_centre ] / β_centre × 100 %        [M]        (8.7a)

For a measurement system this is the quantity that matters, because the measurement error of a feature located at field position (x, y) is:

Δx_meas ≈ D(x, y) / 100 × x        [T]        (8.7b)

That is: a lens with D = 0.5 % at the field edge produces a 250 µm error on a feature 50 mm from the centre — regardless of how small its TV distortion looks. Distortion does not blur; it displaces. This is why distortion is irrelevant to presence/absence detection and decisive for dimensional measurement.

The commonly used radial model (Brown–Conrady form, the basis of most camera-calibration implementations) is:

r_u = r_d (1 + k1 r_d² + k2 r_d⁴ + k3 r_d⁶)        [model]        (8.7c)

where r_d is the measured (distorted) image radius and r_u the ideal (undistorted) radius, both normalised; k1 < 0 indicates barrel distortion, k1 > 0 pincushion. Equation 8.7c is a model, not a measurement: fitting it to insufficient field points produces coefficients that extrapolate badly.

8.7.2 Test equipment. E1, E2, E3, E5 (dot grid or chessboard, ≥15 × 15 nodes, node position uncertainty ≤3 µm), E9, E11, E12, E14.

8.7.3 Test setup.

1. Mount the calibrated grid at the exact best-focus WD, perpendicular to within 0.1°.
2. The grid must cover at least 1.2 × the FOV so that every analysed node is a certified node, not a partially imaged one.
3. Centre the grid on the optical axis to within 1 % of FOV.
4. Use diffuse backlighting for a chrome-on-glass grid; verify the chrome is opaque at the exposure used.
5. Fix the camera settings. The centroid of a node depends on the exposure if the node image is saturated.

8.7.4 Test procedure.

1. Capture the grid. Confirm no saturated nodes and no clipped shadows.
2. Detect every node: threshold to obtain the node blobs, then compute sub-pixel centroids (intensity-weighted first moment, or a 2D Gaussian fit). A binary-value centroid has a quantisation bias of up to ±0.3 px.
3. Identify the node nearest the image centre → the reference node.
4. Determine the local scale factor around each node using its nearest neighbours in x and y:

s_x(i,j) = (X(i+1,j) − X(i−1,j)) / (u(i+1,j) − u(i−1,j))        [M]        (8.7d)

where X are the certified object coordinates of the nodes in mm and u are the measured pixel coordinates. Repeat for s_y using the j neighbours. The use of neighbours rather than a global fit is what makes this a local magnification measurement, and it is what exposes distortion that a global fit would average away. 5. Convert to local magnification: β(i,j) = Δu × p / ΔX, using p in µm and ΔX in µm. 6. Compute D(i,j) from equation 8.7a with β_centre taken from the four nodes nearest the axis. 7. Report: D_max (with its field position), the D contour over the field, the ratio of the magnification at the corner to that at the centre, and the residual after applying a fitted correction. 8. Repeat 5 times; the spread of D_max is the repeatability of the distortion measurement, which is normally limited by node centroiding rather than by the lens. 9. Repeat the whole test at WD_nom ± 0.5 mm. A distortion map that changes significantly with WD indicates either a non-object-side-telecentric system or a tilt that varies with WD.

8.7.5 Calculation.

• Equations 8.7a–8.7d.
• Residual correction: fit equation 8.7c to the measured node displacements by least squares, then apply the inverse mapping to the node positions and recompute D. The remaining |D| is the corrected distortion, and it is the number that should be quoted for a measurement system that applies calibration. Report both the uncorrected and the corrected values, with the order of the polynomial and the number of nodes used. A correction fitted on 20 nodes and evaluated on the same 20 nodes will always look excellent; always validate on a hold-out set of nodes or on a different artefact.
• Maximum measurement error over the field for a stated feature position, from equation 8.7b, using the uncorrected D if no calibration is applied and the corrected D if one is.

8.7.6 Result recording. Grid certificate number and node pitch; N_H × N_V; p; WD; zoom position; number of nodes detected and the number used for the fit; number held out for validation; k coefficients with the fit residual; D_max before and after correction, with field positions; temperature.

8.7.7 Common errors.

8.7.8 Engineering interpretation. - Use distortion at all only when you measure. For a go/no-go inspection, distortion displaces the image but does not change the presence or absence of a feature; a 2 % distortion is harmless. - For measurement, D is a first-order error, not a second-order one. The decision rule used in this document is that the uncorrected maximum distortion error over the working field must be ≤1/10 of the measurement tolerance, or the distortion must be corrected by calibration with a validated residual. If neither holds, the accuracy claim is not supported. - Distortion correction and lens selection are alternatives, not complements. A well-behaved lens plus calibration can beat an expensive near-distortion-free lens on total system accuracy, because calibration is cheap and repeatable while lens distortion is fixed. The exception is a system that cannot be calibrated per unit (for example, a lens that will be swapped in the field), where low intrinsic distortion is the only safe choice. - [POMEAS LAB TEST DATA REQUIRED — DIS-03] A published, corrected distortion map for each POMEAS telecentric model (D_max before and after correction, with the hold-out validation residual) and for the motorized zoom family at each preset zoom position, since a zoom lens has a different distortion map at every magnification. This is a claim no competitor currently supports with data, and it is directly usable by integrators.

8.8 Depth of Field (DOF)

8.8.1 Definition. The range of object positions along the optical axis over which the image is judged acceptably sharp. DOF is only defined together with two parameters that must always be stated:

1. the acceptable blur, expressed either as a circle of confusion c at the image plane, or as an acceptance threshold on a measured metric; and
2. the criterion — geometric (a stated c) or measured (a stated threshold on MTF50 or on feature contrast).

Geometric DOF (object side):

DOF_total = 2 × F# × c × (1 + β) / β²        [T]        (8.8a)

with F# the lens's f-number, c the permitted image-side blur diameter and β the magnification. For β << 1 this reduces to the commonly quoted DOF ≈ 2·F#·c/β².

Equivalent form using the object-side blur:

DOF_total = c_obj / NA_obj,   with c_obj = c / β        [T]        (8.8b)

Worked example (illustrative, not a POMEAS specification). A telecentric lens at β = 2, F# = 8, on a sensor with p = 3.45 µm, with an acceptance criterion of c = 2 px = 6.9 µm:

DOF_total = 2 × 8 × 0.0069 mm × (1 + 2) / 2² = 0.0414 mm ≈ 41 µm

The same lens at β = 0.5 with the same criterion:

DOF_total = 2 × 8 × 0.0069 × 1.5 / 0.25 = 0.662 mm ≈ 662 µm

This 16× difference over a 4× magnification change (β² in the denominator, partly offset by (1+β)) is the single most important fact about DOF in machine vision: DOF collapses rapidly with magnification, which is why a zoom lens is focused at its maximum magnification and why a high-magnification telecentric system needs a mechanically flat part.

8.8.2 Test equipment. E1, E2, E6 or E8, E11, E14. The z-stage is critical: resolution ≤ DOF_expected/20.

8.8.3 Test setup. Mount a slanted edge or a fine-detail region of interest on the z-stage, centred in the field. Set the lens to the magnification and aperture under test. Establish best focus per Section 8.2 and record z₀.

8.8.4 Test procedure.

1. Set the step size to Δz = DOF_expected / 10 (from equation 8.8a, using a c equal to the acceptance criterion).
2. Start at z₀ − 1.5 × DOF_expected, approaching from the outside, and step toward z₀ + 1.5 × DOF_expected. At each step capture one frame and compute the metric. Do not change the exposure or the focus between steps.
3. Plot the metric against z. The result is a through-focus curve.
4. Determine the two axial positions z₋ and z₊ at which the metric equals the acceptance threshold, interpolating between the bracketing steps.
5. DOF_measured = z₊ − z₋.
6. Report the peak metric value as well: a low peak indicates that the system never reaches the required sharpness anywhere, in which case the DOF figure is meaningless.
7. Repeat the sweep 3 times, approaching from the same direction, and report the mean and s of DOF_measured.
8. Optionally repeat at two aperture settings to confirm the F# dependence of equation 8.8a — this is a useful validation of the whole measurement chain, because a DOF that does not scale approximately with F# indicates that something other than geometry is governing (see 8.8.7).

8.8.5 Calculation.

• Equation 8.8a for the geometric prediction; the ratio DOF_measured / DOF_predicted is a measure of how much the model is missing. Values between 0.6 and 1.2 are normal. A ratio below 0.5 usually indicates that aberrations, not geometry, are limiting the system.
• Convert a measured DOF given at one β to another β using the β² dependence, as a first estimate only.
• Where the illumination is oblique, the effective DOF for a feature may be smaller than the DOF for a flat target, because the shadow moves across the feature as z changes. This is a system effect, not a lens effect, and it must be measured with the production illumination.

8.8.6 Result recording. The criterion and the threshold value; the c used; F#; β; the metric used; the step size; the measured DOF with mean and s; the peak metric; the geometric prediction and the ratio; illumination geometry; temperature.

8.8.7 Common errors.

8.8.8 Engineering interpretation. DOF is a system number as soon as illumination and the algorithm are involved. Two integrators can measure different DOF values on the same lens with the same criterion, because their illumination geometry differs. The engineering response is to measure DOF with the production illumination and the production algorithm, and to treat the geometric formula as a sanity check rather than as a specification. When a part cannot be held within the DOF, the available levers are, in order of effectiveness: reduce β (the β² term), open the aperture if the resolution budget allows, add a telecentric lens with an intrinsically larger depth, or change the measurement principle.

8.9 Telecentricity

8.9.1 Definition. The degree to which the chief rays of the imaging bundle are parallel to the optical axis in object space, quantified as the maximum chief-ray angle θ_max over the specified object field, in mrad or degrees.

The reason it is specified as a maximum over the field is that the perspective error is largest at the field edge. An on-axis figure describes nothing useful.

Object-side telecentric: the chief rays in object space are parallel to the axis; the object does not "see" the lens from an angle. This is the condition that makes a measurement independent of the axial position of the feature.

Bi-telecentric: the entrance and exit pupils are additionally at infinity (chief rays parallel on both sides), which makes the image-side magnification independent of the image plane position. Bi-telecentricity does not add measurement value beyond object-side telecentricity for a system with a fixed sensor position; it adds tolerance to sensor-plane placement and is the reason bi-telecentric lenses are specified for systems that may be re-assembled in the field.

8.9.2 Test equipment. E1, E2 (z-stage, resolution ≤1 µm, travel ≥ several mm), E8 (a suitable target), E11, E14.

8.9.3 Test setup. Use a target carrying small, isolated, high-contrast features — a single chrome dot of 5–50 µm, or a small chrome square — at the field position under test. The feature must be small enough that its image is a compact blob whose centroid can be determined, and it must be symmetric so that defocusing does not shift its apparent centre.

8.9.4 Test procedure — the defocus (centroid-shift) method.

This is the practical method and it is what a system integrator should use.

1. Place the isolated feature at the field position under test (start on axis).
2. Find best focus z₀ for that feature and record the centroid u₀ of the feature image.
3. Move the z-stage in known increments Δz (for example ±0.1, ±0.2, ±0.5, ±1.0 mm). At each position record the centroid u(Δz). The image will be blurred; a symmetric feature remains measurable, and the signal-to-noise ratio of the centroid can be maintained by increasing the exposure or by averaging frames. Verify that the centroid is still measurable by checking the blob's peak signal stays above 20 % of full scale.
4. Fit a straight line to u(Δz). The slope is du/dz in pixels per mm.
5. Convert to a chief-ray angle:

θ = arctan( (du/dz) × p / (1000 × β) )        [M]        (8.9a)

with p in µm, du/dz in px/mm and β dimensionless, giving θ in rad. (The factor 1000 converts mm to µm.) 6. Repeat at field positions of 0, 0.5, 0.7, 0.9 and, if the sensor allows, 1.0 of the field radius, in at least two orthogonal directions. 7. Report θ_max with the field position at which it occurs. 8. Cross-check with the magnification method: measure β at WD_nom and at WD_nom ± 1 mm (Section 8.3). For an ideal object-side telecentric lens β is constant. The residual gives:

Δβ/β ≈ (Δz / WD) × ... [measured directly]        (8.9b)

Report the measured Δβ/β per mm of WD as the "magnification stability" figure. It is more directly useful to an integrator than an angle, because it converts straight into a measurement error.

8.9.5 Calculation.

• Equation 8.9a.
• Measurement error from telecentricity, the number to put in a specification review:

Δx = h × tan(θ)        [T]        (8.9c)

where h is the height of the feature above (or below) the nominal measurement plane. A θ of 0.1° (1.75 mrad) with a 1 mm step height gives Δx = 1.75 µm. - System telecentricity including illumination: repeat step 4 with the target moved in z and with the illumination not moved. The difference between the two results is the illumination's contribution, which can dominate. A non-telecentric illuminator with a 45° incidence angle gives an apparent chief-ray angle of 45° for the shadow, and the resulting measurement error is enormous for a feature with height. This is why oblique illumination plus a step-height feature is the classic source of an inexplicable measurement error.

8.9.6 Result recording. Field positions tested; the target used and its feature size; θ at each position, with θ_max and its location; du/dz; Δβ/β per mm WD; whether the illumination was telecentric and whether it was moved with the target; temperature.

8.9.7 Common errors.

8.9.8 Engineering interpretation. Telecentricity is purchased for exactly one purpose: to make the measurement independent of where the feature is in depth. State it as a measurement error (equation 8.9c) over the application's height range, not as an angle, in any specification review. The decision threshold used in this document is that the lateral error from telecentricity over the full working height range must be ≤1/10 of the measurement tolerance. Section 10.3 applies this to the question of when a telecentric lens is necessary at all.

8.10 Numerical Aperture and Aperture Setting

8.10.1 Definition. Numerical aperture is NA = n·sin θ, where θ is the half-angle of the cone of light accepted (or emitted) by the system. For machine vision work in air, n = 1.

Relations between the two sides, with the Abbe sine condition:

NA_obj / NA_img = β        [T]        (8.10a)

and, expressed through the effective f-number on the image side N_eff = F# × (1 + β):

NA_obj = β / (2 × F# × (1 + β))        [T]        (8.10b)
NA_img = 1 / (2 × F# × (1 + β))        [T]        (8.10c)

For β << 1, NA_obj ≈ β / (2 F#); for β >> 1, NA_obj ≈ 1 / (2 F#). The vanishing NA at low magnification is the reason a 0.1× lens has very poor light-gathering power at the object and a very small angular acceptance — and part of the reason why low-magnification lenses are more sensitive to illumination geometry.

8.10.2 Test equipment. E4, E6, E11, E14; optionally a shear plate or a beam profiler for a direct measurement.

8.10.3 Test setup. Use the MTF configuration of Section 8.4.

8.10.4 Test procedure.

1. Measure the MTF curve per Section 8.4, with the frequency axis extending well beyond the expected cutoff. The frequency axis must be trustworthy to the cutoff: state the pixel pitch and the magnification, and note that above the sensor's Nyquist the measured SFR is an aliased, unreliable quantity. The diffraction cutoff cannot be measured reliably with a sensor whose Nyquist is below the cutoff. Check this first: if f_cut,img > f_Nyq, the aperture is not determinable from the SFR, and route 3 below must not be used.
2. Route 1 — from the f-number marking. Set the aperture to a marked value and use F# directly in equation 8.10b. Uncertainty dominated by the accuracy of the marking; verify once against route 2.
3. Route 2 — exit-pupil measurement. Image the exit pupil by placing a ground-glass screen or a diffuser at the image-plane region and measuring the diameter of the illuminated cone with a travelling microscope, or measure the entrance pupil diameter from the object side against a distant, uniform source. NA_img = D_pupil / (2 × distance to the pupil). Requires optical access; suitable for large-format lenses.
4. Route 3 — from the diffraction cutoff (only if f_cut < f_Nyq): find the frequency at which the MTF falls to 0.02–0.05 and take that as f_cut. Then NA_side = f_cut × λ / 2 with λ in mm and f_cut in lp/mm.
5. Consistency check: compute f_cut = 2 NA / λ for the aperture in use and compare with the highest frequency at which the measured MTF is still above 0.05. They should agree within about 20 %. A measured MTF that falls to zero well before the diffraction cutoff indicates a wavefront error or a focus problem, not a smaller aperture.
6. Repeat at each marked aperture stop and record the resulting NA. Verify that the DOF measured per Section 8.8 scales with F#; if it does not, the aperture markings or the pupil ratio are not as assumed.

8.10.5 Calculation. Equations 8.10a–8.10c; the diffraction cutoff f_cut = 2 NA / λ; the diffraction-limited two-point resolution d = 0.61 λ / NA (Rayleigh) and the Sparrow criterion d ≈ 0.5 λ / NA as the more optimistic bound. State which criterion is used when quoting a resolution limit.

8.10.6 Result recording. Aperture setting as marked; NA_img and NA_obj; f_cut,obj; λ used; the method (1, 2 or 3) and its uncertainty; the comparison of the measured high-frequency MTF with the predicted cutoff.

8.10.7 Common errors.

8.10.8 Engineering interpretation. The aperture is the system's central trade-off and it is one-dimensional: opening it improves resolution and light-gathering and shrinks DOF, in a way that is fully predicted by equations 8.4a and 8.8a. For a measurement system, choose the aperture from the DOF requirement first, then check that the diffraction-limited resolution at that aperture still leaves a factor of 2–3 of headroom at the working frequency. If it does not, the design is not feasible with that lens and magnification, and the response is to reduce β, increase the sensor pitch, or change to a lens with a larger NA at the same magnification.

8.11 Parfocality — Motorized Zoom Lenses

8.11.1 Definition. Parfocality is the property that the object stays in focus at the same working distance as the magnification is changed. The measurable quantity is the parfocality error: the object-space axial shift required to restore best focus after a change of zoom position, at a fixed mechanical setting.

8.11.2 Test equipment. E1, E2 (z-stage, resolution ≤1 µm), E6 or E4, E11, E13, E14, plus control of the zoom and focus motors.

8.11.3 Test setup. Mount a slanted-edge or fine-detail target at the nominal WD at the centre of the field. Fixed illumination and camera settings throughout. Record the zoom and focus motor positions with their full resolution (encoder counts), and record the settling time used after each command.

8.11.4 Test procedure — the standard parfocality adjustment and verification sequence.

This sequence is the correct order of operations, and each step exists for a physical reason given in 8.11.5.

1. Record the nominal WD, referenced to the lens datum.
2. Maximum zoom: set the working distance. Move the zoom to the maximum magnification position. Adjust the mechanical working distance (the z-stage, i.e. the object position) until the focus metric is maximal. Record z_ref. This step is done first because the DOF is smallest at maximum zoom (equation 8.8a), so the focus position can be determined most precisely here.
3. Minimum zoom: adjust the focus. Move the zoom to the minimum magnification position without changing the z-stage. The image will go out of focus by an amount equal to the parfocality error. Now adjust the focus control (which moves the image plane, not the object) until the focus metric is again maximal. Record the focus-motor position change.
4. Return to maximum zoom and verify. Move the zoom back to maximum. If the lens is now out of focus, the two adjustments are coupled: split the residual between the WD and the focus setting and iterate steps 2–4 until the residual at both extremes is within the acceptance criterion. Two or three iterations are normally sufficient.
5. Full zoom verification. Sweep the zoom across its entire range in a stated number of steps (at least 11, including both extremes and the presets used in production). At each position, record: the focus metric without touching anything, then the z-shift required to restore best focus. Plot the parfocality error against the zoom position. Report the maximum absolute value and the shape of the curve.
6. Repeatability test. Cycle between the maximum and minimum zoom positions 10 times, returning to a stated preset each time, and record the residual focus error at the preset after each cycle. Report the standard deviation and the range. This separates a repeatability problem (the mechanism does not return to the same place) from a parfocality problem (the lens is not parfocal by design).
7. Directional test. Repeat step 6 approaching the preset from below and from above. The difference between the two means is the mechanical backlash (Section 8.12).
8. Thermal repeatability. Repeat step 6 after a 30 min soak, and again after 2 h of continuous operation, to quantify thermal drift, which in a production environment is often larger than the mechanical repeatability.

8.11.5 Why the sequence is ordered this way. The object-side conjugate (what the lens focuses on) and the image-side conjugate (where the sensor sits) are both free, but a zoom lens couples them through the cam. Adjusting the "focus" of a machine vision zoom lens moves the image-side conjugate (a back-focus adjustment), which changes the effective object distance by 1/β² of the mechanical movement. Consequently:

• At maximum magnification, the image-side movement needed to correct an object-side error is smallest, and the DOF is smallest — so the focus determination is sharpest and the object position is set correctly.
• At minimum magnification, an object-side error is compressed by β² and is therefore hard to see — which is precisely why a lens that looks sharp at low magnification can be badly out of focus at high magnification, and why "I focused it at low magnification and it went soft when I zoomed in" is the most common parfocality complaint.

The rule that follows: set the working distance at maximum magnification, and use the focus control only for the parfocal trim.

8.11.6 Calculation.

• Parfocality error per zoom position: Δz(z) = z_best(z) − z_ref, in mm of object-space defocus.
• Convert to image-space defocus: Δz_img ≈ Δz_obj × β².
• Acceptance criterion: Δz(z) must remain within the DOF at the lowest magnification in the production range. Since DOF ∝ 1/β², the DOF at minimum magnification is the largest in the range, which is what makes this criterion achievable. A practical internal target is Δz ≤ ½ × DOF(β_min). Where the application's focus metric is stricter than the geometric DOF, use the measured through-focus curve at β_min to set the boundary rather than the formula.
• Report the parfocality error both in mm and as a percentage of the DOF at the relevant zoom position, because the latter is what determines whether the application is affected.

8.11.7 Result recording. Zoom motor position (counts) and the corresponding magnification for each test point; z_ref; focus-motor position at each step; parfocality error per zoom position; the maximum; the repeatability (s and range, n = 10); the approach direction; the settling time; the soak time and the temperature at the start and end; the lens serial number.

8.11.8 Common errors.

8.11.9 Engineering interpretation. For a motorized zoom lens used with multiple part sizes, parfocality is the parameter that determines whether the system can change magnification without a refocus step, and therefore whether the cycle time claim is real. Two facts should be established before a zoom lens is specified for a measurement task: (i) the parfocality error over the production zoom range, expressed as a fraction of the DOF; and (ii) whether the system re-verifies focus (for example by a contrast search) after each zoom change, which relaxes the parfocality requirement at the cost of cycle time. Section 12.3 of the troubleshooting guide deals with the case where parfocality error and focus repeatability are both suspected.

8.12 Zoom Repeatability and Backlash

8.12.1 Definition. Three distinct quantities are often merged; they must be separated because they have different causes and different remedies:

8.12.2 Test equipment. E1, E2, E4 (a scale within the field), E11, E13, E14, plus the lens's own control interface.

8.12.3 Test setup. Place a calibrated scale or a high-contrast edge pair in the field at the production WD. Establish the magnification measurement per Section 8.3.

8.12.4 Test procedure.

1. Choose three presets: the minimum, a mid-range and the maximum zoom position. These should be the presets used in production if they differ.
2. Repeatability. For each preset, command the lens to the position, wait for the settling time, then measure the magnification (or the pixel position of a fixed edge, which is faster and equally valid for a relative measure). Return to a common "home" position between repeats. Repeat 10 times.
3. Report: the standard deviation and the range of the measured magnification in ppm, and the standard deviation of the measured position in encoder counts.
4. Backlash. Approach the preset five times from below (from a lower magnification) and five times from above. Compute the mean magnification for each group. Backlash = |mean_above − mean_below|, expressed in ppm of magnification or in µm of object-space displacement.
5. Settling time. Command a large zoom change (minimum to maximum) and capture the focus metric or the edge position every 20 ms. Define the settling time as the interval from the "in position" signal until the measured quantity stays within ±10 % of its final value. Report it — it belongs in the cycle-time calculation.
6. Thermal drift. Repeat step 2 after 2 h of continuous operation and compare the mean values. Drift appears as a slow change of the mean, which is distinguishable from repeatability (a spread around a stable mean). Report the drift separately; do not include it in the repeatability figure.
7. [POMEAS LAB TEST DATA REQUIRED — REP-04] Repeatability, backlash, settling time and 2 h thermal drift for each POMEAS motorized zoom model, at three presets, with the control interface identified (which protocol, which controller, which microstep setting). This is a directly usable specification for AOI integrators, who currently have to characterise it themselves.

8.12.5 Calculation.

• Optical repeatability in object-space terms: σ_obj = σ_β/β × (feature distance on the object). Converting ppm into µm makes the number meaningful to the customer.
• The magnification sensitivity to the zoom position, dβ/dz_zoom, is needed to convert position repeatability into optical repeatability. Measure it by fitting β against the encoder count over the range.
• Backlash converted to a magnification error gives the worst-case error if the production sequence approaches presets from varying directions — a frequent, avoidable cause of intermittent measurement errors.

8.12.6 Result recording. Presets and their encoder counts; the approach direction; number of repeats; σ and range for position and for magnification; backlash; settling time; drift; the control protocol and settings; the ambient temperature profile; the lens serial number.

8.12.7 Common errors.

8.12.8 Engineering interpretation. For a multi-part-size station, the relevant specification is the optical repeatability in µm at the object, because that maps directly onto the measurement error. If the magnification sensitivity dβ/dz_zoom is high, a modest mechanical repeatability still produces an unacceptable optical spread — in which case either the mechanism must be improved or the production sequence must include a calibration check. Where backlash exceeds the tolerance, a simple and effective remedy is to make the production program always approach each preset from the same direction; this converts a specification problem into a software rule and should be documented as such.

8.13 Focus Repeatability

8.13.1 Definition. The spread of the achieved focus state when the same focus command is repeated. Reported either as an object-space defocus spread (µm) or, more usefully, as the spread of the resulting focus metric (MTF50 or the measured feature contrast).

8.13.2 Test equipment. As Section 8.12, with a slanted-edge target.

8.13.3 Test procedure.

1. Defocus deliberately by a fixed amount (for example 5× the DOF), then command the focus back to the preset. Repeat 10 times.
2. At each repetition, measure the resulting MTF50 (or the focus metric) and the object-space focus position from the through-focus curve established in Section 8.2.
3. Report the spread of both. Where the lens has autofocus, additionally report the spread of the resulting metric, because an autofocus algorithm can converge repeatably to a systematically wrong position — a repeatable bias, not a spread. Verify the absence of a bias by comparing the autofocus result with a manual best focus.
4. Repeat after a zoom change (does the focus repeatability degrade?) and after a thermal soak.

8.13.4 Result recording. The metric spread, the position spread, the number of repeats, the deliberate defocus applied, the approach direction, whether autofocus was used and its settings.

8.13.5 Common errors. Insufficient deliberate defocus (a small defocus produces a deceptively good repeatability because the metric is insensitive near the peak — the through-focus curve is flat at the top, so a large position spread produces a small metric spread); autofocus bias mistaken for good performance; not re-verifying after a zoom change.

8.13.6 Engineering interpretation. A focus mechanism can be repeatable in position and still produce a variable image, if the magnification sensitivity couples the focus position into the measurement. Report the metric spread, because that is what the inspection algorithm experiences.

8.14 Sensor Compatibility and Image Circle

8.14.1 Definition. A lens is compatible with a sensor when (i) the image circle covers the sensor's active area with adequate performance to the corners, and (ii) the mechanical interface does not interfere with the optical path before the sensor.

Two separate criteria, both required:

IC ≥ d_sensor × k        [T]        (8.14a)

where IC is the image circle diameter, d_sensor the active sensor diagonal (2 × √(H² + W²) with H, W the half-dimensions), and k a margin factor ≥1.0, recommended ≥1.05.

E_corner = irradiance at the corner / irradiance at the centre × 100 %        [M]        (8.14b)
MTF50_corner / MTF50_centre ≥ a stated fraction        [M]        (8.14c)

Equation 8.14a alone is not sufficient: a lens can formally cover the format while the corner MTF is unusable, which is the usual reason a "2/3-inch compatible" lens disappoints on a real 2/3-inch camera.

8.14.2 Test equipment. E1, E10 (integrating sphere or opal diffuser flat-field source), E6, E11, E14.

8.14.3 Test setup. For relative illumination: place a uniform source so that it fills the entrance pupil of the lens (for most lenses, the source placed close to the front of the lens is the correct choice, because filling the pupil is what reproduces the illumination geometry of a real object at infinity or at the working distance — the choice must be stated, because it changes the result).

8.14.4 Test procedure.

1. Set the exposure so that the centre is at 50 % of saturation. Confirm that no pixel anywhere in the frame is above 80 %.
2. Capture a flat field. Average at least 16 frames.
3. Compute the mean grey value in a small window at the centre and in identical windows at the four corners and at four edge midpoints, each window placed at least 20 px inside the active area (to avoid boundary effects).
4. Compute E per equation 8.14b. The lens's own contribution is the measured value minus any contribution from the source and from the camera's microlens shading and any camera-side shading correction. Disable camera-side shading correction for this test, or the result will be artificially flat.
5. Measure MTF50 at the centre and at the corners per Section 8.4 and compute the ratio (8.14c).
6. Check for mechanical vignetting: examine the corner region for a straight-edged shadow, which indicates an adapter, a filter or the barrel intruding. A smoothly varying falloff is optical; a sharp-edged cut is mechanical.
7. If the sensor is larger than the lens's specified format, expect a hard circular boundary; measure its diameter directly on the flat field. This is a direct measurement of the usable image circle and is more trustworthy than a datasheet figure.

8.14.5 Result recording. Sensor model and active dimensions; lens model and specified format; the source type and its placement; E at the four corners and four edge points; the corner/centre MTF50 ratio; the measured usable image circle; whether camera shading correction was disabled; the adapters and filters used.

8.14.6 Common errors.

8.14.7 Engineering interpretation. Sensor compatibility is a system decision that links three specifications that are usually quoted separately: the lens's image circle, the sensor's active diagonal, and the required corner performance. The practical rule for a vision system is to require the corner MTF50 to be at least 60 % of the centre value, because the part may be inspected anywhere in the field, and to check the relative illumination against the exposure budget. Where the corner performance is marginal, the response is usually to accept a slightly larger image circle than strictly necessary, which is a low-cost margin.

8.15 Illumination Conditions

8.15.1 Definition. This section is a test condition rather than a lens parameter, but it is treated here because in practice the illumination determines the measured resolution, the measured DOF and the measured telecentricity of the system, and because a test report that does not record the illumination is not reproducible.

8.15.2 What must be recorded.

8.15.3 Test procedures.

1. Uniformity. With the production illumination and no target, image a uniform white reference at the target plane. Compute the mean grey value over a 5 × 5 grid of windows. Report max/min and the standard deviation as a percentage of the mean.
2. Stability. Capture the same flat field every 60 s for 30 min and plot the mean grey value. Separate the warm-up drift (the first 10–30 min) from the steady-state noise.
3. Telecentric illumination test — the system test that predicts real measurement error. This is the same procedure as Section 8.9.4, but with the production illumination in place and not moved while the target is translated in z. Report the resulting apparent chief-ray angle, or, more usefully, the measured lateral shift per mm of z. This single number is the best available predictor of the measurement error caused by a feature that stands proud of the reference plane. In a system with oblique illumination and a 10° incidence angle, the apparent perspective shift can be an order of magnitude larger than the lens's own telecentricity error, which is why a telecentric lens with a non-telecentric light frequently disappoints.
4. Reflection and contrast check. Using the production illumination, measure the grey-level contrast of the actual feature on the actual part. A feature contrast below about 20 % of full scale has a degraded edge position uncertainty and will not reproduce the resolution measured on a chrome-on-glass target.

8.15.4 Common errors. Recording "LED ring light" without the angle and the distance; measuring resolution on a backlit chrome target and then applying the figure to a front-lit production scene, where the effective resolution is much lower; a non-telecentric illuminator combined with a step-height feature; a strobed source whose pulse is not synchronised to the exposure, producing frame-to-frame intensity variation that appears as noise; illumination drift during a long measurement series.

8.15.5 Engineering interpretation. The single most consequential rule in this document is: a performance figure measured under one illumination condition is not transferable to another. Resolution, DOF, contrast and effective telecentricity all depend on the illumination geometry. Any POMEAS technical figure that is published should therefore carry its illumination condition explicitly — this is what makes a figure citable by a third party, and it is also what makes it defensible.

8.16 Calibration

8.16.1 Purpose. Calibration is what converts a contrast image into a measurement. This section defines the minimum calibration content of a machine vision optical measuring system, and the evidence that must be retained. It is the section that a quality auditor will ask for.

8.16.2 Required reference standards.

The requirement for a separate verification artefact is the point that is most often missed. A system calibrated with artefact A and then verified with artefact A only proves that the fitting routine is self-consistent.

8.16.3 Calibration content.

1. Scale factor (mm per pixel) at the field centre and at ≥4 field positions, with the polynomial or map describing its field dependence.
2. Distortion map (Section 8.7) with the validation residual on held-out nodes.
3. Z-dependence check: the change in the measured scale factor over the working height range, which is the operational telecentricity of the system (Section 8.15.3).
4. Focus reference: the z-position and the focus-motor position corresponding to best focus, recorded so that drift can be detected.
5. Calibration record: date, operator, ambient temperature, certificate numbers and due dates of every reference, software version, camera settings (gain, exposure, black level, and confirmation that sharpening is off), lens serial number, magnification and aperture setting, and the illumination condition.

8.16.4 Recalibration triggers.

8.16.5 Verification. Measure the verification artefact at ≥5 field positions, at the production magnification, at the production working distance. Compare with the certificate. The acceptance criterion for the system is derived from the application tolerance using the decision rules of Section 13.4. Record the result whether it passes or fails.

8.16.6 Common errors.

8.16.7 Engineering interpretation. Calibration is cheap and its residual is measurable; lens distortion is fixed and its effect is not. This is the strongest argument for calibrating a moderately distorted lens rather than purchasing an extremely low-distortion one — provided that the calibration is validated on a held-out artefact. The exception, stated again: a system whose lens may be swapped without recalibration must rely on intrinsic lens quality, not on calibration.

9. Calculation methods — consolidated reference

All equations from Section 8 in one table, for use in a spreadsheet or in a measurement program. The bracket after each ID states whether the result is [T] theoretical (calculated from geometry and component data) or [M] measured.

Rules 9.26–9.28 are industry rules of thumb, not physical laws. They are stated as rules so that they can be replaced by an application-specific number when the application justifies it. Every use of a rule of thumb should be recorded as such in a specification review.

10. Acceptance criteria and engineering interpretation

10.1 Accepting a lens against a specification

A measured value that is close to a specification limit cannot be decided by simple comparison. The decision rules of ISO 14253-1:2017 apply:

where U is the expanded uncertainty of the measurement (Section 13). The practical consequences:

• A supplier must prove conformance using the supplier's own uncertainty, and a customer must prove non-conformance using the customer's own uncertainty. The uncertainty therefore always works against the party making the claim.
• The third row is not a failure of the lens; it is a failure of the specification, and it should be resolved by widening the tolerance, by reducing the measurement uncertainty, or by agreeing in advance on a documented decision rule. It should never be resolved by quietly reporting the mean and ignoring U.
• A specification that is not accompanied by a stated uncertainty is not a specification.

10.2 Parameter-by-parameter acceptance criteria used in this document

10.3 When is an object-side telecentric lens the correct choice?

This is the decision that most often determines whether a machine vision measurement project succeeds, and it is not a question about marketing categories. It is decided by three numbers: the height variation Δz of the feature, the chief-ray angle θ of the candidate lens over the field, and the tolerance T.

Step 1 — Is the measurement plane fixed?

If every measured feature lies in a single plane that is mechanically reproducible to much better than the tolerance, and the part is presented against a hard stop, then a standard FA or zoom lens is sufficient, and a telecentric lens adds cost without adding accuracy. This covers a large fraction of real inspection tasks: presence/absence, counting, OCR and barcode reading, colour checks, print quality, and defect detection on a nominally flat surface. Distortion is irrelevant in all of these (Section 8.7.8).

Step 2 — If the plane varies, quantify the perspective error.

For a non-telecentric lens, the apparent lateral shift caused by a feature standing h above the measurement plane is:

Δx = h × tan θ

with θ the chief-ray angle of the lens at the field position of the feature. For a typical C-mount FA lens, the chief-ray angle at the field edge is not small. Consider a lens whose entrance pupil is 40 mm in front of the object plane, imaging a field of 17.6 × 13.2 mm (a 2/3" sensor at β = 0.5). At the field edge, 11 mm from the axis, θ ≈ arctan(11/40) ≈ 15°.

Decision rule. If h × tan θ > T/10, a standard lens cannot support the measurement and an object-side telecentric lens is required (or the height variation must be removed mechanically, which is often the cheaper answer). Note how quickly the rule bites: with a typical tolerance of ±50 µm, a part tolerance band of 100 µm, and a 0.5 mm height variation, the allowable error is 10 µm — and even a good long-ratio FA lens at the field edge exceeds it. This is the honest reason telecentric lenses exist, and it is stated here as a calculation rather than as a preference.

Step 3 — Check the cases where a telecentric lens is required for a reason other than height.

Step 4 — Check the cases where a telecentric lens is the wrong answer.

Step 5 — Do not confuse the lens and the illumination. The measured system connects the lens and the light. Section 8.15.3 gives the test that measures the combination, and it should be performed before a telecentric lens is rejected as "not helping".

10.4 Selecting between a fixed telecentric lens, a fixed FA lens and a motorized zoom lens

10.5 What a specification should contain

A machine vision optical specification that can be accepted or rejected without argument contains, for each parameter: the value, the test method (a reference to this document or an equivalent), the test conditions (WD, zoom position, aperture, illumination, sensor, magnification, temperature), the criterion (for DOF and resolution, always), and the uncertainty U. A specification missing any of these five is an invitation to a dispute. Section 11 is a report template that enforces all five.

11. Test report template

Reproduce this template for each unit tested. Fields marked ● are mandatory for the report to be usable by a third party.

11.1 Identification

11.2 Test conditions

11.3 Results

11.4 Attachments

• Through-focus curves for each magnification (metric versus z).
• MTF curves at the centre and at the worst field point.
• Distortion map (contour of D over the field), before and after correction.
• Flat-field image and the relative-illumination profile.
• Photograph of the test setup, showing the datum used for WD.
• Statement of conformity per Section 10.1, including the decision rule applied.

12. Common measurement errors — cross-cutting troubleshooting

The per-parameter error tables in Section 8 deal with measuring the lens. This section deals with the harder problem: the image or the measurement is wrong in the application, and there are several plausible causes. Each row gives the discriminating test, so that the cause can be isolated rather than guessed.

12.1 The headline case: focus is lost after changing magnification

"The image is sharp at low magnification, but after zooming in it is out of focus."

This is the most frequently reported motorized zoom problem. It has at least eight distinct causes, with different remedies — replacing the lens is the correct answer in only one of them.

Because causes 1 and 2 produce the same complaint and take five minutes versus several hours to distinguish, run tests 1 and 2 first, always.

12.2 Distinguishing systematic from random errors

12.3 Other high-frequency application errors

12.4 A note on retrying

None of the failures in this section are cured by repeating the same measurement. A value that fails to reproduce is evidence of a condition that has not been recorded. The correct response is to identify the unrecorded condition — WD, temperature, illumination, zoom approach direction, focus state — and to add it to the report template rather than to average it away.

13. Measurement uncertainty

13.1 Purpose

A measurement result is a complete statement only with its uncertainty. This section gives the structure of an uncertainty budget for the parameters of this document, following ISO/IEC Guide 98-3 (GUM). The values in the worked example are illustrative magnitudes for a typical machine vision measurement station, not POMEAS specifications, and must be replaced with measured values for a specific system.

13.2 Uncertainty budget — worked example

Measurand: the width of a 5.000 mm feature at a field position 30 mm from the axis, measured with a telecentric system at β = 1.0 on a 3.45 µm sensor, with a chrome-on-glass calibration artefact.

Reading of the result: the largest single contributions are the artefact certificate (1.00 µm) and the residual distortion (0.69 µm). Improving the measurement equipment would therefore produce little benefit; improving the reference artefact and validating the distortion correction would produce most of it. This is the normal conclusion of an uncertainty budget, and it is the reason the budget is worth producing.

13.3 Rules for using a budget

• Type A contributions are evaluated from repeated observations (standard deviation of the mean, s/√n). Type B contributions are evaluated from certificates, datasheets, experience or judgement.
• Correlated contributions must not be added in quadrature as if independent. A single artefact certificate contributes correlated uncertainty to both the scale factor and the distortion map; in that case the correlation must be handled explicitly, or the two contributions combined before use.
• A budget that accounts for less than 90 % of the observed spread is incomplete. Test this by comparing the predicted u_c with the observed standard deviation of a real measurement series. If the observed spread is substantially larger, there is an unmodelled contribution — normally thermal drift, illumination variation, or mechanical repeatability.
• Report u_c, U, k and the coverage probability, and name the dominant contribution. A budget whose conclusion is "everything matters equally" has usually not been thought through.

13.4 Applying the uncertainty to a decision

Combine the budget with the decision rules of Section 10.1. For the example above, with T = 100 µm and U = 2.8 µm: the guard band is 2.8 µm (2.8 % of T), so the practical acceptance limit is ±47.2 µm instead of ±50 µm. Where the process capability index Cpk is already marginal, this 5.6 % reduction is significant and should be part of the acceptance-rules discussion between the supplier and the customer, agreed in advance.

14. References

References marked ✔ have been verified against the issuing body's catalogue at the release date of this document. References marked △ are cited in the machine vision community but were not verified here and must be checked before being used in a contractual context.

14.1 Standards ✔

1. ISO 12233:2024 — Digital cameras — Resolution and spatial frequency responses, Edition 5, published 2024-09, ISO/TC 42. Slanted-edge (e-SFR) and sine-wave (s-SFR) methods, test charts and reporting.
2. ISO 9335:2025 — Optics and photonics — Optical transfer function — Principles and procedures of measurement, Edition 3, published 2025-02, ISO/TC 172/SC 1. Supersedes ISO 9335:2012.
3. ISO 9334:2012 — Optics and photonics — Optical transfer function — Definitions and mathematical relationships.
4. ISO 9039:2008 — Optics and photonics — Quality evaluation of optical systems — Determination of distortion, Edition 2, published 2008-02, ISO/TC 172/SC 1.
5. ISO 1:2022 — Geometrical product specifications (GPS) — Standard reference temperature for the specification of geometrical and dimensional properties, Edition 4, published 2022-06-14, ISO/TC 213. Standard reference temperature 20 °C (ITS-90).
6. ISO/IEC Guide 98-3 — Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in measurement (GUM).
7. ISO/IEC Guide 99 — International vocabulary of metrology — Basic and general concepts and associated terms (VIM).
8. ISO 14253-1:2017 — Geometrical product specifications (GPS) — Inspection by measurement of workpieces and measuring equipment — Part 1: Decision rules for verifying conformity or nonconformity with specifications, Edition 3, published 2017-10, ISO/TC 213.
9. ISO 5725-1 / ISO 5725-2 — Accuracy (trueness and precision) of measurement methods and results.
10. ISO 9022 (series) — Optics and photonics — Environmental test methods. Not applied in this document; referenced as the source of environmental test methods where a lens must be qualified for an environment.
11. EMVA 1288 — Standard for Characterization of Image Sensors and Cameras, Release 4.0 (modules Linear and General), effective June 2021, hosted by the European Machine Vision Association. An industry standard, part of the G3 initiative with A3, CMVU, JIIA and VDMA. It is not an ISO or IEC standard and must not be cited as one.

14.2 Technical references △

12. Test chart software and slanted-edge/Siemens-star chart resources referenced in the informative annexes of ISO 12233, published by the standards imaging community (imaging.org).
13. CIPA test charts, referenced informatively in ISO 12233.
14. Brown, D. C. (1966) — Decentering distortion of lenses; and Conrady, A. E. — the origin of the radial-plus-tangential distortion model quoted in Section 8.7.1 as the Brown–Conrady form.
15. Manufacturer application notes on depth of field and image-space telecentricity, from major machine vision lens suppliers. These are useful cross-checks but are not standards and should not be cited as such.

14.3 POMEAS documents in this series

15. Frequently asked engineering questions

This section answers the questions that arrive most often from integrators, system builders and inspection engineers — and that AI answer systems most often need to extract. Each answer is written to stand alone: the answer comes first, the method behind it is referenced in brackets. Where an answer depends on a POMEAS-specific measured value that is not yet published, the item is marked [POMEAS LAB TEST DATA REQUIRED] and is listed in Appendix B.

15.1 How do you test telecentric lens distortion?

Image a certified grid or dot target filling the whole field at the lens's specified working distance, then compute the local magnification from neighbouring nodes around each point — not from a single global fit — and form D = (β_local − β_reference)/β_reference at every node. Report D_max over the field, the sign convention, the target certification and the WD. A global polynomial fit hides the local residual that actually limits a measurement, which is why the local-neighbour method is specified here (Section 8.7). Two facts are worth stating plainly: a telecentric lens is not automatically distortion-free — it removes perspective error, which is a different error — and a distortion figure without the reference magnification and the field radius is not a specification.

15.2 How is machine vision lens resolution measured?

By imaging a slanted edge of 2°–7° and computing the edge spatial frequency response (e-SFR) per ISO 12233, then reporting MTF50 — the spatial frequency at which the modulation transfer function falls to 50 % — with the units, the field position and the test conditions stated. Report it at the image plane in lp/mm and, for the application, at the object plane as f50,object = f50,image × β. A single MTF50 number is not a lens specification: the same lens gives different values at the centre, at 0.7 field and at the corners, and at different apertures. Report centre plus four 0.7-field positions plus corners (Sections 8.4, 8.5).

15.3 How do you test zoom lens parfocality?

In a fixed order that matters: set maximum zoom and adjust the working distance there (because that is where the depth of field is narrowest and the WD error is largest), then go to minimum zoom and trim focus only, then verify across the full range by stepping through every preset and recording the defocus Δz needed to restore best focus (Section 8.11.4). Express the parfocality error in fractions of the DOF at that zoom position, not in millimetres alone — 0.3 mm is negligible at 0.7× and disqualifying at 6×. Report the result as a curve over zoom position, plus the residual after the standard adjustment (Section 8.11).

15.4 What is the difference between optical resolution, pixel resolution and system resolution?

Optical resolution is what the lens transfers, expressed as an MTF curve. Pixel resolution is what the sensor samples, expressed as the pixel pitch and the Nyquist limit. System resolution is the product of the lens MTF and the sensor MTF, evaluated on the same axis (Section 9.15), and it is always worse than either element alone. The practical consequence: the weaker element dominates. If f50,sensor is far above f50,lens, adding pixels changes nothing that matters; if the lens is far better than the sensor, the lens is not your limit (Section 8.5).

15.5 Why does the measured field of view not match the datasheet?

Four causes, in order of frequency. (1) The datasheet used the total pixel count while the image uses the active count — read the number that the camera actually transmits. (2) The measurement was taken at a different working distance from the one specified, and the FOV of a non-telecentric lens depends on WD. (3) The measurement was taken to the frame edge, which is not at the specified image height. (4) The camera's sensor is not the size the datasheet number assumed. Measure FOV from two certified graduations inside the frame and derive the scale factor from the certified distance; do not measure from the frame edge (Section 8.1.7).

15.6 How should depth of field be specified for a machine vision lens?

Only together with two things: an acceptance criterion — an image-side blur circle c, or a threshold on a measured metric such as MTF50 — and the illumination geometry, because a backlit silhouette and a dark-field illumination have very different usable depth. The standard method is a through-focus sweep: translate the target in z in small steps, record the metric at each step, and take DOF as the distance between the two crossings of the acceptance threshold (Section 8.8). DOF is a property of the system and the criterion, not of the lens. A DOF figure quoted without its criterion is not comparable with any other DOF figure.

15.7 How do you measure telecentricity, and what value is good enough?

Measure it by the centroid-shift method: place an isolated certified feature (a chrome dot on a clear substrate), focus it, then translate it in z through the working range and record the lateral shift of the image centroid at each step. The slope of a straight-line fit to centroid-versus-z gives the chief-ray angle θ by θ = arctan(Δy/Δz) (Section 8.9). Then answer "good enough" from the tolerance, not from the datasheet: the lateral error caused by the expected height variation must be a small fraction — a tenth is the usual working rule — of the measurement tolerance. A lens with θ = 0.1° on a part with ±0.5 mm height variation contributes 0.87 µm, which is negligible against a 100 µm tolerance and disqualifying against a 5 µm tolerance. Measure the system telecentricity including illumination wherever the illumination is coaxial, since the illumination can add as much lateral error as the lens (Section 8.15.3).

15.8 The image is sharp at low zoom but soft after zooming. What do I check?

Work through the causes in this order, because each one is cheaper to check than the next. (1) Working distance was set at low zoom. The WD and the focus band move with the zoom position; the correct sequence is in 15.3. (2) Focus is being used to fix a WD error — the focus control cannot correct a WD error on a telecentric system, and on a motorized zoom lens it shifts the whole zoom range. (3) The parfocal adjustment has not been made, or was made in the wrong order. (4) Mechanical repeatability: the lens does not return to the same optical position for the same command — measure the position repeatability and the backlash separately, and check whether approaching a preset from high or low magnification gives a different focus (Sections 8.11, 8.12, and the ordered diagnostic table in Section 12.3). A repeatable, direction-dependent focus error is a mechanical result, not a software tuning problem.

15.9 Does a higher-resolution camera improve the resolution of my system?

Only while the sensor still limits. System MTF is the product of the lens and sensor MTFs, so if the lens already dominates the loss, a finer-pitched sensor adds data but not information — you will resolve noise and pixel-level artefacts more clearly, not the feature. The sensor also stops helping once the pixel pitch falls below the lens's diffraction limit, and it makes alignment, illumination uniformity and vibration tolerance stricter. Measure f50,lens and f50,sensor before buying a camera, and compare both against the feature size at the object plane (Sections 8.4, 8.5, 8.10, 9.15).

15.10 Do I need a telecentric lens, or is a standard FA lens enough?

Decide from the error budget, not from the product category. A telecentric lens exists to remove one specific error — the measurement change caused by a change in object height — so use one when that error would consume a meaningful share of the tolerance. The rule applied here (Section 10.3): if (height variation × N.A. or perspective angle) is more than about a tenth of the tolerance, or if edge position must be independent of focus, a telecentric lens is the right choice. If the part is flat, or if the requirement is presence/absence rather than a dimension, a standard FA or fixed-focal lens is adequate, cheaper, usually has a larger field and is easier to illuminate. A telecentric lens used where it is not required adds cost, reduces the field, shortens the WD and demands more light. This document does not argue for telecentric lenses in general; it defines how to establish which one is correct.

15.11 How do I compare two lens datasheets fairly?

You cannot compare them from the numbers alone; require the conditions. Any resolution, distortion or DOF figure is comparable only when all of the following are stated: the field position; the aperture; the working distance or magnification; the sensor size and pixel pitch used; the wavelength or the illumination spectrum; the acceptance criterion for a DOF or a resolution figure; whether the value is theoretical, datasheet-typical or measured on a specific unit; and, for a zoom lens, the zoom position. A figure missing any of these is a marketing number, whatever its precision. Section 11 is a report template that enforces all of them, and Section 15.2 states the minimum reporting set for resolution.

15.12 What measurement uncertainty should I expect from a vision measurement station?

For a well-calibrated telecentric station measuring a 5 mm feature, an expanded uncertainty (k = 2) in the range of a few micrometres is a reasonable planning assumption — the worked budget in Section 13.2 gives ≈ 2.8 µm for such a configuration, dominated by the reference artefact certificate and by the residual of the distortion correction. That number is an example, not a POMEAS specification, and it must be replaced by the budget for the actual station. Two properties of these budgets are worth knowing before you plan: the artefact and the residual distortion usually dominate, so improving the camera gains little; and the budget must be validated against the observed scatter of real measurement sequences, because a budget that explains less than about 90 % of the observed spread has missed a contribution.

15.13 Can these methods be used as an acceptance test between a supplier and a customer?

Yes, and they are written to be usable that way — but four things must be agreed before the test, not argued after it. (1) The test conditions of Sections 5 and 6. (2) The meaning of the specification limit and the decision rule, following ISO 14253-1: whether a value outside the limit by less than the uncertainty is accepted or rejected. (3) The guard band, which reduces the acceptance zone by U (Section 13.4). (4) The reporting format of Section 11, including the uncertainty. Without these, an out-of-tolerance result will be read differently by each party, and the argument will be about interpretation rather than about the lens.

15.14 Why do two machines — or two operators — give different values for the same part?

Because a vision measurement is a system result, and any unrecorded condition becomes a difference between the two setups. The most frequent causes, in the order they should be checked: a different working distance; a different illumination geometry or intensity; a different calibration artefact or an expired calibration; a different distortion correction or none; a different focus state; a different measurement algorithm, edge threshold or sub-pixel model; a different part temperature; and motion or settling differences. The remedy is the same in every case: record the condition, then compare. A value that does not reproduce is evidence of an unrecorded condition, not of a bad lens (Sections 12.1, 12.4).

15.15 What is the status of this document, and how do I cite it?

This document is a technical reference developed by POMEAS — not a national, international or industry standard, and it does not claim conformity with, or approval by, ISO, IEC, GB, DIN, ANSI, IEEE or EMVA. Where an external standard is cited, it is identified by number, title and edition, and every such reference was verified against the issuing body's catalogue at the release date (Section 14).

POMEAS, POMEAS Technical Reference TR-001: Machine Vision Optical Imaging Systems — Performance Test Methods, Version 1.0, 2026-09-16.

The document may be downloaded, stored, forwarded and cited with attribution. It may not be modified and re-published under another name, and it may not be presented as a standard (Section 17).

15.16 How do I measure field of view directly, rather than calculating it?

Put a certified chrome-on-glass scale at the working distance, identify two graduations separated by at least 60 % of the frame across both axes, and locate their positions by sub-pixel centroid. The scale factor is s = (x₂ − x₁)/(u₂ − u₁) in mm per pixel and FOV = s × N, where N is the active pixel count that the camera actually transmits. Two cautions decide whether the result is valid: using the frame edge instead of certified graduations, and using the total pixel count including dummy and optical-black pixels — either alone gives a 0.5–2 % error, which on a 100 mm field is 0.5–2 mm (Section 8.1).

15.17 Is TV distortion the same as geometric distortion?

No, and the difference matters for a measurement. TV distortion is the bowing of a nominally straight line near the edge of the field, normalised to the image height, and its datasheet convention differs between suppliers by a factor of two — a lens reported at 0.05 % by one supplier can be reported at 0.1 % by another without any optical difference. It is a shape descriptor. What governs a measurement is the relative local magnification error D(x, y) = [β(x, y) − β_centre]/β_centre, because the measurement error at a field point is approximately D/100 multiplied by the distance from the field centre. A lens with 0.1 % local magnification error contributes 0.1 % of the distance from the centre, so 30 mm off-axis becomes 30 µm of error (Sections 8.6, 8.7).

15.18 What circle of confusion should be used for depth of field?

State it explicitly, because a depth of field figure is meaningless without it, and do not inherit it from photography. For machine vision, tie it to the sensor you are using — one to two pixels of image-side blur is the usual working choice — and state whether the criterion is a blur circle or a threshold on a measured metric such as MTF50. The geometric relation is DOF = 2 · F/# · c · (1 + β)/β² with c the permitted image-side blur, which shows why DOF falls fast as magnification rises: the β² term in the denominator. A photographic criterion derived from a 36 mm full-frame format is far looser than anything a machine vision measurement will accept (Section 8.8).

15.19 How many pixels do I need across a feature?

As a working rule, at least three pixels across the smallest feature to be detected, and at least five across the smallest feature to be measured. This sets the object-side pixel size L = p/β, hence the required magnification, and therefore the field of view — which is why field of view and precision are not two decisions but one decision seen from two sides. If the required field and the required feature size cannot both be satisfied with the chosen sensor, the sensor has to change; no amount of algorithm work creates information that was not sampled (Sections 8.5, 10.2).

15.20 How should a machine vision lens be evaluated overall?

Parameter by parameter, and every number with its test conditions and its uncertainty. The minimum set used in this document: field of view and its sensitivity to working distance; magnification and its variation across the field; MTF50 at several field positions including the worst-to-centre ratio; distortion as a local magnification map, not only as TV distortion; depth of field with a stated criterion and illumination geometry; telecentricity expressed as a measurement error over the working height range rather than as an angle alone; repeatability measured optically, not read back from an encoder; and the uncertainty budget of the station. A value without its conditions cannot be compared, accepted or disputed — it can only be believed (Sections 9, 10, 11).

15.21 Is a measurement result valid when it sits close to the specification limit?

Not by simple comparison. Under the decision rules of ISO 14253-1, conformance is proven only when the measured value plus the expanded uncertainty lies inside the limit, and non-conformance only when the measured value minus the uncertainty lies outside it. In between, neither can be proven, and the outcome must be resolved by reducing the uncertainty, by widening the tolerance, or by applying a decision rule agreed in advance — the guard band of Section 13.4 does exactly this, and in the worked example it narrows a ±50 µm acceptance zone to ±47.2 µm. Agree the rule before the test, or the same result will be read two ways (Sections 10.1, 13.4).

15.22 Can I calibrate out lens distortion instead of buying a low-distortion lens?

Often yes, and it is usually the cheaper route — provided the correction is validated on a held-out set of grid nodes or on a second artefact. The reasoning is that a calibration is repeatable and its residual is measurable, whereas intrinsic lens distortion is a fixed property you cannot improve later. Two conditions apply. First, the residual must be reported with the map, not just the improvement. Second, on a system where the lens may be replaced without recalibration, the intrinsic quality is the only safe basis, because the correction belongs to the specific lens unit and the specific WD (Section 8.7).

15.23 What illumination information must be recorded in a lens test report?

Seven items: the type (bar, dome, ring, coaxial, backlight, dark-field); the drive mode and PWM frequency, since a pulsed source measured with a rolling shutter or in a different phase gives a different result; the geometry, including the working angle and the distance; the spectrum; whether the illumination is telecentric in object space; the uniformity across the field; and the short- and long-term stability. Resolution, depth of field and effective telecentricity all depend on the illumination geometry, so a performance figure measured under one illumination condition is not transferable to another — which is the single most common reason two sites measure the same lens differently (Sections 5.2, 8.15).

16. Revision history

Planned revisions. - 1.1 — Insert the measured values identified in Appendix B (POMEAS laboratory data), and publish the companion distortion and MTF datasets. - 1.2 — Add measured examples for the 16 K line-scan and large-format sensor configurations, and for the 5 µm inspection-class systems. - 2.0 — After TR-002…TR-006 are released, restructure this document as the general framework and delegate the parameter-specific detail to the later documents.

17. About POMEAS

POMEAS (Dongguan Pomeas Precision Instrument Co., Ltd.) designs and manufactures machine vision optics and optical measurement instruments, including:

• Motorized continuous zoom lenses for machine vision and automated optical inspection
• Object-side and bi-telecentric lenses for dimensional measurement
• FA / fixed focal length industrial lenses
• Line-scan and large-format lenses for high-resolution inspection
• 3D laser profile sensors and spectral confocal displacement sensors
• White light interferometers and vision measuring machines
• Automatic and motorized zoom autofocus microscopes

This document is produced by POMEAS's applications and metrology function. Its purpose is to make optical performance testable and reproducible by the customer rather than to be accepted on trust. POMEAS publishes the methods it uses so that a customer can reproduce them, disagree with them with evidence, and select a lens on measured performance rather than on a datasheet.

Contact. For technical questions about this document, about reproducing a method, or about applying these methods to a specific application: see the contact details at www.pomeas-vision.com. Please quote the document number and section when raising a question, so that the answer can be added to the revision history.

Citing this document.

POMEAS, POMEAS Technical Reference TR-001: Machine Vision Optical Imaging Systems — Performance Test Methods, Version 1.0, 2026-09-16.

Copyright and reuse. © 2026 POMEAS. This document may be downloaded, stored, forwarded and cited with attribution. It may not be modified and re-published under another name, and it may not be presented as a national, international or industry standard.

Document identity statement (repeated for clarity)

This document is a technical reference developed by POMEAS based on optical engineering principles, laboratory testing practices and machine vision application experience. It is intended to support optical system specification, testing, comparison and integration. It is not an official national, international or industry standard.

本文件为 POMEAS 基于光学工程原理、实验室测试实践及机器视觉应用经验编制的技术参考文件，用于机器视觉光学系统的选型、测试、比较和系统集成，不属于国家标准、国际标准或行业标准。

Appendix A — Original figures and test charts

Eight figures are defined for this document. They are the assets intended for reuse by third parties, for Google Images, and for extraction by AI answer systems. Each is listed with its purpose, what it must contain, its required photographic or diagrammatic form, its ALT text and its caption. Figures A1–A4 and A7 are published as vector diagrams in the web version of TR-001; figures A5, A6 and A8 require photographs from a POMEAS laboratory bench and are marked accordingly.

Appendix B — POMEAS laboratory test data register

This appendix lists every place in this document where a POMEAS-specific measured value is required and does not yet exist. Items are listed with the document section where the value belongs and the figure or table it feeds. The full experiment design, the equipment list, the photographs required and the data fields to record for each item are given in the companion deliverable TR-001 Laboratory Test Data Plan.

Publication note. Each item in this register, once measured, should be published as a table on the corresponding product page as well as in the next revision of TR-001. A measured value published with its test conditions is the asset that makes this series citable; a datasheet value without conditions is not.