Measure lens distortion without a datasheet: the two-pitch method

A lens with no distortion figure on its data sheet leaves you guessing: will a couple of percent of stretch at the frame edge break the measurement, or is it irrelevant? You do not need the datasheet to answer. One flat dot-grid target, one focused frame and two pitch measurements give the same TV distortion percentage a datasheet would have printed, with the sign that separates barrel from pincushion. This guide sets up the rig, works the arithmetic end to end on a real case, and ends with the decision: accept the lens as measured, re-aim the part toward the center, or calibrate before you gauge anything.

What you need

You need the camera and lens mounted exactly as they run: same working distance, same focus position, same f-number if the iris is locked. A distortion number belongs to those settings, and one taken at another distance does not transfer.

The target is a flat dot grid that covers the whole field of view, corners included. Dots suit this job better than line or checkerboard targets, because you locate a dot by its centroid; the soft, smeared edges a wide lens draws near the frame border then do not bias the result.

Print a grid at full scale with page scaling off and mount it on glass or a flat plate, or use a ready-made glass-mounted grid such as the LS-LXR-0029, which puts a 0.5 mm dot diameter on a 76 × 76 mm board:

Keep at least one full dot pitch between the outermost dots you measure and the target edge. If you are unsure whether a target covers a given lens and distance, work the coverage margins in calibration target field of view and lens coverage margins. Ready-made grids sit in the lens accessories range, and the accessories finder filters them by type.

You also need even, diffuse light - backlight through a translucent print is ideal - and any tool that reports the pixel coordinates of dot centroids, from a short script to the measure tool in your vision software.

The two-pitch measurement, step by step

1. Square the rig. Stand the target vertical and flat. Aim the camera so the grid's center dot sits on the frame center and the dot fields left and right of it are equally wide. A tilted target produces keystone, which masquerades as distortion.
2. Light and expose evenly. Diffuse front light or backlight, no specular hot spots. Expose so the brightest dots stay below saturation; a bloated dot pulls its own centroid.
3. Focus at the production working distance and fill the frame. Grid rows parallel to the frame edges. Stop down until the edge dots sharpen, typically F4 to F5.6 on a lens that opens to F1.8; wide open, coma and field curvature blur exactly the dots you need.
4. Capture three frames without moving anything. One frame gives the number; three frames tell you whether to believe it.
5. Measure B, the center pitch. Mark dot centroids along the horizontal centerline and average the center-to-center spacing over the four to six pairs straddling the frame center. Repeat on the vertical centerline if you also want the vertical-field figure.
6. Measure A, the edge pitch. Average the spacing of the outermost complete pairs at the left and right frame edges on the same centerline, then average left and right so a small alignment error cancels.

If the grid will not fill the frame because the lens cannot focus close enough, a larger target is the cleaner fix and a spacer the compact one: a 15 mm C/CS extension tube such as the LS-LXR-0284 pulls the close-focus limit in until the grid covers the frame. The extension tube guide covers the magnification arithmetic, and lens focuses only at close distance covers the case where focus range itself is the problem.

An extension tube makes the lens focus closer than the production distance, and distortion drifts slightly with focus distance. Treat a number measured through a tube as a first pass, and re-measure at the true working distance if the result lands near a decision band.

The formula, and which way the sign points

A is the average edge pitch in pixels and B the average center pitch, both from the same centerline. The factor 2 converts the pitch change at the frame edge into the displacement percentage datasheets summarize as TV distortion: the pitch error is zero at the center and accumulates outward, so the edge point ends up displaced by roughly half its local pitch error. The conversion assumes that error grows linearly with radius; the common single-coefficient profile grows with the square of radius and reads about a third lower. Quote the result to one decimal place and let the decision bands absorb that spread.

The sign carries information. An edge pitch larger than the center pitch means the periphery is stretched: pincushion, positive. A smaller edge pitch squeezes the periphery: barrel, negative. Datasheets often print the magnitude only, so compare magnitudes when checking a published claim. The vocabulary behind the numbers, geometric versus TV distortion and where each belongs, is laid out in geometric vs TV distortion: read lens datasheets for measurement.

Worked example: a 5 mm C-mount lens with no published figure

The case: a wide C-mount board lens, 5 mm focal length, manual focus and adjustable iris, no distortion specification published anywhere. It has to locate part features across the full frame with a position tolerance of ±0.1 mm, at a pixel scale of 20 px/mm; the object space pixel size guide shows how to get that scale from magnification. Measurements from a frame filled with a flat dot grid, taken on the horizontal centerline:

• B = 200 px, the average center pitch over six dot pairs straddling the frame center.
• A = 208 px, the average of the outermost left- and right-edge pairs.
• Three frames repeated both pitches within 1 px, and the left and right edge pitches matched, so the rig was square.

Rule in words: percentage distortion equals edge pitch minus center pitch, divided by twice the center pitch, times 100.

Arithmetic: (208 − 200) / (2 × 200) = 8 / 400 = 0.02; × 100 = 2.0%.

Result: +2.0% at the frame edge, pincushion. The edge pitch is the larger one, so the periphery is stretched.

What the number costs: the percentage is the displacement of a point at that radius relative to its distance from the image center. A feature 900 px out is displaced by 0.02 × 900 px = 18 px, with the profile spread above bracketing the true value at 12 to 18 px. At 20 px/mm that is 0.6 to 0.9 mm of error at the frame edge, six to nine times the ±0.1 mm (±2 px) tolerance.

Decision: the fractional error falls with the square of the radius, so the uncorrected error stays under ±2 px only inside roughly 400 px of the image center; at r = 400 px, 2.0% × (400 / 900)² × 400 px ≈ 1.6 px. Fixture the part into that central zone and this lens is usable as measured. Gauge across the full frame and software correction comes first. Either way the verdict is a correction decision, not a scrap decision: 2% is normal for a wide board lens, and it is the pairing with a ±0.1 mm tolerance that forces the calibration.

Decide what to do with your number

The bands pair your measured distortion with your tolerance; a lens is not good or bad on its own. Measurement-grade FA lenses publish the figure so you can make that pairing before buying: the LS-FFL-0567, for example, prints distortion below 0.3% for its 16 mm, 20 MP design, which is the class of number the top band describes.

When correction is the answer, the same dot-grid frame doubles as calibration input. Lens distortion correction for accurate pixel-to-mm measurements walks the pixel-to-mm pipeline, build a lens distortion profile for a board camera without an LCP file covers making a profile when no lens file exists, uniform pixel grid overlay for dot-target calibration turns the dot frame into the correction grid, and how to measure barrel distortion correction accuracy closes the loop by validating the result.

When the two-pitch number is not enough

Three cases need more than two pitches.

• Fisheye and other non-rectilinear lenses. The method assumes the lens is designed to keep lines straight. A fisheye bends lines by design, so a percentage distortion is not a meaningful acceptance figure; fit the projection model, as fisheye undistortion: how the pixel mapping works explains.

• Zoom and varifocal lenses. Distortion changes with every focal setting. Measure at the setting you run, and re-measure after any change; a number from one end of the zoom says little about the other.
• Gauging to a few hundredths of a millimeter. A single percentage cannot carry a tight metrology budget. Fit a full radial model from the dot frame, correct every pixel, then validate on a known dimension.

Checks before you trust the number

Run these before writing the figure into a drawing or a specification.

• Left and right edge pitches agree within a pixel or two. If they do not, the target is tilted or off-center; fix the rig, not the arithmetic.
• The vertical centerline returns a similar magnitude with the same sign.
• Three frames repeat both pitches within about a pixel.
• The grid's center dot sits within half a pitch of the frame center.
• The working distance, focus position and f-number are written down next to the result, because the number belongs to them.

Next step

If the number lands inside your band, order the target and start measuring; if it does not, pick a lens whose datasheet prints the figure. Browse machine vision lenses or filter the lens finder by sensor format, work through the lens configurator, or reach the applications team through the contact page with a frame and a tolerance for a second opinion on the band. The lenses topic page gathers the rest of the lens guides, including how to choose a machine vision lens focal length.