A hand-eye calibration usually fails for a simple reason: the board sits too small in the image, or a corner leaves the frame halfway through the pose sweep. The solve then reports inflated residuals, or worse, finishes cleanly while the robot still misses by millimetres. Target size is the one variable you set before any data is collected, and it follows from two numbers you already know: the field of view at the calibration distance and the board's square pitch. This guide gives the sizing rule, at least a third of the image width, the arithmetic that turns it into a physical board, and a worked example for a 7x8, 30 mm checkerboard at an 800 mm stand-off. By the end you can order or print the right target before the cell is ready.
The rule: a third of the image width, minimum
Size the pattern to fill at least a third of the image width at the calibration distance, measured at the most tilted pose. Equivalently, the field of view at that distance can be at most three board widths. A 240 mm-wide pattern tolerates a 720 mm field; a camera that sees 1.2 m across needs a board at least 400 mm wide.
The basis is pixel coverage. On a 2448-pixel-wide camera, a third of the frame is 816 pixels, so an 8-column pattern shows about 102 pixels per square. Checkerboard corners localize to a fraction of a pixel, and even a conservative 0.1-pixel corner error is then 0.03 mm at the target, far below the sub-millimetre repeatability robot guidance asks for. Fill less of the frame and corner noise grows in object space in exact proportion. Fill more and the pose sweep starts clipping corners out of view.
Tilt foreshortens the pattern, so apply one correction before committing. A board tilted 30° from frontal projects about 87% of its width, because cos 30° = 0.87, so the 240 mm pattern behaves like 208 mm. Keep the fill above a third after that correction, not before.
What the pattern spans: squares times pitch
Convert the rule into a printing or ordering dimension by counting squares. An 8 x 7 array of 30 mm squares spans 240 x 210 mm, and the detector works from the 7 x 6 inner corners inside it. Border beyond the squares does not count toward the pattern, but keep 20-30 mm of rigid border so clamps and gripper fingers stay clear of the corners.
| Pattern (columns x rows, pitch) | Squares span | Field of view ceiling |
|---|---|---|
| 5 x 6, 20 mm | 120 x 100 mm | 360 mm |
| 7 x 8, 12.5 mm | 100 x 87.5 mm | 300 mm |
| 7 x 8, 30 mm | 240 x 210 mm | 720 mm |
| 7 x 8, 40 mm | 320 x 280 mm | 960 mm |
Read the table the other way when you already own a board: find its row and keep the field of view at the calibration distance under the last column. Pitch accuracy feeds the intrinsic part of the solve; a uniform pitch error mostly scales the result, while a warped board bends it, which is why flatness outranks print resolution later in this guide.
From field of view to focal length
The sizing rule consumes a field of view, so the next step is the optic that delivers it. Away from macro distances the pinhole estimate holds within a few percent:
Work in millimetres throughout. Sensor width 8.8 mm, stand-off 800 mm and a wanted field of 600 mm give f = 800 × 8.8 / 600 = 11.7 mm, so a 12 mm lens lands close to the mark. The working distance and field of view formula derives the exact version, and the calculator below runs it on your numbers.
If you are selecting rather than reusing, the lens finder filters machine vision lenses by sensor format and focal length. Long stand-offs are a lens problem rather than a board problem, so pick an optic whose distance range spans the stand-off. The LS-FFL-1676 covers WD 214-1536 mm in M58 mount around a 60 mm focal length, which lets one optic serve the calibration distance and the runtime field alike.
- Type
- Fixed focal length
- Sensor format
- Large format
- Mount
- M58
- Resolution
- Over 25 MP
Worked example: a 7x8, 30 mm checkerboard at 800 mm
Inputs, with their source:
- Pattern: 7 x 8 squares at 30 mm pitch, a common generic format. The squares span 8 x 30 = 240 mm wide and 7 x 30 = 210 mm high.
- Sensor: 2/3-inch type, 2448 x 2048 pixels, 8.8 mm wide, so 3.6 µm pixels; these are illustrative 6 MP values.
- Stand-off: 800 mm, chosen to keep a parallel gripper out of the view.
The ceiling comes first: 3 × 240 = 720 mm. To land mid-window near a 40% fill, aim for a 600 mm field, so f = 800 × 8.8 / 600 = 11.7 mm, rounded to the standard 12 mm. The delivered field is then 800 × 8.8 / 12 = 586.7, call it 587 mm.
In image terms, the pixel scale is 587 / 2448 = 0.240 mm per pixel, one 30 mm square spans 30 / 0.240 = 125 pixels, and the board spans about 1000 of the 2448 columns, which is the 41% fill. At the worst pose, 30° of tilt projects the width to 240 × 0.87 = 208 mm, which is 208 / 587 = 35% of the field and still above the floor. A 0.1-pixel corner error is 0.1 × 0.240 = 0.024 mm at the target.
The decision: this board suits any field between about 360 mm and 720 mm at the calibration distance. At 360 mm the fill reaches two-thirds and the corners stay inside frame through a tilt sweep; at 720 mm the board sits exactly on the one-third floor. Below 360 mm the pattern crowds the frame, and above 720 mm it is undersized. In a 900 mm logistics field the same board covers 27%, so step up to a 40 mm pitch: a 320 x 280 mm pattern raises the ceiling to 960 mm and puts the fill at 36%.
Checkerboard versus marker board
Dense checkerboards pack the most corners into the smallest area, which is why the sizing rule treats pattern width as the currency. Marker boards in the ArUco style trade that density for tolerance of occlusion and uneven exposure, and the ID readout removes orientation ambiguity. The cost is area: each marker must resolve like a checkerboard square would at that distance, so a marker board chosen from its outer paper size tends to run small.
Size a marker board from its elements instead. Give each marker the image area a square would get, roughly (image_width_px / 3) / columns, and keep the quiet spacing between markers well under the marker width. When the solve consumes a point cloud rather than an image, as with structured-light 3D cameras, the same arithmetic applies to the depth image. A structured-light 3D camera such as the MV-DPS200P-02 supplies that point cloud, and the 3D camera working distance guide maps where its depth accuracy peaks.
- Type
- Stereo / structured light
Eye-in-hand versus eye-to-hand: same rule, different mounting
Eye-in-hand puts the camera on the flange and leaves the board fixed in the cell. The sizing rule is identical, but the distance now changes with every pose, so check the fill at the farthest pose, where the field is widest and the board smallest. Place the board mid-reach rather than at the edge of the envelope, so the wrist can add real tilts; choosing robot poses for eye-in-hand calibration covers the spread the solver wants.
Eye-to-hand bolts the camera down and moves the board in the gripper. The field of view is constant, and the new risk is occlusion, because fingers over the pattern remove corners. Machine the plate larger than the squares, keep the fingers outside the pattern edge in every programmed pose, and confirm detection per capture; failures cluster at the grazing angles that make the calibration valuable.
Rigid, flat, matte: holding the target
A board waved by hand or taped to a box adds pose noise the solver cannot separate from the transform, so fix the board to a stand. The LS-MNT-0040 carries a 700 mm column and a 400 x 450 mm base, and the camera stands range includes slide stages for a target that must move between set-ups; the accessories finder lists them alongside the brackets.
- Type
- Camera stands
Flatness then outranks print quality. Bond the print to aluminium composite or cast acrylic and sight across it with a straightedge; when paper calibration targets are flat enough gives the size limits. Shoot matte rather than laminated: gloss turns into a glare patch at some tilt angle, and a corner lost to glare is a pose deleted from the dataset.
When the one-third rule fights the cell
Fixed-magnification optics set the field by design rather than by distance. The LS-TCL-0574, for instance, is a 0.4x lens with a 227 mm working distance, and its object-side field is the sensor width divided by 0.4. Do not move the stand-off to fix the fill; choose the pitch instead. If that field works out near 100 mm wide, the one-third rule asks for a pattern about 33 mm across, which a 7 x 8 array at 4 mm pitch delivers.
Large fields invert the problem. Logistics and pallet fields of 1-2 m turn a one-third board into a furniture problem: either build the big target, as building a 1 m calibration grid walks through, or place the board where the picks happen and treat the result as local to that region. Extra poses help a small board somewhat, but residuals rise as the fill drops well below a third, and no dataset restores corners the lens never resolved.
Depth cameras add a constraint the 2D case hides: the pattern must sit inside the sensor's accurate depth range, and depth noise smears the corners exactly where the solver wants them crisp. Keep the stand-off in the sweet spot, check that the board's point cloud reads flat before collecting, and read the depth-camera target-size failure for how this presents at distance. Browse 3D sensors by profiler and stereo type while the cell is being specified.
Close-range fields under 150 mm squeeze from the other side. A one-third fill means a pattern under 50 mm wide, so pitch drops to 5-10 mm and printing accuracy sets the ceiling. Checkerboards stay standard practice at this scale; measure the pitch with calipers before blaming the solve.
Checks before you collect the dataset
- Measure the fill on a live capture at the most tilted pose: pattern width divided by image width. Above 0.33, proceed; below, resize the board or the field first.
- Confirm corner detection in every capture before moving to the next pose. A pose whose corners drop silently poisons the whole solve.
- On a 3D camera, inspect the target's point cloud: it should read flat. Ripples mean the stand-off or exposure is wrong.
- Sort out camera intrinsics before the hand-eye solve; fixing the camera intrinsics first explains the order.
- After the solve, measure the miss: command the robot to a point the camera reports and compare. Testing a hand-eye result before you trust it gives the procedure.
When the sizing points to new hardware, the camera finder filters sensors by type and resolution, the lens configurator pairs a focal length to your sensor and stand-off, and the stand configurator settles the mounting side. If your cell does not fit the tables here, talk to the applications team with your field of view and stand-off, and the board size follows in one calculation. The 3D vision guides hub collects the rest of the workflow from capture to robot pick.
Questions
How much of the image should the calibration target fill?
At least a third of the image width, measured at the calibration distance in the most tilted pose. A 240 mm-wide pattern needs a field no wider than 720 mm; in a 600 mm field it covers 40%, leaving margin for oblique poses. Under a third, the solve still runs, but the corners become a small pixel target and residuals grow with every metre of robot travel.
What checkerboard square size suits a 300 mm field of view?
The minimum pattern width is 100 mm, so a 7x8 array with 12.5 mm squares spans exactly 100 x 87.5 mm. On a 2448-pixel-wide sensor that field gives 0.123 mm per pixel, or about 102 pixels per square. At this size, printed pitch tolerance and flatness dominate the error budget, so check the print with calipers before mounting it.
Can I use a paper-printed checkerboard for hand-eye calibration?
Yes, for smaller patterns. Flatness matters more than material: a paper print bonded to a rigid plate works well up to about A3 size. For a 240 mm board, mount the print on aluminium composite or cast acrylic and check it with a straightedge, because a bowed target bends the hand-eye result the same way it bends intrinsic calibration.
How many poses should I capture for a hand-eye calibration?
Plan on 10 to 20 captures. Spread them across the working range with clear tilts in at least two axes plus some in-plane rotation: the solver separates the hand-eye transform from the camera's own parameters only when poses differ enough. Ten near-identical frontal views contribute less than six well-spread poses with real angle changes.
The board looks too small in my images. Can I fix it without a new target?
Narrow the field of view at the same distance: swap a 12 mm lens for a 16 mm on the 2/3-inch, 2448-pixel example and the field drops from 587 mm to about 440 mm, lifting the 240 mm board from 41% to 55% of the image width. Moving the camera closer works too, provided the board stays sharp and detected at the shorter distance.