Camera field of view at a given mounting height: how to size it

When a camera hangs over a conveyor or rides a robot wrist to a taught snapshot position, the mounting height is usually fixed before the lens is chosen: gantry clearance, robot reach and part presentation all get a vote. Two numbers then decide the whole view — that height, and the lens's angle of view. One short formula ties them together, so you can compute the covered area before anyone machines a bracket, or run it backwards to find the height a known workspace needs. This page gives the formula both ways, a worked example that sizes a 400 × 300 mm pick view, the pixel-size check that decides whether a feature is detectable, and the tilt and depth-of-field corrections that move the answer.

The coverage rule at a fixed height

A camera looking straight down from height H onto a flat work plane covers a rectangle. Each field edge reaches H · tan(θ/2) out from the vertical, where θ is the lens's angle of view along that edge, so:

W and V are the covered width and height on the plane, sW the sensor's active width, f the focal length, and H runs from the plane up to the lens's entrance pupil. The right-hand shortcut is the machine-vision form: at these distances the tangents cancel and the footprint is just sensor width times height over focal length. It ignores the sensor-to-pupil gap, an error of about f/H — 1.4% for an 8 mm lens at 0.58 m, 5% at 160 mm.

The forward problem — coverage from a sensor and focal length already chosen — is worked through in Lens field of view: why sensor size and focal length set it. Here the height is the given, which is why no spec table is needed for the detection area: height and angle of view alone set it.

Solve it backwards for the height you need

Divide instead of multiply, per axis, and keep the larger height:

Before either, size the required field 20% larger than the workspace — 10% margin per side. The slack absorbs calibration residuals, distortion at the frame edges and presentation jitter, and it costs resolution linearly: every 10% of extra field thins the pixels by 10%. Then browse machine vision lenses by focal length and image circle. The same margin logic for calibration targets is set out in Calibration target field of view and lens coverage margins.

Worked example: a 400 × 300 mm pick view at 0.58 m

The task: one downward-looking camera must cover a 400 × 300 mm presentation area well enough to localise parts for a pick. The rig: a 12 MP USB3 area scan camera with a 1/1.7" sensor, a 4000 × 3000 resolution and a 30 fps readout, carrying an 8 mm FA lens specified for 2/3" sensors with an 8-11 mm image circle:

The arithmetic, axis by axis:

• Sensor active area: a 1/1.7" format works out to about 6.7 × 5.0 mm, so one pixel spans 6.7 mm / 4000 ≈ 1.7 µm.
• Angles: θH = 2 · arctan(6.7 / 16) = 45.4°; θV = 2 · arctan(5.0 / 16) = 34.7°.
• Required field with 10% per side: 480 × 360 mm.
• Height: H ≥ 480 / (2 × 0.419) = 573 mm and H ≥ 360 / (2 × 0.3125) = 576 mm. The vertical axis governs — specify 580 mm.
• Check at that height: W = 2 × 580 × 0.419 = 486 mm; V = 2 × 580 × 0.3125 = 362.5 mm. Both clear the requirement, leaving 43 mm spare beyond each workspace edge in width and 31 mm in height.
• Cross-check with the shortcut: W = 6.7 × 580 / 8 = 486 mm; shortcut error f/H = 8 / 580 ≈ 1.4%.
• Pixel size on the part: 486 mm / 4000 px = 0.12 mm/px.

Decision: mount at the 580 mm just computed and expect a 486 × 362 mm view at 0.12 mm per pixel. If the same height must inspect fine details instead, the 35 mm option narrows the view to 2 × 580 × (6.7 / 70) = 111 mm by 83 mm at 0.028 mm/px — about 4 times the resolution over a quarter of the area. The lens for that second case:

Pixel size decides detection, not coverage alone

Coverage answers whether the camera sees the part; pixel size answers whether it sees the feature. Ground sample distance is field width divided by horizontal pixels. Plan on a feature spanning at least 3 pixels to detect it and 5 or more to measure it. At 0.12 mm/px the worked view detects features down to about 0.36 mm and measures from 0.6 mm, so a 2 mm feature sits comfortably inside the window. For close-range macro set-ups the same quantity falls out of magnification rather than height — see Calculate object space pixel size from magnification. And when one snapshot position cannot cover the table at all, the overlap arithmetic for a second position is in Multiple wrist camera snapshot positions to cover a large table.

Height is measured to the entrance pupil — and tilt reshapes the footprint

H runs from the work plane to the lens's entrance pupil, not to the C-mount flange. On compact FA lenses the two sit 20-30 mm apart; on long-barrelled designs the difference passes 100 mm. A height taken from the flange therefore predicts more coverage than the lens delivers.

Tilt breaks the single-height picture. With the optical axis leaned α off vertical, the footprint along the tilt direction runs from H · tan(α − θ/2) at the near edge to H · tan(α + θ/2) at the far edge. Tilt the worked example by 30°: near edge 580 × tan(7.3°) = 74 mm, far edge at the same H × tan(52.7°) = 761 mm. The view stretches to about 687 mm and the far side renders about 1.6× coarser, because its ray travels further. Calibration flattens the keystone afterwards; Camera angle of view from calibration reads the real angles back out of images. Robot-mounted snapshot positions add one further trap: neighbouring positions whose fields must overlap. Fixing overlapping camera fields of view in robot vision walks one such repair end to end.

Depth of field and exposure set the height tolerance

Coverage places the plane at 0.58 m; depth of field decides what part-height variation the view survives. With blur held to one 1.7 µm pixel (circle of confusion c), the hyperfocal distance is f²/(N·c) and the focus limits follow:

Set to F2.8 and focused at that distance, the example view holds focus from about 556 to 606 mm, roughly ±24 mm. At F8 the same view holds 517-660 mm, +80/−63 mm — enough for a tall part or a loose fixture. The bill arrives in light: F8 passes (8/2.8)² ≈ 8× less, so exposure stretches about eightfold unless the lamp brightens to match. The depth of field calculator repeats the arithmetic for any f-number. Motion sets its own exposure cap: a part crossing at 300 mm/s must be caught within 0.12 mm / 300 mm/s = 0.4 ms to keep blur inside one pixel.

Checks before you cut the bracket

• Compute both axes and keep the governing height; in the example the vertical axis decided the mount, not the horizontal.
• Measure to the entrance pupil, not the flange, and to the top of the tallest part, not the belt.
• Confirm the image circle clears the sensor diagonal: the 1/1.7" format needs about 8.4 mm, so any 2/3"-class circle carries margin.
• Keep the horizontal angle near or below 60° for calibration-friendly distortion; the example's 45.4° is comfortable.
• Check the focus window against part-height variation plus repeatability at the snapshot position; stop down until it fits, then re-budget exposure and light.
• For moving parts, cap exposure at pixel size divided by part speed.
• Lay a grid target in the plane and re-measure after mounting; the taught position, not the drawing, is the truth.

From numbers to parts

Once height and field are fixed, the camera finder filters area scan cameras by resolution, sensor format and interface, and the lens finder does the same by focal length and image circle; the lens configurator step pairs the two directly. The worked set-up is the 12 MP, 1/1.7" USB3 camera with the 8 mm FA lens, and the detail-inspection option is the 35 mm, 6 MP C-mount lens. For the lens-choice method beyond geometry — distortion, F-number, depth of field — see How to choose a machine vision lens focal length, and the lens guides topic page collects the rest. Support comes free with every order if you want your numbers checked against a drawing.