Line scan camera field of view: how to calculate it

A line scan camera images one narrow line at a time, so its field of view has two parts: the width across the sensor, set by optics, and the length along the motion, assembled from consecutive lines. Most questions about mounting height are really about the width. This guide gives the three numbers that drive it, the formulas that connect them, a worked example, and the coverage checks that stop you ordering a lens that cannot illuminate the sensor.

The three numbers that set the scan width

For the cross-motion direction you need:

1. Sensor length = number of pixels × pixel size. An 8K camera with 7 μm pixels has 8192 × 7 μm ≈ 57.3 mm of sensor.
2. Lens magnification m = sensor image size / object size, which follows from the focal length and working distance.
3. Field of view = sensor length / m, and mounting height follows directly from m and the focal length.

Note that the pixel size and pixel count alone do not fix the field of view. The same 8K camera can scan 100 mm or 1,000 mm wide; the lens and the height decide. What the sensor fixes is the resolution: field of view divided by pixel count. If you need 0.1 mm per pixel across a 400 mm part, you need at least 4,000 usable pixels, so a 4K or 8K camera fits and a 2K camera does not.

The formulas

The magnification relation m = f / (WD − f) is exact for a thin lens when WD is measured from its object-side principal plane. For a real machine vision lens, use it as a preliminary estimate rather than a mechanical mounting dimension. At close range, especially at magnifications above about 0.1x, use the lens data sheet's own magnification and working distance figures because principal-plane position and internal focusing affect the result.

You can estimate the field of view from the angle of view, FOV ≈ 2 × WD × tan(θ/2), but the magnification route is safer: angle figures on data sheets assume a specific sensor format, and a long line sensor rarely matches it. The camera angle of view article covers when the angle route is useful, for example when you work backwards from a live calibration.

Worked example: scanning a 450 mm web

Suppose you inspect a plastic web 450 mm wide, moving under the camera, and you want 0.06 mm per pixel for fine defect detection.

Step 1 — pixel count. 450 mm / 0.06 mm ≈ 7,500 pixels, so an 8K camera is the natural choice.

Step 2 — sensor length. With 7 μm pixels, s = 8192 × 0.007 mm ≈ 57.3 mm.

Step 3 — magnification. m = 57.3 / 450 ≈ 0.127x.

Step 4 — focal length and height. Pick a working distance of 300 mm for room for the light. Then f = WD × m / (1 + m) = 300 × 0.127 / 1.127 ≈ 34 mm. A lens near that focal length gives a starting estimate for the scan width; confirm its actual working distance from the lens data sheet. If you already own a 50 mm lens, invert instead: WD = 50 × 1.127 / 0.127 ≈ 444 mm.

Use the lens focal length calculator below to run your own numbers:

Choosing the camera: pixel count and pixel size

The choice of camera sets the resolution ladder. More pixels across the same width means finer detail; larger pixels mean more light per line, which matters at high line rates. A compact 4K camera with 7 μm pixels suits webs up to a few hundred millimetres at moderate resolution:

For wide webs or fine resolution you move to 8K and beyond, with larger sensors and correspondingly larger lens coverage demands. An 8K camera with a 10GigE interface is an option for these applications:

At the top end, 16K sensors with 5 μm pixels reach about 82 mm of sensor length, which changes the lens requirement significantly, as the next section shows.

The coverage check most people skip

A line scan lens must illuminate the whole sensor length. The formal test: the lens image circle must exceed the sensor diagonal, and for a line sensor the diagonal is essentially its length. Three practical cases:

• A 4K sensor with 7 μm pixels is about 29 mm long. Check the exact sensor diagonal against the lens's specified image circle rather than relying on rounded coverage labels.
• An 8K, 7 μm sensor at 57.3 mm needs a lens whose specified image circle exceeds that diagonal; lenses in the 60-90 mm coverage class are candidates.
• A 16K, 5 μm sensor at about 82 mm needs coverage beyond that diagonal. Check the exact image-circle specification, not just the mount or coverage-class label.

If the image circle is too small, the ends of every line can darken or lose usable image quality. This is why an ordinary area-camera lens cannot be assumed suitable for line scan, even when the mount fits. The full selection procedure, including pixel-scale matching between lens and sensor, is in the line scan lens selection guide.

Browse the line scan lenses or use the lens finder filtered by image circle and mount. Smaller-format fixed focal length lenses for area cameras live in the general machine vision lenses category, but check coverage before using one on a line camera.

Values as printed in each product's data sheet; open a part for its drawing and full specifications.

Both lenses above are built for line sensors, but they sit at opposite ends of the range: one covers an APS-H class line in the 30-45 mm image circle band, the other is listed in the 60-90 mm band. Match the exact coverage to the sensor diagonal first, then check the required magnification.

Setting the mounting height in practice

1. Fix the required resolution across the part and derive the pixel count and magnification.
2. Choose a lens with adequate image circle and a focal length that puts the working distance in a sensible range, typically 100-500 mm for many web applications.
3. Compute an estimated working distance, check the lens data sheet's measurement reference, and mark the mounting position on the stand. Then verify on the bench: image a ruler across the scan line and measure the visible span against the pixel count.
4. Allow focus margin. Mechanical vibration and part height variation consume depth of field quickly. Stopping down can increase depth of field, but diffraction and reduced light limit how far you can go. Use the depth of field calculator below as a starting point, then check image sharpness at the actual aperture.

For the motion axis, remember the field of view along travel is assembled from consecutive lines. The line rate must match web speed so pixels stay square, which the line rate set-up guide walks through.

When the usual answer is wrong

Three situations break the simple geometry:

• Very short working distances. At magnifications above about 0.1x, treating a real lens as a thin lens can give an inaccurate mounting distance. Telecentric designs require their own specified magnification and working distance. Use the lens's printed magnification-versus-distance information, and see the machine vision lens focal length guide for the broader selection process.
• Tilted optical axis. If the camera is angled to clear a mechanism and distance varies along the scan line, focus and scale can vary across the field. Scheimpflug-style adjustment may help align the focus plane, but it does not remove perspective scale variation.
• Curved or bulging parts. A single line records a projected profile, not the surface's arc length. Size the field to the widest projected profile plus margin, and check focus across the full height range.

Pre-order checklist

• [ ] Required resolution across the part in mm per pixel, and derived pixel count
• [ ] Sensor length computed as pixels × pixel size for the chosen camera
• [ ] Magnification and working distance computed and checked against the lens data sheet
• [ ] Lens image circle greater than the sensor diagonal, with margin where available
• [ ] Mount matches: M42, M72, M58, F-mount or V-mount, with the right back-focus hardware
• [ ] Line rate set from web speed so pixels are square along travel

If you would rather have the arithmetic checked, start with the camera configurator, or send the application details through the contact page and we will run the numbers with you.

The general frame around all of this — sensor, lens, light and interface chosen as one system — is covered in the industrial camera specifications buyer's guide, and the line scan cameras category is the place to compare pixel counts, pixel sizes and interfaces side by side.