Blister inspection working distance and field of view formula

You have the camera, a 35 mm lens and a dome light; what is missing is the geometry — how high the lens sits above the blister web, what the frame will cover, and where the dome goes. This guide gives the formula that ties field of view to focal length and working distance, runs a real blister example with the arithmetic shown, sizes the dome, and lists the checks worth making before the bracket is cut. The worked numbers assume a 1/2 in sensor of 6.4 × 4.8 mm; substitute your sensor's width and the same equations hold.

What is the formula that links field of view, focal length and working distance?

Field of view is sensor size times working distance over focal length — FOV = sensor × WD / f — so a 6.4 × 4.8 mm sensor behind that lens at 300 mm covers about 55 × 41 mm of the blister web.

At these magnifications the lens behaves as a pinhole: the field grows in proportion to working distance and sensor size, and shrinks in proportion to focal length. Working from a fixed lens toward a mount height, use the second line.

WD is measured from the lens, and m is magnification — the number that converts pixels to millimetres at the part. If you instead have a fixed camera slot and a free lens choice, how to choose a machine vision lens focal length walks that direction. A second walkthrough of the same equation, with sensor tables, is in FOV and working distance calculation for pharmaceutical blister inspection.

How accurate is the formula at close range?

Below about ten focal lengths the first-order line reads wide: at 300 mm it claims 55 mm where the exact lens equation gives 48 mm on a 6.4 mm-wide sensor — a 13% gap.

The pinhole form ignores that the object sits at a finite distance. The thin-lens equations close the gap:

At 300 mm, m = 0.132, so the true field is 6.4 / 0.132 = 48 mm wide against 55 mm from the pinhole line; the error is f / (s − f) = 13%. The pinhole line is within 5% once the working distance passes 20 focal lengths (700 mm here) and about 11% off at ten (350 mm). Below that, use the lens equation. Edge distortion on machine-vision glass of this class adds another 0.3-1% toward the corners.

How high above the blister should you mount the camera?

Mount the lens 420 mm above the web: a 70 × 50 mm target field — a 60 × 40 mm card plus 5 mm of margin per side — on the 6.4 × 4.8 mm sensor needs 418 mm by the exact lens equation.

The arithmetic, step by step:

1. Target field: the card is 60 × 40 mm; add 5 mm per side for placement tolerance → 70 × 50 mm.
2. Magnification: m = 6.4 / 70 = 0.0914.
3. First pass: WD = 70 × f / 6.4 = 383 mm.
4. Exact: WD = f × (1 + 1/0.0914) = 35 × 11.94 = 418 mm.
5. Height check: 4.8 / 0.0914 = 52.5 mm, so the 4:3 sensor covers 70 × 52 mm and the 50 mm card height fits with room.

Drill at 420 mm and keep ±10 mm of fine travel in the bracket. A ±5 mm web bounce moves magnification 1.4% (m drops to 0.090), about half a millimetre at the field edge — irrelevant to presence, calibrate it out if the image feeds measurement.

Run your own sensor and lens through the same arithmetic:

The LS-FFL-0679 is a 35 mm, 2/3-inch, 6 MP C-mount machine vision lens.

That 2/3 in rating covers any smaller sensor, so the 1/2 in sensor in this example sits well inside the circle, and the resolution rating leaves headroom for a later 5 MP camera. Filter the lens finder on C-mount glass of this focal length and compare close-focus limits and distortion before ordering.

How many pixels does a missing pill need?

A 2 MP camera (1600 × 1200 pixels of 4.0 µm filling the sensor) maps the 70 mm field to 44 µm per pixel, so a 10 mm pill spans about 230 pixels and a 1 mm chip spans 23.

Object-space pixel size is the sensor pixel divided by magnification: 4.0 µm / 0.0914 = 44 µm. Detect a feature with 3 to 5 pixels on it, measure one with 10: presence and completeness are comfortable at 2 MP. Embossed logos and hairline cracks are the cases that push toward 5 MP and a tighter field.

With c set to two pixels (8 µm), f/8 gives a total depth of field of 2 × 8 × 8 µm / 0.0914² ≈ 15 mm. That ±8 mm covers pill crowns and web bounce together; f/4 halves it, and past f/11 diffraction begins to blur 4 µm pixels, so f/8 is the working aperture for this station.

Motion sets the exposure. At 200 mm/s of web speed, two pixels of blur is 88 µm, so exposure must stay under 88 µm / 0.2 m/s = 0.44 ms — strobe the dome at 0.4 ms. Automatic iris, exposure and gain control in machine vision covers the camera side of that trade.

How big must the dome be, and where does it sit?

Pick a dome whose emitting aperture is 1.5 to 2 times the long side of the field — 105 to 140 mm for a 70 mm field — and hold the blister a few millimetres below that aperture, inside the near field.

The LS-DOM-0085 is a Ø166 mm dome light with a Ø116 mm emitting area.

That aperture sits mid-range for the 70 mm field. A part farther than about half the aperture diameter from the diffuser starts picking up direction again, and glare returns — keep the blister close. The camera shoots through the port: leave a few millimetres of clearance between the lens barrel and the port edge, or the port vignettes the corners. The dome adds mechanical height, never optical working distance; focus stays on the blister plane.

Dome geometry in depth — size, curvature, where domes fail — is in dome lights for shiny, curved and wrinkled parts. For pill colour and sheen, which LED colour gives the best contrast in machine vision is the next read, and shadow traps around pill edges are treated in pill stain detection lighting.

If the station shape rules out a tall dome, the LS-DOM-0133 is a 134 mm spherical integral light and the LS-DOM-0062 is a 3.0 dome light, 194 mm outer diameter. Flatter and larger builds sit in the dome lights category:

What checks catch mounting mistakes before the line runs?

Run five checks before cutting the bracket: image-circle cover, field margin, focus travel at the real distance, port clearance around the lens barrel, and a strobe short enough to freeze the web — 0.4 ms at 200 mm/s here.

• Image-circle cover: the lens must be rated for the sensor format or larger; a smaller circle darkens the corners of every frame.
• Field margin: lay a checker or dot target at the blister plane and count visible squares — calibration target field of view and lens coverage margins gives target sizes and the margin rule.
• Focus travel: confirm the helicoid reaches 418 mm before the bracket exists; if it stops short, fit an extension ring and re-run the field numbers.
• Port clearance: lens barrel outside diameter against dome port inside diameter, a few millimetres each side.
• Strobe: shoot a scale moving at line speed and confirm edges blur by two pixels or less.

When is a dome the wrong light for a blister line?

For clear thermoformed film carrying opaque tablets, a backlight under the web beats a dome: tablets block the light, empty pockets stay bright, and one threshold separates them.

Put the light under a translucent web and the camera above it. One installed tablet-placement station runs its camera about 36 cm above the line with an LED backlight 10 cm below it — see an installed tablet placement inspection set-up for the layout.

The dome earns its place when the surface is the message: glossy capsule shells, embossed tablets, curved softgels, chips and dust on shoulders. There the direction-free field shows the surface without one specular hotspot. Stations needing both run two exposures — dome strobe, then backlight — the pattern covered in sequential machine vision lighting for multi-view inspection; the full geometry menu is in machine vision illumination types: choosing the right geometry.

For single-cavity work, the LS-TCL-0574 is a 0.4x fixed-magnification lens with 227 mm WD. Its magnification does not move when part height moves, which is exactly the property the third row buys.

That is the whole geometry decision: 420 mm of height, a dome aperture near 116 mm for a 70 mm field, 2 MP of camera, f/8, 0.4 ms of strobe. Start the configurator at the lens step and carry the same numbers into the light step, browse the neighbouring topics in the lens guides, or bring the card size and line speed to the quote desk and we will check the stack with you.