What the camera must see

How it is calculated

The tool solves two problems. Forward: from sensor size, required field of view and working distance it finds the lens focal length, resolution on the object, the smallest detectable defect, the exposure limit for a moving object and the depth of field. Inverse: from the field of view and a defect size or a measurement tolerance it computes how many pixels the camera needs. Sensor size comes from the camera datasheet (pixel count × pixel size); the diagonal for an optical format comes from the format table, never from a formula. All results use the exact formulas below; rounding happens only on output.

Formulas

Notation: s — sensor size along an axis, mm; FOV — field of view along the same axis, mm; WD — working distance from object to lens, mm; f — focal length, mm; m — magnification.

• Magnification: m = s / FOV.
• Focal length (exact thin-lens form): f = WD · m / (1 + m). The shortcut f = s · WD / FOV overestimates by a factor of about 1 + m and is not used.
• Field of view for a given lens: FOV = s · (WD − f) / f.
• Working distance for a given lens and field: WD = f · (1 + m) / m.
• Resolution on the object: px/mm = N_px / FOV; object pixel size µm = 1000 / (px/mm).
• Smallest detectable defect: d = n_px / (px/mm), where n_px is the number of pixels per defect: 3 px — presence only, 5 px — reliable detection (default), 10 px — size measurement, 16 px per character height — reading text and codes.
• Required camera resolution: N_px = FOV / d · n_px.
• Measurement mode: allowed object pixel p_max = tolerance / k, required pixels per axis N = ceil(FOV · k / tolerance), where k is pixels per tolerance (3, 5 or 10). This is a sampling requirement; the final system accuracy is confirmed by calibration on the actual setup.
• Motion blur: blur_px = v · t · (px/mm); exposure limit t_max = blur_allowed / (v · px/mm). Default 1 px, 0.5 px for measurement.
• Depth of field: circle of confusion c = k · p / 1000 (k = 2 pixels, p — pixel size in µm), DOF = 2 · N · c · (1 + m) / m², N — f-number.

Worked examples

Example 1. Focal length. A 2448 × 2048 px camera with 3.45 µm pixels has an 8.45 × 7.07 mm sensor. You need a 100 mm wide field from 300 mm. Magnification 0.0845, focal length 300 · 0.0845 / 1.0845 = 23.36 mm. The shortcut formula gives 25.34 mm, 8.4 % too long. A 25 mm lens at 300 mm covers only 92.9 mm; to capture 100 mm with a 25 mm lens the distance must grow to 321 mm. The tool picks the nearest standard focal length so that the object is guaranteed to fit and recomputes field and distance.

Example 2. Resolution and defect. 2448 px over 100 mm is 24.48 px/mm, i.e. 40.85 µm per pixel. A defect is visible at 3 px from 0.12 mm and reliably detected at 5 px from 0.20 mm. To catch a 0.1 mm defect at 3 px you need 3000 px across: a 5-megapixel camera is not enough, a camera with at least 3072 px width is.

Example 3. Motion. The object moves at 500 mm/s with 24.48 px/mm. To keep blur within 1 px the exposure must not exceed 81.7 µs; for a measurement task (0.5 px) 40.8 µs. Such exposures call for strobed lighting or a very bright scene.

Example 4. Depth of field. Same camera, magnification 0.0845, aperture f/4: circle of confusion 0.0069 mm, depth of field 8.39 mm. At f/8 it doubles, but four times more light is needed.

Example 5. Measurement mode. Field 300 × 200 mm, tolerance ±0.05 mm, 3 px per tolerance: 18 000 × 12 000 px required. No single area-scan camera provides that; the options are a narrower field, several cameras or a line-scan camera.

Common mistakes

• Using the shortcut focal-length formula: the 8–10 % error equals one step of the standard lens series and the object no longer fits.
• Rounding the focal length up to the nearest standard value: the field shrinks and the object edges leave the frame. Round down or increase the distance.
• Deriving sensor size from the optical format by division: 1/2″, 2/3″, 1″ are historical labels; the diagonal comes from the table only.
• Budgeting 1–2 pixels per defect: detection becomes random. Use 5 px for reliable detection and 10 px for measurement.
• Ignoring motion: an exposure of hundreds of microseconds at metres per second produces tens of pixels of blur.
• Equating measurement accuracy with object pixel size: without calibration, stable lighting and telecentric optics the error is considerably larger.

Questions and answers

No confirmed active width is available for: 1/3". APS-C is not present in the core optical-format table.

Horizontal field of view

Resolution on the object

Minimum detectable feature