From inspection requirement to a justified camera, lens and light.

How it calculates

• Pixel scale = field of view ÷ sensor pixels, on each axis; the axis that needs the smaller scale limits. Pixels across a feature = feature ÷ pixel scale.
• Required resolution = field of view × 1.10 margin ÷ (feature ÷ pixels per feature). Defaults: 5 px for presence, defect and guidance, 4 for print and codes, 8 for measurement; 2 px is sampling only, 3 to 5 preliminary screening, 5 to 10+ the usual start, all subject to validation. Detection also depends on contrast, optics, lighting, focus, noise, motion and the algorithm.
• Focal length: thin lens f = u·v ÷ (u + v) with v = m·u, so f = u·m ÷ (1 + m), m = sensor ÷ field. The far-field figure f ≈ sensor × WD ÷ FOV is shown alongside for reference. The lens is then checked for image circle, mount, focus range and working distance, not chosen by focal length alone.
• Depth of field ≈ 2·N·c·(m + 1) ÷ m², circle of confusion c = one pixel, N the working aperture. An estimate; stopping down costs light.
• Motion blur = speed × exposure, converted to pixels; flagged above ½ pixel; below 50 µs exposure a strobe is needed. A moving part also needs speed ÷ (0.8 × field height) frames per second.
• Uncertainty budget: the sampling interval and the half-pixel figure are theoretical references, not accuracy. Lens distortion and perspective are computed from published figures and your inputs. Sensor noise, lighting, calibration, mechanics and algorithm repeatability are marked not quantified, data required until a trial or a datasheet supplies them. The partial combination is a root-sum-square of the quantified terms only, and says so.
• Lighting is a hypothesis by surface and task until an image trial confirms it.