Industrial Lens Selection: Calculations and Common Errors

Lens selection goes wrong when it starts from the focal length instead of from the requirement. Two numbers decide whether a lens can do the job: the field of view that has to be covered, which sets the magnification once the sensor is known (FOV = sensor size / M), and the smallest feature that has to be measured, which sets the object-side pixel (sensor pixel / M). Everything else — image circle, mount, working distance, aperture, lens MTF — is a check against those two.

Working backwards from the tolerance

Divide the tolerance by the number of pixels you want inside it, then divide the sensor pixel pitch by the result. A 0.05 mm tolerance with five pixels inside it needs a 0.01 mm object-side pixel, which with a 3.45 µm sensor pixel is about 0.35×. Check the consequences immediately: the field at 0.35× on a 1.1 inch sensor (14.1 × 10.4 mm, 17.6 mm diagonal) is about 40 × 30 mm, and the depth of field is now a fraction of a millimetre per unit of f-number. If either fails the requirement, the answer is a different architecture rather than a different lens.

The five mistakes that surface during commissioning

1. Choosing by focal length without checking the image circle against the sensor diagonal: 9.0 mm for 1/1.8 inch, about 11.0 mm for 2/3 inch, 16 mm for 1 inch, 17.6 mm for 1.1 inch.
2. Ignoring the working distance the machine actually allows; it is a property of the design, and spacers change both magnification and aberration balance.
3. Pairing a high-resolution camera with a lens that cannot pass the sensor's Nyquist frequency — 145 lp/mm for a 3.45 µm pixel, about 270 lp/mm for 1.85 µm.
4. Using a general-purpose FA lens for a tight dimensional measurement, where magnification versus object distance dominates the error.
5. Ignoring the object itself: transparent, mirror-like or stepped surfaces change what the optics must do far more than a different focal length would.

Checklist before placing the order

Four paper checks — image circle against sensor diagonal, lens MTF at Nyquist and at the intended aperture, working distance against the mechanical envelope, and mount plus flange distance (C-mount is 17.526 mm with an image circle that rarely exceeds a 1 inch format) — then one bench test with a resolution and scale target that measures the field, corner sharpness, distortion, uniformity and the object-side pixel actually achieved. Thirty minutes at the bench prevents most commissioning surprises.

Related reading: telecentric lens selection: FOV, WD, DOF, telecentric versus FA lens, and the lens range. The detailed selection questions are answered below — send the sensor, the field and the tolerance and we will narrow it down.