Machine vision glossary: the terms that matter for lens choice

A lens datasheet is a list of terms, and each term hides a number: field of view, working distance, flange distance, F-number, magnification, distortion, telecentricity. Specify one of them wrong and the lens comes back out of the camera two weeks later. This glossary defines each term the way machine vision lens datasheets use it, with the value or formula that acts on it: the 17.526 mm C-mount flange distance, the 145 lp/mm Nyquist limit of 3.45 µm pixels, the 1% scale error per millimetre of depth drift. Read the terms in this order and you can size a focal length, check a quote sheet and decide whether the job needs a telecentric before you spend anything.

Field of view, sensor format and image circle

The field of view (FOV) is the area the camera sees at the object, in millimetres. Three inputs set it: the sensor size, the focal length and the working distance. Sensor formats carry their physical size in the name: a 1/2" sensor is 6.4 × 4.8 mm, a 2/3" sensor is 8.8 × 6.6 mm with an 11 mm diagonal, and a 1" sensor is 12.8 × 9.6 mm with a 16 mm diagonal.

The image circle is the disc of light the lens projects, and it must cover the sensor diagonal. A lens listed for 2/3" projects an 11 mm circle: it fills a 2/3" sensor and clips the corners of a 1" sensor. Check the circle before the focal length, because no focus adjustment recovers a clipped corner. The lens sensor format guide walks the common formats and diagonals.

Working distance and flange distance

Working distance (WD) runs from the front end of the lens mechanics to the object plane, at best focus. It is not the distance to the sensor and not the barrel length; datasheets print all three as separate rows, so read the right one. WD moves when you refocus, add extension rings or change magnification.

Flange distance (flange focal distance) is the fixed number behind the lens: the distance from the mount face to the detector plane, set by the mount standard and machined to hundredths of a millimetre, because focus error eats depth of field directly. The flange focal distance reference tabulates the mounts. C-mount is 17.526 mm, CS-mount is 12.5 mm, and F-mount is 46.5 mm. A C-mount lens on a CS-mount camera therefore needs a 5 mm spacer, and without it the lens never reaches focus. The C-mount vs CS-mount guide covers the adapter arithmetic, and the adapter focus check shows how to confirm the fit.

Extension rings pull a fixed focal length lens closer, and the response is steep: extension e sets magnification m = e/f. A 5 mm ring on a 25 mm lens gives m = 0.2x and best focus near f(1+m)/m = 25 × 1.2 / 0.2 = 150 mm from the principal plane, so the front-of-barrel WD lands a little shorter. A 10 mm ring gives m = 0.4x and focus near 25 × 1.4 / 0.4 = 87.5 mm. Doubling the ring moved focus by 60 mm, which is why long extensions go in steps.

Focal length and magnification

Magnification m is image size over object size, and for sizing work you read it as sensor width divided by field of view. Focal length then follows from the working distance you want:

Fixed focal length FA lenses mostly demagnify below 0.3x. Telecentric lenses come in declared classes of 0.1-0.3x, 0.3-0.6x, 0.6-1x, 1-2x and above 2x, and macro territory starts around 0.5x. The focal length how-to runs the full sizing walk-through.

A 35 mm FA lens built for 6 MP on a 2/3" C-mount camera:

F-number, aperture and depth of field

F-number (F#) is focal length divided by entrance pupil diameter: a 50 mm lens with a 6.25 mm pupil is F8. Lower F# gathers more light, because image brightness scales with 1/N²: going F4 to F8 costs two stops and needs 4× the exposure or gain. Higher F# buys depth of field and pays in diffraction:

At 550 nm the blur spot is about 5.4 µm at F4 and 10.7 µm at F8. Against 3.45 µm pixels, F8 already smears across three pixels, so the highest useful F# is set by your pixel pitch and the lowest by the depth your tolerance needs. Pick it from those two numbers, not from habit. The automatic iris, exposure and gain guide covers the light side.

A 16 mm lens for 20 MP 1.1" sensors with an F2.8-22 iris and distortion under 0.3%:

Resolution, contrast and MTF

System resolution is the worse of lens and sensor. The sensor's ceiling is Nyquist, 1/(2 × pixel pitch): 3.45 µm pixels top out at 1/(2 × 0.00345 mm) ≈ 145 lp/mm, and 5.86 µm pixels at about 85 lp/mm. The lens must still hold contrast at that frequency; that is the MTF curve, and for equal-width black-and-white bar patterns the same quantity is the contrast transfer function (CTF), as the optical transfer function reference defines it. A lens whose contrast has collapsed at your Nyquist frequency gives grey edges at any focus setting. Read how to read lens performance curves and check the curve at your own frequency, not the headline value.

Telecentricity

A telecentric lens keeps its chief rays parallel to the optical axis on the object side, so magnification holds when the part moves in depth. An ordinary entocentric lens scales with distance: at a 100 mm WD, a part 1 mm closer reads about 1% larger, which is 0.2 mm on a 20 mm dimension. That number decides the question. If 1% of scale drift exceeds your tolerance, go telecentric; if the part sits at a fixed stop, a standard lens calibrated in place is usually enough. The entocentric vs telecentric comparison and when you need a telecentric lens for gauging work the decision in full.

Telecentrics are specified by magnification class and working distance, and many carry a coaxial light port for shiny flat parts; the telecentric depth of field guide explains why their focus behaviour differs from FA lenses. A 0.5x telecentric with a 110 mm WD on a 1" sensor and built-in coaxial light:

Distortion and telecentricity error

Distortion bends straight lines without blurring them, and datasheets print it as a percentage of radial image distance. At 0.3% and 10 mm off-centre, a point sits 0.003 × 10 mm = 30 µm from true position on the sensor; at 0.34x magnification that is 30 µm / 0.34 ≈ 0.09 mm at the object, larger than many gauging tolerances before any other error is counted. Either calibrate it out, as lens distortion correction shows, or specify a lower-distortion design. Telecentricity error, the residual magnification change across the field, is the separate number to check on a telecentric datasheet; telecentric distortion and telecentricity explained covers it.

Worked example: a 25 mm field at 100 mm working distance on a 5 MP 2/3" camera

Say the part measures 22 × 18 mm and you want 25 × 20 mm of field with margin. The camera carries a 5 MP 2/3" sensor of 2448 × 2048 pixels at 3.45 µm, which is 2448 × 3.45 µm = 8.45 mm wide and 2048 × 3.45 µm = 7.07 mm high, an 11 mm diagonal matching the 2/3" circle. The drawing calls ±0.05 mm on the 20 mm width, so the 0.1 mm tolerance band must span at least 8 pixels: pixel size at the object ≤ 0.1 mm / 8 = 12.5 µm.

The rules: m = sensor width / field of view, then f = WD × m/(1+m), then object pixel size = pixel pitch / m. The arithmetic:

• Magnification: m = 8.45 / 25 = 0.338.
• Focal length: f = 100 mm × 0.338 / 1.338 = 25.3 mm, so the nearest standard is 25 mm.
• Working distance shifts with the 25 mm lens: WD = 25 × 1.338 / 0.338 = 99 mm.
• Object pixel size: 3.45 µm / 0.338 = 10.2 µm = 0.0102 mm.
• Pixel budget: 10.2 µm ≤ 12.5 µm, an 18% margin.
• Height check: 20 mm / 0.0102 mm ≈ 1960 pixels, 88 inside the 2048 available.

Decision: with the part at a fixed height, a 25 mm lens at about 99 mm WD meets the gauge, with software distortion correction handling the bend. If the part height can vary ±1 mm at that WD, the entocentric scale error is about 1%, which is 0.2 mm on the 20 mm width, four times the whole tolerance band; move up to the 0.3-0.6x telecentric class at the same magnification and accept the longer barrel. The object space pixel size guide runs the same arithmetic from the pixel side, and the calculator below reproduces the focal length.

Terms the application sheets add

A few terms describe the job rather than the optics. AOI (automated optical inspection) is camera-based inspection of populated circuit boards; OCR reads printed characters; metrology is measurement with traceable accuracy. Backlighting places the light behind the part to silhouette its outline, the standard set-up for dimension gauging, and collimated versus diffuse backlight changes the edge quality, as the collimated backlight comparison shows. A line scan camera exposes a single row of pixels and builds the image as the part moves. Scheimpflug is the rule that tilts the plane of focus when you tilt the lens, used to sharpen a long slanted surface in one shot; Scheimpflug optics explained walks the geometry.

Which term decides what, and the order to fix them

Fix the terms in this order and the datasheet selects itself:

1. Field of view and sensor format give magnification: m = sensor width / FOV.
2. Tolerance versus height variation decides telecentric or not; budget about 1% scale error per millimetre of depth change at a 100 mm WD for a standard lens.
3. The pixel budget checks magnification: object pixel = pixel pitch / m, with the tolerance band spanning at least 8 pixels.
4. Working distance gives focal length: f = WD × m/(1+m).
5. Depth versus light gives the F-number: diffraction of 2.44 × λ × F# on one side, exposure on the other.
6. Contrast at Nyquist: read the MTF curve at 1/(2 × pixel pitch).
7. Distortion: assign it to software calibration or buy it down in the optics.

Before you order, check that you have:

• Sensor format, resolution and pixel pitch written down.
• Field of view with a 5-10% margin over the part.
• Magnification and object pixel size computed, not guessed.
• Working distance from the machine layout, with the lens length checked against the space.
• An F-number chosen from tolerance and light budget.
• A distortion budget assigned to software or to the lens.

The machine vision lens selection guide turns these terms into a full selection workflow. Browse the lenses and telecentric lenses categories, use the lens finder, or start at the lens configurator; more guides sit on the lenses topic page.