Choosing a lens for 3.45 micron pixel pitch 5 MP sensors

Five-megapixel cameras with 3.45 µm pixels dominate the 2/3-inch machine vision class, and they expose a mismatched lens fast: the preview looks sharp, the corners smear, and decode rates drift. The cure is arithmetic before shopping. This guide gives you the target spatial frequency for a 3.45 µm pixel, the image-circle floor for the format, the aperture range where the pixels still earn their keep, and one worked example that turns a field of view and a working distance into a focal length and a lens class. Afterwards you can read any lens data sheet the way its designer wrote it, at a spatial frequency, an image height and an aperture, and shortlist the part that holds 145 lp/mm where your part sits.

The target: 145 lp/mm at the sensor

Pixel pitch sets the sampling rate, and the sampling rate sets the finest pattern the sensor can record. A 3.45 µm pitch packs about 290 pixels into every millimetre of sensor, and one line pair needs two pixels, so the Nyquist frequency follows directly:

One Nyquist pair spans 6.9 µm, exactly two pixels. Anything finer aliases into moiré instead of resolving, so contrast at 145 lp/mm is the quantity you are buying, not a centre-resolution headline. When a data sheet rates a lens for 5 MP on 2/3-inch, the designer balanced the optics so usable contrast survives near 145 lp/mm across the full image circle. The Nyquist budget method for matching lens resolution to pixel size arrives at the same number from the pixel side.

An 11 mm image circle, or the corners go dark

The same sensor class runs 2448 × 2048 pixels. Pitch times pixel count gives the active area: 8.45 × 7.07 mm with an 11.0 mm diagonal. That diagonal is the 2/3-inch format, and it is the hard floor for the image circle: a lens projecting less than 11 mm vignettes every corner of every frame.

Format names are shorthand, not guarantees. A 1/2-inch lens covers an 8 mm circle and darkens this sensor's corners; a 1-inch or 1.1-inch lens covers 11 mm with margin, and oversizing costs nothing optically. The lens sensor format explainer maps the inch names to circles. Still choosing the camera half? The area scan cameras category filters by resolution, format and shutter.

Where the resolution goes: aperture, distance, corners

Three variables decide whether the rating reaches your bench.

Diffraction sets the ceiling. A perfect lens at f-number N cuts off at 1/(λN); at 550 nm that gives:

These are ceilings for an aberration-free lens; real optics sit below them, worst in the corners. Treat f/8 as the narrowest useful aperture on a 3.45 µm sensor, and past f/11 diffraction alone erases the Nyquist contrast. In 850 nm IR light the same table drops by about a third, with the f/4 ceiling falling from 60% to 40%. The Airy disk and diffraction limit guide derives the cutoff.

Distance and wide apertures raise the aberrations. A rating is measured at stated conditions, typically mid-range distances and moderate apertures. The corner contrast you get wide open at 500 mm can be a fraction of the plotted value, so read the curves at your own distance: the sensor resolution in lp/mm guide converts pitch to the plot's axis, and MTF curves for lens selection shows how to read them.

Corners are the weak half. The 2/3-inch circle has a 5.5 mm radius, and plots print separate curves out to that corner. Centre sharpness says nothing about the top-right corner where your barcode sits; read the 5.5 mm curve at your aperture first.

Worked example: 100 mm field of view at 300 mm working distance

Inputs. The part is a 90 mm wide connector housing; with margin the field needs 100 mm of width (task requirement). The camera is the standard 5 MP 2/3-inch class: 2448 × 2048 pixels at 3.45 µm, sensor width 8.45 mm, diagonal 11.0 mm (pitch × pixel count). The stand holds the lens about 300 mm above the part (bench geometry). Blur of one Nyquist pair, c = 6.9 µm, is acceptable (the two-pixel limit), and the start aperture is f/4.

Rules. Magnification is sensor width divided by field of view; focal length follows from the working distance; total depth of field grows with f-number and the accepted blur circle:

Arithmetic.

1. m = 8.45 mm ÷ 100 mm = 0.0845
2. f = 300 mm × 0.0845 ÷ 1.0845 = 23.4 mm; no standard class sits there, so take 25 mm and refit the distance: WD = 25 mm × 1.0845 ÷ 0.0845 = 321 mm
3. Object resolution: 2 × 3.45 µm ÷ 0.0845 = 82 µm features, equivalently 145 lp/mm × 0.0845 = 12.3 lp/mm at the part
4. Depth of field at f/4: 2 × 4 × 0.0069 mm × 1.0845 ÷ 0.0845² = 8.4 mm total, ±4.2 mm; at f/5.6 the same arithmetic gives ±5.9 mm with the diffraction ceiling still at 45%

Result and decision. Order a 25 mm, C-mount lens rated 5 MP or better on 2/3-inch, run it near 321 mm working distance, and you get 82 µm two-pixel resolution with ±4 mm of depth at f/4, ±6 mm at f/5.6. If the features must drop below 80 µm, this field is too wide: the same sensor resolves 40 µm at a 49 mm field (m = 6.9 µm ÷ 40 µm = 0.1725). If depth must reach ±8 mm, either accept f/8 and its 25% ceiling or reduce magnification; never stop past f/11. The aperture and depth of field guide works the DoF formula in full, and the camera resolution guide for dimensional inspection covers the more-pixels route.

Focal length to field of view at 300 mm working distance

For quick bracketing, thin-lens estimates with m = f ÷ (WD − f) and the 8.45 mm sensor width; real lenses shift the true distance by a few percent, so set the final focus on the stand:

Every lens in the table must still be rated 5 MP on 2/3-inch; a 3 MP-class optic at the same focal length loses the feature numbers in the corners. The machine vision lenses category filters by focal length, format, resolution and type.

Three catalogue routes for this sensor

Standard bench geometry: a 2/3-inch, 6 MP-rated C-mount fixed focal in the focal length the table calls for. The 8 mm wide-angle and the 35 mm below bracket most fields; the 36.61 mm anti-vibration model is the one for stands that shake:

All 3 share: Mount C-mount. Values as printed in each product's data sheet; open a part for its drawing and full specifications.

Measurement and headroom: when the station gauges dimensions, distortion is the printed number to hold. The 16 mm optic below rates 20 MP on a 1.1-inch circle with <0.3% distortion:

That larger circle covers the 2/3-inch diagonal with room to spare, which is exactly the headroom route: the format survives a later retrofit to a higher-resolution sensor, and the distortion figure is already at gauging grade.

Gauging without perspective error: a fixed-magnification telecentric keeps the image scale constant across the depth range, which ordinary lenses cannot. The 0.4x model below works at 227 mm:

At 0.4x, the 8.45 mm sensor width maps to a 21 mm field, the classic size for small-part dimensional checks. The lens finder filters type to telecentric when the part demands it.

Checks before you order

• Image circle at or above 11 mm on the data sheet, for the 2/3-inch diagonal.
• The 5 MP rating stated on 2/3-inch, not only on a smaller format.
• MTF at 145 lp/mm at the 5.5 mm image height, at your aperture and distance, not just the centre curve.
• Focal length from your FOV and WD arithmetic, with the focus ring reaching your distance at the working aperture.
• Distortion under 0.3% if the station measures dimensions.
• Mount: this sensor class is C-mount; a CS-mount optic needs the 5 mm adapter, and the C-mount vs CS-mount guide covers the back-focus change.
• Focus and iris rings locked after alignment; the lens locking screws guide explains how unlocked rings walk off focus.
• Fans, presses or robots on the frame point you to the anti-vibration build.

When the 145 lp/mm rule bends

• Sub-pixel edges. Tenth-pixel edge algorithms are routine on sharp, high-contrast edges, but they locate edges; they do not separate two features closer than the two-pixel limit.
• Moving parts. Motion blur adds straight to the feature budget, so keep the smear under one sensor pixel and pick a global shutter for moving targets.
• Changing distances. If the working distance moves between setups, liquid lens autofocus saves a refit.
• Features well under 50 µm across a wide field. No 5 MP 2/3-inch combination gets there; step up the sensor pixels or go line scan. The 25 µm at 10 cm working distance example shows what short-distance macro demands instead.

Shortlist from the numbers, then settle focus on the bench. Start the configurator to pair the camera and lens, and send your field of view, working distance and feature size through the contact page for a second pair of eyes on the MTF curves. The lenses topic page collects the rest of the selection guides.