Sensor resolution in lp/mm: match lens MTF to pixel pitch

Sensors have outpaced lenses. A modern industrial camera parks 2.4 µm and smaller pixels behind a C-mount, and every one of those pixels asks the lens for contrast at spatial frequencies many FA lenses never reach. The classic symptom is a 20 MP image that resolves like 5 MP: crisp in the center, smeared in the corners. The fix is one conversion. Turn the pixel pitch into the sensor's Nyquist frequency in lp/mm, then buy the lens against that number instead of against the megapixel count. This guide shows the conversion, the data-sheet reading that goes with it, the diffraction ceiling at your working aperture, and worked camera-lens pairings for the common pixel pitches.

What does lp/mm on a lens data sheet actually measure?

A resolution figure in lp/mm counts how many alternating dark and light stripe pairs per millimeter the lens still delivers with usable contrast, so a lens quoted to 145 lp/mm puts one full black-and-white pair every 6.9 µm on the sensor.

A line pair is one black stripe plus one white stripe, so at 145 lp/mm each stripe is 3.45 µm wide — the unit pairs naturally with pixel pitch. No lens passes every frequency at full contrast: contrast falls as the stripes get finer, and the graph of contrast against frequency is the modulation transfer function, or MTF. Most industrial lens sheets quote the frequency where MTF falls to 30%, some to 10% or 20%, so check which contrast level a quoted figure assumes before comparing two lenses. Listings in the machine vision lenses catalog often state it as a center/corner pair — 160/130, for example — and the lens contrast and resolution guide walks through the full curve.

How do you convert pixel pitch into the lp/mm a lens needs?

Divide 1,000 by twice the pixel pitch in micrometers to get the Nyquist frequency in lp/mm: a 3.45 µm pixel gives 1,000 ÷ (2 × 3.45) = 145 lp/mm, a 2.4 µm pixel gives 208 lp/mm, and a 4.5 µm pixel gives 111 lp/mm.

One pair spans two pixels at the limit, hence the factor of 2. If the camera sheet hides the pixel pitch, rebuild it: sensor width divided by horizontal pixel count. A 7.1 mm wide sensor with 4,000 pixels across has 1.78 µm pixels and a Nyquist frequency near 281 lp/mm.

The camera-side view of the same limit — what a sensor can and cannot record at Nyquist — is the subject of Nyquist limit and camera resolution: match sensor to lens.

Which MTF number on the data sheet do you compare it with?

Compare the sensor's Nyquist frequency with the lens's MTF percentage at that same frequency, read at both the center and the corner of your sensor's format; if the sheet quotes only one resolution figure, treat it as a center value and expect the corner to be lower.

A lens whose sheet says 160 lp/mm at MTF 30% passes 30% contrast out to 160 lp/mm — at the point where the measurement was taken, normally the center. Your 3.45 µm camera needs useful contrast to 145 lp/mm, so that lens clears the bar in the middle, but the corner is a different measurement made out at the edge of the image circle, where aberrations have already bent the curve. Both corner curves matter, because the tangential value (stripes across the radius) and the sagittal value (stripes along it) fall differently. Confirm too that the image circle covers the sensor diagonal; the format logic behind that check is in Lens sensor format: 1/1.8 inch, 2/3 inch and 1 inch lenses.

How sharp can a lens be at your working aperture before diffraction caps it?

Even a perfect lens loses contrast as you stop down, so keep the diffraction cutoff — 1,000 ÷ (0.55 × f-number) lp/mm in visible light — at about twice your Nyquist frequency: roughly F5.6 or brighter at 145 lp/mm, and F4 or brighter at 208 lp/mm.

The cutoff f_c = 1,000/(λ × N) is the finest pattern diffraction lets through at all. At a cutoff of 2× the Nyquist frequency, perfect optics still hold roughly 40% contrast at f_N, and real lenses hold less, which is why the working target is 2× or better.

As a rule, keep the f-number no slower than the pixel pitch divided by the wavelength in µm: N ≤ 3.45/0.55 = 6.3 for a 145 lp/mm sensor in white light. Stopping down also tames aberrations, so deepest focus and highest resolvable detail pull against each other; Optical aberrations in machine vision lenses: how stopping down helps covers the aberration half of that trade.

Why does lens resolution drop at the corners of the sensor?

Pixel pitch does not relax toward the corner — a pixel pitch of 3.45 µm at the edge of a 1.1-inch format still demands 145 lp/mm — while off-axis aberrations pull the lens's corner MTF down and split it into separate tangential and sagittal curves.

Light reaching the corner crosses the lens at an angle, so field curvature, astigmatism, coma and lateral chromatic aberration all grow with field angle. The tangential and sagittal curves separate, and a corner can pass 140 lp/mm in one orientation and 90 lp/mm in the other at the same aperture. Match the corner figure to Nyquist when a measurement or a reading must be trustworthy anywhere in the frame: gauging, OCR across a full label, defect hunting with no preferred zone. Center-class performance is acceptable only when the feature sits in a known central region, such as a code a fixture always presents at the same spot.

Which camera and lens pairs pass all three tests?

Three tests decide a pairing: the lens's corner MTF holds at least 30% contrast out to the sensor's Nyquist frequency, the working aperture keeps the diffraction cutoff near twice that frequency, and the image circle covers the sensor diagonal.

What does the arithmetic look like end to end?

Take the MV-CH120-11UC, a 12 MP USB3 camera with an IMX304 sensor in the 1.1-inch format and a global shutter. The pixel pitch follows from the sensor generation and matches the worked example above: 4,096 pixels across 4,096 × 3.45 µm = 14.1 mm, exactly this format's geometry.

Nyquist frequency: 1,000 ÷ (2 × 3.45) = 145 lp/mm. Aperture margin: at F2.8 the cutoff is 1,000 ÷ (0.55 × 2.8) = 649 lp/mm, 4.5× the Nyquist frequency; at F5.6 it is 325 lp/mm, still 2.2×; beyond F8 the margin is gone. The lens that clears all three tests on this format is the LS-FFL-0567, a 16 mm C-mount lens covering 1.1-inch at a 20 MP rating, F2.8-22, distortion below 0.3%.

The shortlist pick for this exact pairing:

The fine-pixel case is harder. The MV-CS200-10GC is a 20 MP color GigE camera on a 1-inch IMX183 sensor with a rolling shutter, and that sensor generation runs 2.4 µm pixels. Nyquist frequency: 1,000 ÷ (2 × 2.4) = 208 lp/mm. The aperture rule gives N ≤ 2.4/0.55 = 4.4, so F4 is the slowest usable stop in white light, and only 20 MP-class lenses stay in the running.

The camera that defines the fine-pixel class:

The coarse end is forgiving. The LS-FFL-0679 is a 35 mm C-mount lens rated for 6 MP sensors on the 2/3-inch format. That sensor class runs the same pixel pitch and 145 lp/mm requirement on a smaller circle, where corner performance comes easier at any given aperture.

The 65 MP row compresses the pitch again and moves to M58 and M72 mounts; Large format machine vision lens: M58 and M72 for 65 MP and up covers that family, which includes the LS-FFL-1676, a 60 mm M58 lens for 65 MP sensors with working distance from 214 to 1536 mm.

Three fixed-focal lenses from the catalog line up across those classes:

Values as printed in each product's data sheet; open a part for its drawing and full specifications.

When is a camera change better than a sharper lens?

When no lens in your mount and working distance holds 30% MTF to the sensor's Nyquist frequency at the corners, the honest fix is the camera: a 12 MP sensor at 145 lp/mm behind good glass out-resolves a 20 MP sensor at 208 lp/mm behind a lens that stops at 130 lp/mm.

A 20 MP 1-inch sensor delivers its advertised detail only if the whole chain passes 208 lp/mm center and corner; otherwise the extra pixels average blur, not information. The small pixel camera selection guide frames that trade from the sensor side, and the pixel rule for sizing defect-detection resolution tells you how many pixels the feature actually needs. Work backwards through the chain: required object-space detail first, pixel rule second, Nyquist frequency third, lens last — not the megapixel headline first.

What do you check before ordering the pair?

Run five checks before you order: compute the Nyquist frequency from the pixel pitch, confirm the image circle covers the sensor diagonal, read the corner MTF at Nyquist in both orientations, set the aperture for diffraction headroom, and confirm the mount reaches true focus on your flange.

1. Compute pixel pitch as sensor width ÷ horizontal pixels, then the Nyquist frequency as 1,000 ÷ (2 × p) in lp/mm. Write the number on the project sheet; every lens decision refers back to it.
2. Check image circle against sensor diagonal, with margin for focus travel and filter shifts.
3. Read corner MTF at the Nyquist frequency, tangential and sagittal both; 30% is the usual sheet benchmark.
4. Set the aperture so the cutoff stays near 2× Nyquist: N ≤ p/0.55 in white light, tighter under 850 nm illumination.
5. Check mount and flange depth so the lens reaches true focus; C mount vs CS mount: adapters, focus and clearance covers the adapter arithmetic.

Decision restated: the lens must hold usable MTF out to 1,000 ÷ (2 × pixel pitch) lp/mm at the corners of your sensor's format, at an aperture no slower than about pixel pitch ÷ wavelength. Shortlist by that number in the lens finder, match cameras in the camera finder, or step through the lens configurator. The lenses topic page collects related guides, and pairing questions go to us through the contact page.