Räumliche Auflösung in der Bildverarbeitung: mm pro Pixel, kleinste erkennbare Größe und Beugungsgrenze
Field of view, pixel count, lens resolving power, and aperture combine to set the smallest feature a camera system can detect.
Spatial resolution is the real-world size one pixel samples at the working distance: the sampling interval, not the smallest feature the system can resolve. Divide the field of view by the pixel count across it: a 100mm wide FOV on 2592 horizontal pixels gives 0.039mm per pixel. The smallest reliably detectable feature must span several pixels, typically 3 to 5 for detection and 10 or more for measurement.
Pixel math sets the ceiling, not the result. The lens must resolve the spatial frequency the pixel pitch demands (the Nyquist rule, lp/mm = 1 ÷ (2 × pixel pitch in mm)), and the aperture controls the diffraction Airy disk (d = 2.44 × λ × F#): once the disk grows past roughly two pixel pitches, diffraction erodes fine detail gradually. This guide covers all four layers: pixel math, angular sampling (IFOV), lens resolving power, and diffraction.
What Is Spatial Resolution in Machine Vision?
Spatial resolution is the real-world size one pixel samples at the working distance, written as mm per pixel: a sampling interval (strictly, the object-space sampling distance; ground sample distance in remote sensing), not the smallest feature the system resolves. Two numbers set it: field of view and pixel count along that axis. A 12MP camera (4032 × 3024) on a 600mm wide tote has 0.149mm per pixel; on a 60mm connector it has 0.0149mm per pixel, ten times finer. Only the field of view changed.
If one pixel covers 0.1mm, a 0.05mm scratch is sub-pixel and usually lost unless its contrast is high; a 0.4mm scratch spans four pixels and is detectable. Its distance-independent counterpart is the per-pixel angle, covered in the IFOV section. A megapixel count is only a pixel budget, so this guide also covers resolving power and diffraction, with Commonlands M12 and C-mount examples.
How Do You Calculate mm per Pixel?
Divide the field of view by the pixel count along the same axis. A 100mm wide scene on 2592 horizontal pixels gives 0.0386mm per pixel. The reciprocal is pixels per mm.
Use mm per pixel for inspection sizing. Lens resolving power is quoted in lp/mm at the image plane, a different plane from object-space pixels per mm: divide an object-space frequency by the magnification to compare, or work in image space, where one line pair needs two pixels (lp/mm = 1 ÷ (2 × pixel pitch in mm)). Model any sensor, focal length, and working distance with the Commonlands FOV calculator. With noticeable distortion, the average does not hold at the frame edges.
What Is the Minimum Detectable Size in Machine Vision?
Minimum detectable size is the smallest feature a system reliably identifies. Multiply spatial resolution by the pixel coverage the task needs: minimum size = (FOV ÷ pixel count) × required pixels. Two pixels is the theoretical sampling floor, a Nyquist figure for periodic patterns that noise or blur erases; a high-contrast sub-pixel particle can still be detected, but not sized. Production inspection typically needs 3 to 5 pixels across a defect, and measurement 10 or more; both are starting heuristics moved by contrast, SNR, and algorithm.
| Aufgabe | Pixel über das gesamte Merkmal hinweg | Anmerkungen |
|---|---|---|
| Theoretische Untergrenze der Stichprobengröße | 2 | Hängt von der Subpixel-Ausrichtung und einem nahezu perfekten Kontrast ab; kein Designaspekt |
| Kontrastreiche Darstellung von „vorhanden“ und „nicht vorhanden“ | 3–5 | Praktikabler Spielraum für einen dunklen Riss auf hellem Hintergrund unter kontrollierten Lichtverhältnissen |
| Klassifizierung nach Form oder Ausrichtung | 5–10 | Genügend Details, um kreisförmige von länglichen Merkmalen zu unterscheiden |
| Kontrastarme oder strukturierte Defekte | 8–15 | Je mehr Pixel, desto mehr Signal wird über der Rauschschwelle gesammelt |
| Maßprüfung | 10+ | Subpixel-Algorithmen führen eine Verfeinerung auf ~0,1–0,3 px durch, jedoch nur an klar erkennbaren Rändern. |
Target: detect a 0.2mm scratch with 5 pixels of coverage. Required spatial resolution = 0.2 ÷ 5 = 0.04 mm/pixel. On a 2448-pixel-wide sensor, the maximum horizontal FOV = 0.04 × 2448 = 98mm. Find the focal length that produces a 98mm FOV at your working distance.
Motion Blur Eats the Pixel Budget
A part moving at velocity v during exposure t smears the image by v × t. Keeping that smear under half a pixel at your spatial resolution is a common heuristic; past it, features near the minimum detectable size start disappearing.
What Is IFOV in Machine Vision?
Instantaneous field of view (IFOV) is the angle a single pixel subtends. It is a sampling quantity, not optical angular resolution: separating two points is a Rayleigh or MTF question, and a system can sample finer than its optics resolve. IFOV = FOV ÷ pixel count gives the frame average, since the per-pixel value varies with field position. An 80° FOV across 3840 pixels averages 0.021° per pixel, or 48 pixels per degree. Multiplied by the working distance, that becomes the pixel footprint on the object.
| Objektiv | FOV (axis named) | IFOV on a 4K frame | Pixel pro Grad |
|---|---|---|---|
| CIL250 25-mm-Teleobjektiv M12 | 20° diagonal at 8.8mm reference circle; 9.4mm full image circle covers 1/1.7" | 0.0045° (diagonal) | ~220 (diagonal) |
At fixed sensor resolution, wide coverage and fine angular sampling are in tension. Because real-world contrast, noise, and blur are worse than on the bench, many teams carry a 2× to 3× design margin over the theoretical minimum pixel count; the factor depends on MTF, task contrast, sensor noise, and the detector or decoder's minimum-sampling spec.
What Does a Megapixel Rating Mean on a Machine Vision Lens?
Die Angabe der Megapixelzahl bei einem Objektiv bezeichnet die Sensorgröße, für die es ausgelegt ist (Pixelabstand plus Bildformat), nicht jedoch sein optisches Auflösungsvermögen. Das Auflösungsvermögen wird in Linienpaaren pro Millimeter auf der Bildebene gemessen, und die Nyquist-Regel legt die Anforderung fest: lp/mm = 1 ÷ (2 × Pixelabstand in mm).
| Pixelabstand | Erforderliche lp/mm (Nyquist) | Beispielsensoren |
|---|---|---|
| 5,0 µm-Klasse | 100 lp/mm | Global-Shutter-Sensoren mit größeren Pixeln |
| 3,45 µm | 145 lp/mm | Sony Pregius IMX250, IMX264 (5 MP), IMX253, IMX304 (12 MP) |
| 2,74 µm | 182 lp/mm | Sony Pregius S IMX547 (5,1 MP), IMX546 (8,1 MP), IMX541 (20,4 MP) |
| 2,0 µm | 250 lp/mm | Sony IMX678 (8 MP, 1/1,8") und ähnliche eingebettete Sensoren |
| 1,55 µm | 323 lp/mm | Eingebettete Sensoren mit hoher Dichte und Sensoren in Smartphone-Qualität |
Coverage is the second requirement: the lens image circle must be at least the sensor diagonal, or the corners vignette. The MTF check evaluates contrast near 0.5 to 0.7× the Nyquist frequency the pixel pitch sets, a Commonlands starting band rather than a standard (validate against your task), held out to the corners. Nyquist itself is a sampling ceiling, not an MTF target; a cutoff above it does not guarantee contrast holds that far. If either check fails, the lens limits the system regardless of megapixel labels.
What Is the Diffraction Limit in Machine Vision?
The diffraction limit is the minimum blur spot a lens can produce at a given aperture, set by the wave nature of light, not manufacturing quality. Stopping down shrinks aberrations but grows the Airy disk linearly with F#, so a smaller aperture eventually caps resolution.
The MTF of a diffraction-limited lens falls to zero at a cutoff frequency of 1 ÷ (λ × F#). At 550nm and F/8, that cutoff is roughly 227 lp/mm. At F/16, still at 550nm, it drops to 114 lp/mm, below the 145 lp/mm a 3.45µm sensor needs. "Diffraction-limited" is not a defect label: the lens is corrected well enough that diffraction, not residual aberration, decides image quality at that aperture.
What Is an Airy Disk?
The Airy disk is the bright central spot of the diffraction pattern from a point source imaged through a circular aperture. The first dark ring bounds it; about 84% of the pattern's energy falls inside (Hecht, Optics, 5th ed.). No lens can focus light to a smaller spot at that aperture and wavelength.
| F# | Luftscheibe bei 550 nm | Spannweiten bei 3,45 µm großen Pixeln | Spannweiten bei 2,74 µm Pixelgröße | Spannweiten bei 1,55 µm Pixelgröße |
|---|---|---|---|---|
| F/1,9 | 2,5 µm | 0,7 px | 0,9 px | 1,6 px |
| F/2,8 | 3,8 µm | 1,1 px | 1,4 px | 2,4 px |
| F/4 | 5,4 µm | 1,6 px | 2,0 px | 3,5 px |
| F/5,6 | 7,5 µm | 2,2 px | 2,7 px | 4,8 px |
| F/8 | 10,7 µm | 3,1 px | 3,9 px | 6,9 px |
| F/11 | 14,8 µm | 4,3 px | 5,4 px | 9,5 px |
| F/16 | 21,5 µm | 6,2 px | 7,8 px | 13,9 px |
Wavelength scales the disk linearly. At 850nm the Airy disk is about 55% larger than at 550nm for the same F#, so NIR systems hit diffraction at wider apertures than visible-light systems. See the NIR imaging guide for wavelength-specific notes.
Pixel-Pitch Matching: When the Sensor Out-Resolves the Lens
Compare the Airy disk to twice the pixel pitch as a marker, not a cliff: diffraction contrast falls off gradually, so useful detail survives past it. At 550nm and far conjugates, that marker lands near F/5.1 for 3.45µm pixels, F/4.1 for 2.74µm pixels, and F/2.3 for 1.55µm pixels; close in, substitute the working f-number.
With aperture and format equal, a 2.74µm 20MP sensor samples finer detail than a 3.45µm 12MP one while lens MTF keeps up; past the 2.74µm marker, diffraction erases that edge first, so the full system, not pixel count, decides.
Opening from F/11 to F/5.6 admits roughly 4× the light and halves the Airy disk. Brighter or strobed light buys back the exposure lost to a stopped-down aperture; deconvolution can partially restore diffraction-attenuated contrast, at a noise cost; nothing recovers detail past the cutoff. Pick the aperture from the depth of field your scene needs with the depth of field calculator, then check the Airy disk against twice the pixel pitch and the MTF there. The Commonlands f-number guide covers the full tradeoff.
Lens Examples Across the Resolution Range
These Commonlands lenses are a shortlist for each resolution tier. Here, supported means the published MTF holds at the sensor Nyquist band under the conditions on each product page.
Lens Picks by Resolution Requirement
| Auflösungsstufe | Empfohlenes Objektiv | Montage | F# | Kleinster unterstützter Pixelabstand | Anmerkung |
|---|---|---|---|---|---|
| 1–2 MP Eingangskontrolle | CIL028 2,6 mm | M12 | Siehe Produktseite | Nicht die einschränkende Bedingung bei 1–2 MP | Covers up to 6MP at 2.2µm; pick the lowest-cost lens that covers your format. |
| 5 MP für allgemeine Zwecke | CIL059 5.9mm | M12 | F/1,7–F/5,6 | Siehe Produktseite | Fixed-aperture M12 variants chosen at purchase. The F/1.7 build is rated 4–6MP; the F/4.0 build reaches 12MP as residual aberrations drop. |
| Prüfung mit 8–12 MP | CIL160 16 mm | M12 | F/1,9–F/5,6 | Siehe Produktseite | Varianten mit fester Blende bieten eine Auflösung von 12 MP bei F/2,8–F/4,0. Bei der F/5,6-Ausführung sinkt die Auflösung aufgrund zunehmender Beugung auf 8 MP. |
| 8–12 MP Messtechnik | CIL514 25 mm | C-Mount | F/2,8–F/16 | 3,45 µm | Adjustable iris. The Airy disk reaches two pixel pitches near F/5.1 at 550nm. |
| 8–12 MP, feiner Rasterabstand | CIL535 35 mm | C-Mount | F/2,0–F/16 | 2.2µm | Adjustable iris, rated for 2.2µm pixels at 12MP. At 550nm the Airy disk reaches two pixel pitches near F/3.3, so buy depth of field with working distance or focal length, not the iris. |
Above 12MP on formats larger than about 1.1 inch, fixed-focal C-mount FA lenses from Kowa, Fujinon, and Moritex are the established choices. The Commonlands M12 and C-mount optics above target the 1/4" to 1.1" formats. Size the field of view for any pick in the FOV calculator.
Brennweitensteuerung: Stellen Sie das Sichtfeld (FOV) und die mm pro Pixel ein
Blendensteuerung: den Kompromiss bei der Beugung bewältigen
Häufig gestellte Fragen
Was versteht man unter räumlicher Auflösung in der Bildverarbeitung?
Spatial resolution is the real-world size one pixel samples at the working distance, expressed in mm per pixel. Divide the field of view by the pixel count across it: a 100mm FOV on 2592 horizontal pixels gives 0.039mm per pixel. That is the sampling interval, not the smallest detectable feature: reliable detection needs a feature to span several pixels, typically 3 to 5.
Was ist die kleinste erkennbare Größe in der Bildverarbeitung?
Die minimale Erkennungsgröße ist das kleinste Merkmal, das ein Bildverarbeitungssystem zuverlässig identifizieren kann. Multiplizieren Sie die räumliche Auflösung mit der Anzahl der für das Merkmal erforderlichen Pixel: (Sichtfeld ÷ Pixelanzahl) × erforderliche Pixel. Bei einem Sichtfeld von 100 mm und 2048 Pixeln ergibt sich ein Wert von 0,049 mm pro Pixel; ein Erkennungsziel von 5 Pixeln bedeutet also, dass Merkmale von mindestens 0,24 mm erkannt werden können.
Was bedeutet IFOV bei einer Kamera?
IFOV (instantaneous field of view) is the angle subtended by one pixel. IFOV = FOV ÷ pixel count gives the average across the frame; the per-pixel value varies with field position. A camera with an 80° horizontal FOV and 3840 pixels averages about 0.021° per pixel, or 48 pixels per degree. Multiply IFOV in radians by working distance to get the pixel footprint on the object.
Was bedeutet „Megapixel“ im Zusammenhang mit einem Objektiv für die industrielle Bildverarbeitung?
A megapixel rating describes the sensor class a lens is designed to cover, a combination of pixel pitch and format, not its optical resolving power. Resolving power is measured in lp/mm. Two lenses with different megapixel labels can resolve identically in lp/mm. The higher label often just reflects a larger image circle for a bigger sensor at the same pixel pitch.
Was ist die Beugungsgrenze in der Bildverarbeitung?
Die Beugungsgrenze ist der kleinste Unschärfefleck, den ein Objektiv bei einer bestimmten Blende erzeugen kann, und wird durch die wellenartige Natur des Lichts bestimmt. Ein beugungsbegrenztes Objektiv bei F/8 und 550 nm kann keine Details unterhalb von etwa 227 lp/mm auflösen, und seine Airy-Scheibe hat einen Durchmesser von 10,7 µm, was mehr als drei Pixeln auf einem 3,45-µm-Sensor entspricht.
Match a Lens to Your Resolution Requirement
Send us the defect size, working distance, and sensor. The Commonlands engineering team will work through the FOV, pixel coverage, lp/mm, and aperture numbers with you, or you can run the math yourself first.