So lesen Sie MTF-Kurven: Kontrast, Raumfrequenz und Sensorabgleich für die industrielle Bildverarbeitung
MTF steht für den Kontrasttransfer im Verhältnis zur räumlichen Frequenz. Dieser Leitfaden behandelt sowohl die beiden Diagrammformate als auch sagittale und tangentiale Kurven, Daten zur Bildfeldposition, die Sensoranpassung anhand des Pixelabstands sowie den Unterschied zwischen der theoretischen MTF und der gemessenen MTF.
An MTF curve plots how much contrast a lens transfers from scene to sensor, on a scale of 0 to 1, against spatial frequency in line pairs per millimeter (lp/mm).
To read one: calculate the Nyquist frequency of your sensor, read the lens contrast across the frequency band your task actually samples, which we start at 0.5× to 0.7× of that frequency, at the field positions your algorithm uses, and check that the sagittal and tangential curves stay close together. A lens that looks strong at the center can still fall short at the edge of the image circle, so field-position data matters as much as the on-axis curve.
Was ist MTF?
MTF, the modulation transfer function, is the ratio of image contrast to object contrast as a function of spatial frequency, measured in line pairs per millimeter (lp/mm). An MTF of 1.0 means the lens transfers full contrast at that frequency, while 0.3 means only 30% survives. Every MTF value is tied to a specific frequency, field position, and test condition.
One line pair is one dark bar plus one adjacent bright bar. A spatial frequency of 50 lp/mm packs 50 such pairs into one millimeter on the sensor, so higher lp/mm means finer detail. A 10µm line width in a periodic pattern, 20µm per pair, is 50 lp/mm; a 5µm line width is 100 lp/mm. An isolated feature has no single frequency and does not convert this way.
MTF is field-dependent: the same lens usually measures higher at the center than at the edge, so a full characterization reports curves at several image heights.
Wie liest man eine MTF-Kurve?
Identify the plot format first. MTF vs spatial frequency fixes the field position and sweeps detail fineness. MTF vs image height fixes the frequency and sweeps from center to corner. Read contrast at the frequencies your sensor samples and the field positions your algorithm uses, on both curves.
A datasheet with only one format is half a specification. Commonlands publishes both for its measured M12 lenses.
Ablesen der Frequenzachse
On an MTF vs spatial frequency chart, the x-axis runs in lp/mm and the y-axis runs from 0 to 1.0, or 0 to 100% on some datasheets. The information is in how fast the curve falls and where it sits at the frequencies you care about.
Datasheets usually overlay curves for several field positions: on-axis, around 0.7 field (70% of the lens's specified maximum image height), and full field. That maximum is the image-circle radius, not necessarily half the sensor diagonal. Each position carries sagittal and tangential traces. Higher and flatter is better across the band your application samples. The sensor-matching section derives that band from pixel pitch.
Was bedeuten sagittale und tangentiale MTF-Kurven?
Sagittal curves plot contrast for features oriented radially, along the line from the image center outward. Tangential curves plot contrast for features perpendicular to that radius. The two are identical on-axis for a perfectly centered, rotationally symmetric design.
A wheel makes it concrete: sagittal features run like spokes; tangential features run like the rim. Off-axis in an astigmatic lens, spoke-oriented and rim-oriented detail focus at slightly different distances, so one orientation is sharp while the other is soft at a single focus setting.
The separation is a diagnostic signal. On-axis, an S-T split points to assembly asymmetry such as decenter or tilt, though test-fixture misalignment can produce the same signature. Off-axis, a widening gap indicates astigmatism building toward the image boundary: round holes image as ellipses near the corners, and edge thresholds tuned at one orientation misfire at another. When feature orientation is fixed, verify the lower of the two curves at your operating frequency.
Wie liest man MTF- und Feldpositionskurven?
An MTF vs field curve plots contrast at a fixed spatial frequency against image height, the distance from the optical axis in millimeters. The center sits at 0mm, while the maximum is the image height the lens is specified to cover, the radius of its image circle. Only a matched format puts the sensor half-diagonal at that endpoint. A flat curve means uniform performance. A steep drop usually marks where correction runs out.
Convert your sensor geometry to image height before reading. A 1/1.7" sensor has a diagonal of about 9.4mm, so its corner sits near 4.7mm image height. Format names do not map exactly to millimeters, so take the diagonal from the sensor datasheet, not the format label. The sensor size and lens compatibility guide covers image circle coverage and format math.
Two shapes call for different responses. A smooth, moderate decline that still clears your contrast threshold at the corner is normal for a well-corrected design. A cliff at a specific radius usually marks a design boundary, and no focus adjustment fixes the soft corners a sensor gets by reaching past it.
Confirm the cause before you accept that reading: defocus, field curvature, vignetting, sensor or target tilt, fixture misalignment, and assembly decenter bend a field curve the same way, and a through-focus sweep separates them. Wide-angle designs face the hardest field demands, so a 4mm lens covering 98° needs field MTF verified at several image heights, not a center measurement extrapolated outward.
Wie passt man die MTF des Objektivs an den Pixelabstand des Sensors an?
Calculate the sensor's Nyquist frequency, 1000 divided by twice the pixel pitch in µm, then read the lens MTF at every field position your algorithm uses. Commonlands starts at 0.5× to 0.7× of Nyquist and at an MTF near 0.3. Both are heuristics, not standards, so validate them against your task: the band that matters follows from your feature size and contrast, and whether the lens limits the system depends on the whole chain of sampling, sensor, ISP, noise, and task tolerance.
That band sits below Nyquist because the sampled response there is set by more than the lens: pixel aperture, a color filter array and its demosaic, an optical low-pass filter, sampling phase, noise, and the ISP. A monochrome sensor with no OLPF holds contrast much closer to Nyquist, at the price of aliasing.
For a 1.85µm sensor, that band spans roughly 135 to 190 lp/mm. Against the 0.3 starting point, a lens that clears it there carries contrast the sensor can digitize, while one near 0.2 at half-Nyquist leaves those extra pixels resolving less detail than their count implies. Both readings are starting calls, not verdicts.
Festlegen des Kontrastschwellenwerts
No universal MTF threshold guarantees reliable machine vision, and an application name alone does not fix an image-plane frequency. That comes from the smallest feature the task reads, carried into the image plane by magnification, and it shifts with field position, spectrum, and scene contrast. Fix those first. The rows below are Commonlands starting heuristics, not published engineering standards; derive your own from feature size, magnification, field, wavelength, aperture, and a task acceptance criterion.
| Anwendung | Typical image-space frequency (lp/mm at the sensor) | MTF-Zielwert (Ausgangswert) | Anmerkungen |
|---|---|---|---|
| Lesen von 1D-Barcodes | 10–40 lp/mm | 0,4 bei der Frequenz der schmalen Balken | Breite Balken sind fehlertolerant; schmale Code-128-Balken mit hoher Dichte hingegen nicht |
| OCR | 40–80 lp/mm | 0,3 bei der Hubfrequenz | Die Strichbreiten der gedruckten Zeichen betragen auf dem Objekt in der Regel etwa 100–400 µm, je nach Schriftgröße und Druckverfahren |
| Prüfung auf Oberflächenfehler | Festgelegt anhand der Mindestfehlergröße | 0,3 bei der Defektfrequenz | Aus der Kombination von Defektgröße und Vergrößerung ergibt sich die Strukturgröße auf dem Sensor, woraus sich die Frequenz ergibt |
| Maßprüfung | 50–150 lp/mm | 0,4 bei der halben Nyquist-Frequenz, gleichmäßig über das gesamte Feld verteilt | Bei der Subpixel-Kantenerkennung muss zudem das Verzerrungsbudget separat überprüft werden |
| Objekterkennung mittels KI/CNN | 20–60 lp/mm | 0,3 im mittleren Frequenzbereich, gleichmäßiges Feld | CNNs vertragen „weiche“ Optiken besser als kantenbasierter Code, aber die Optiken für Training und Einsatz sollten übereinstimmen |
Zusammenhang zwischen der Frequenz im Bildraum und der Größe der Merkmale in der Szene
MTF is specified in the image plane, so object-space features must be converted through magnification. Image-space frequency equals object-space frequency divided by the magnification m (image size over object size). At m = 0.1, a 10 lp/mm pattern in the scene lands at 100 lp/mm on the sensor, so that is the frequency to read. The field of view calculator gives the magnification for your geometry.
Aperture belongs in the same calculation: stopping down one to two stops often lifts off-axis MTF as aberrations shrink faster than diffraction grows. On the fixed-aperture M12 lenses Commonlands measures, that operating point is set at purchase. A C-mount iris can be tuned at the fixture.
Was ist der Unterschied zwischen der theoretischen MTF und der gemessenen MTF?
Design MTF is computed from the lens prescription in optical design software, with every element at its nominal position. Measured MTF is instrument data from a physical lens. It includes the decenter, tilt, spacing error, and glass variation a real build carries, so as-built MTF is typically lower than the design curve. Tolerance analysis predicts a distribution rather than one line. Two units of the same design measure differently, so acceptance should use measured data.
A standard report covers MTF vs spatial frequency and MTF vs field at 9 field points across 3 azimuths, plus EFL and distortion at 21 points. It also covers lateral and longitudinal chromatic aberration at 480nm, 546nm, and 644nm. Astigmatism and field curvature are included, with through-focus MTF on request.
Curves are measured on a Trioptics ImageMaster HR2, with calibration documentation available on request, so a report can back incoming inspection and lot acceptance. The $199 report is open to customer-supplied lenses, and near-infrared users can request 850nm and 940nm. Current scope and pricing are on the MTF testing service page.
Eine Kurve bei F/2,0, Unendlich-Fokus und 546 nm lässt sich nicht direkt mit einer Kurve bei F/5,6, 500-mm-Konjugat und breitbandigem Weißlicht vergleichen. Beides sind gültige Messwerte für unterschiedliche Betriebspunkte. Ein Anbieter, der nur die MTF-Kurve in der Bildmitte bei voller Blendenöffnung und einer einzigen Wellenlänge angibt, präsentiert damit den günstigsten Wert – nicht den Wert, den Ihre Anlage tatsächlich erzielen wird.
MTF-Messoptionen im Vergleich
Three routes produce MTF data, and they do not measure the same thing. Pick the cheapest route that isolates the variable you need to qualify.
| Vorgehensweise | Was damit gemessen wird | Relative Kosten | Optimale Passform |
|---|---|---|---|
| Interne Prüfung mit schrägkantigem Messstab (ISO 12233-Testbild plus Auswertungssoftware) | MTF auf Systemebene: Objektiv, Sensor und Bildsignalprozessor (ISP) zusammen, bei Ihrem Arbeitsabstand | Am günstigsten: ein ausgedrucktes Zielbild und Software auf Hardware, die Sie bereits besitzen | Gut/Schlecht-Prüfungen an Ihrer eigenen Produktionslinie |
| Commonlands MTF testing on the Trioptics ImageMaster HR2 | MTF der Linse auf Komponentenebene auf einem kalibrierten Prüfstand, in Abhängigkeit von der Frequenz und dem Bildfeld an 9 Positionen über 3 Azimute hinweg | 199 Dollar pro Objektiv, keine Anschaffungskosten | Incoming inspection or lot acceptance without owning a bench |
| Spezielle Laborgeräte oder Laborzeit bei Trioptics oder Optikos | MTF auf Komponentenebene sowie umfassendere optische Messtechnik, angepasst an Ihren Durchsatz | Höchster Wert; Investitionsgüter oder Wartungsdienstleistungen pro Stunde | Eingangsprüfung in großem Umfang oder ein internes Messtechniklabor |
MTF-geprüfte Objektive und der MTF-Prüfservice
Commonlands measures lens designs on the Trioptics ImageMaster HR2, so selection decisions can rest on measured curves rather than design plots. Three MTF-tested options cover the demand space: the CIL560 4mm C-mount for wide-field coverage, the CIL561 6mm C-mount for a tighter field on the same 1/1.7" format, and the CIL122 IR-corrected 12mm M12 for near-IR work. The test service applies the same instrument to lenses you supply.
Commonlands stocks a broad range of M12 lens variants in the US, with C-mount and filter inventory alongside. Orders placed before 12 PM PT ship same day from San Diego, CA. ISO 9001:2015 certified.
Häufig gestellte Fragen
Was bedeutet MTF bei einem Objektiv?
MTF, the modulation transfer function, is the ratio of image contrast to object contrast at a given spatial frequency, expressed in line pairs per millimeter (lp/mm). An MTF of 1.0 means full contrast transfer, while 0.3 means only 30% survives. It is a curve across frequency and field position, not a single sharpness score.
Wie liest man ein MTF-Diagramm?
Bestimmen Sie zunächst das Format: Bei MTF-Diagrammen im Vergleich zur räumlichen Frequenz wird der Kontrast in lp/mm an festen Bildfeldpositionen dargestellt, während bei MTF-Diagrammen im Vergleich zur Bildhöhe der Kontrast in Abhängigkeit von der Bildfeldposition bei festen Frequenzen dargestellt wird. Lesen Sie den Kontrast in dem Frequenzband ab, das Ihr Sensor abtastet, an den Bildfeldpositionen, die Ihr Algorithmus verwendet, und vergleichen Sie die sagittalen und tangentialen Kurven hinsichtlich des Astigmatismus.
Was bedeutet „sagittal“ im Vergleich zu „tangential“ in einem MTF-Diagramm?
Sagittal curves describe contrast for features oriented radially, like spokes pointing at the image center. Tangential curves describe features perpendicular to the radius. They are identical on-axis for a centered design. On a measured unit, an on-axis split points to asymmetry in the assembly such as decenter or tilt, though test-fixture misalignment can produce the same signature. A large gap off-axis indicates astigmatism: round objects image as ellipses, and edge sharpness depends on orientation at that field height.
Wie passt man die MTF an den Pixelabstand an?
Calculate the Nyquist frequency: 1000 / (2 × pixel pitch in µm). A 1.85µm pixel gives 270 lp/mm. A 3.45µm pixel gives 145 lp/mm. Then check lens MTF across the band your task samples, at the field positions your algorithm uses. Commonlands starts near 0.5× to 0.7× Nyquist and at an MTF near 0.3; both are heuristics to validate against your task, not standards, and final resolution depends on the whole imaging chain.
Was ist der Unterschied zwischen der theoretischen MTF und der gemessenen MTF?
Die Konstruktions-MTF ist die aus der optischen Verschreibung in der Konstruktionssoftware abgeleitete Vorhersage, bei der jedes Element perfekt gefertigt und positioniert ist. Die gemessene MTF wird mit einem Messgerät ermittelt, das eine physische Linse prüft, und berücksichtigt Fertigungstoleranzen wie Dezentrierung, Neigung und Abstandsfehler. Tatsächlich gefertigte Linsen liegen in der Regel unterhalb der Konstruktionskurve, daher sollten bei der Abnahmeentscheidung die gemessenen Daten herangezogen werden.
Benötigen Sie MTF-Daten für ein bestimmtes Objektiv?
Send the Commonlands engineering team your sensor, pixel pitch, working distance, and the field positions your algorithm uses. We will pull measured curves or run a Trioptics HR2 report on the lens in question.