Sichtfeld in der industriellen Bildverarbeitung: Berechnung, Bildwinkel und häufige Fallstricke
The FOV formula takes three inputs, and it fails for three reasons: nominal sensor names, distortion, and fisheye projection. This guide covers the formula, the angle-of-view relationship, and the checks that keep the numbers honest.
Field of view (FOV) in machine vision is the physical size of the scene the camera captures at a given working distance. For a rectilinear lens it is FOV = (sensor width × working distance) / focal length, a far-conjugate approximation (distance from the entrance pupil in the pinhole model), where sensor width is the active imaging dimension in millimeters, not the nominal format name.
The formula fails when engineers use nominal sensor dimensions, ignore lens distortion, or apply it to fisheye lenses. Verify final numbers with the field of view calculator before ordering hardware.
Was versteht man unter „Sichtfeld“ in der Bildverarbeitung?
Field of view (FOV) in machine vision is the physical area of the scene the camera captures at a given working distance, expressed in linear units at the object plane. A 120mm horizontal field of view means the camera sees a 120mm-wide strip at the inspection distance.
FOV is not a property of the lens alone. It depends on three inputs:
- A longer focal length narrows the field of view.
- A larger active sensor widens the field of view.
- Moving farther from the object widens the field of view.
Change any one of these and the field of view changes, which makes FOV a system-level calculation, not a lens spec lookup. Working distance is a design variable early in a project and fixed once the mechanics are committed. The Commonlands working distance guide covers that tradeoff.
Wie berechnet man das Sichtfeld einer Kamera?
For a rectilinear lens, horizontal field of view equals active sensor width times working distance, divided by focal length. Use the active sensor dimensions from the camera datasheet, not the nominal format name. The angular projection is anchored at the entrance pupil, not the principal planes or the housing front; in wide-angle and retrofocus designs these points sit many millimeters apart.
Horizontal and vertical coverage use the same relation with the corresponding sensor dimension, and the diagonal follows from Pythagoras. The relation is a far-conjugate approximation, close when the working distance is long compared with the focal length. At short conjugates use thin-lens conjugates: with m = sensor width / scene width, f = WD × m / (1 + m), measured from the object-side principal plane (Hecht, Optics, 5th ed., §5.2).
Use the active imaging width from the camera datasheet, not the nominal format name. A sensor labeled 1/2" has an active width near 6.4mm. Entering 12.7mm (half of 25.4) produces a result nearly double the real field of view.
Beispiel mit Lösung
Ein 1/2,3-Zoll-Sensor hat eine aktive Breite von etwa 6,17 mm. Bei einem Arbeitsabstand von 300 mm mit einem 6-mm-Objektiv:
Auswahl der Brennweite anhand eines gewünschten Sichtfelds
Ordnen Sie die Formel um, um die Brennweite zu berechnen, wenn Sie die abzubildende Bildgröße kennen:
Round to an available focal length and re-check the coverage: a 12mm lens gives 213mm and a 16mm lens gives 160mm at that distance. The Commonlands focal length selection guide walks through the tradeoff.
Ground sample distance (scene width per pixel) is FOV_H divided by the pixel column count, and it decides whether the system resolves the required feature sizes. The Commonlands spatial resolution guide covers how it interacts with lens MTF and pixel size.
Was ist der Unterschied zwischen Bildwinkel und Sichtfeld?
Angle of view is an angular property of the lens and sensor, measured in degrees, and stays effectively constant except at close focus, where focus breathing shifts the effective focal length and distortion, so the angle drifts. Field of view is the physical scene coverage, in millimeters, that the angle produces at a specific working distance on a specific sensor. The two are related by FOV_H = 2 × WD × tan(AoV_H / 2).
| Eigenschaft | Blickwinkel (AoV) | Sichtfeld (FOV) |
|---|---|---|
| Einheit | Abschlüsse | Millimeter, Meter oder Zoll |
| Hängt das vom Arbeitsabstand ab? | Im Grunde genommen nein; bei einer bestimmten Kombination aus Objektiv und Sensor fest eingestellt, außer bei sehr naher Fokussierung | Ja; sie verdoppelt sich, wenn sich der Arbeitsabstand verdoppelt |
| Nützlich für | Objektivspezifikationen – Vergleich der Sensorformate | Erfassung des Geschehens bei bekannter Inspektionsentfernung |
Because sensors are rectangular, the angle differs by axis: HFOV uses the active width, VFOV the active height, and DFOV the diagonal. On a 6.3mm × 4.7mm active area, a 4mm lens gives roughly 76° HFOV, 61° VFOV, and 89° DFOV. Datasheets do not always state which axis a quoted angle uses, so check before comparing lenses.
Use the Commonlands angle of view calculator to confirm a lens and sensor combination hits a target angle.
Wie wirken sich Brennweite und Sensorgröße auf das Sichtfeld aus?
Field of view scales directly with active sensor width and inversely with focal length: doubling the sensor width doubles the FOV, and halving the focal length doubles it. Angle of view responds nonlinearly, so short focal lengths need tighter specification. The same scaling lets pairings match: an 8mm lens on a 2/3" sensor and a 6mm lens on a 1/1.8" sensor give similar horizontal coverage at the same distance.
Aktiver Bereich vs. nomineller Formatname
Nominal sensor format names are historical designations from tube camera outer diameters. They do not describe the imaging-area size, and using them as dimensions corrupts the FOV calculation:
| Nominales Format | Übliche Nutzbreite (mm) | Übliche Arbeitshöhe (mm) | Fehler, wenn das Format „Bruch“ als Breite verwendet wird |
|---|---|---|---|
| 1/4" | ~3.6 | ~2.7 | Bei Verwendung von 6,35 mm ergibt sich ein Fehler von ca. 76 % |
| 1/3" | ~4.8 | ~3.6 | Bei Verwendung von 8,47 mm ergibt sich ein Fehler von ca. 76 % |
| 1/2,3" | ~6.17 | ~4.55 | Bei Verwendung von 11,04 mm ergibt sich ein Fehler von ca. 79 % |
| 1/2" | ~6.4 | ~4.8 | Bei Verwendung von 12,7 mm ergibt sich ein Fehler von ca. 98 % |
| 1/1,8" | ~7.18 | ~5.32 | Bei Verwendung von 14,11 mm ergibt sich ein Fehler von ca. 97 % |
| 2/3" | ~8.8 | ~6.6 | Bei Verwendung von 16,93 mm ergibt sich ein Fehler von ca. 92 % |
Active dimensions vary by manufacturer and pixel count within a nominal format, so check the specific camera model. The CMOS sensor size guide explains the naming convention, and the Commonlands image sensor reference lists active dimensions for common sensors.
Warum verändern Verzerrung, Fischaugenprojektion und Bildkreis das tatsächliche Ergebnis?
The rectilinear FOV formula assumes straight lines map to straight lines on the sensor. Barrel distortion, fisheye projection, and an image circle mismatched to the sensor each break that assumption, so the formula can misstate usable coverage.
Barrel Distortion Splits Coverage Into Raw and Usable
Barrel distortion makes the formula answer two questions with one number, so read its result against the quantity you care about:
| Anzahl | What barrel distortion does | Formula error |
|---|---|---|
| Total angular field | Local magnification falls with field height, so the lens sees more scene than a rectilinear lens of the same focal length | Understates the true angular coverage |
| Usable low-distortion region | Geometry stays accurate only over a smaller central radius | Overstates the coverage you can measure on |
| Edge pixel scale | Each edge pixel covers more scene, so a rectified image must stretch the edges back out | Understates the scene width each edge pixel spans |
Many standard machine vision lenses approximate rectilinear projection closely enough that the gap is small. Departure from that model depends on projection and distortion correction, not focal length alone, and wide-angle designs show it most. Treat the formula result as a rectilinear reference field; the true raw field follows the measured projection and distortion curve. Derate for the low-distortion region the task needs, and specify low-distortion lenses for measurement or alignment. The Commonlands low distortion lens guide covers how they are specified.
Fisheye-Objektive erfordern eine völlig andere Berechnung
Fisheye lenses do not follow the rectilinear model. They use alternative projections such as equidistant, equisolid, stereographic, or orthographic mapping. Neither the arctan formula nor the tan conversion applies:
A 180° fisheye images a 90° half-angle cone, and converting that to a scene width needs the projection function, not the tan formula. Use the manufacturer's mapping data, which the Commonlands fisheye and wide-angle distortion guide treats in depth.
Bildkreis und Sensorausschnitt
Lenses project a circular image. If the sensor diagonal exceeds the lens image circle, the corners vignette or degrade first; the horizontal and vertical edges lose coverage only if the circle cuts inside the sensor's width or height, set by circle diameter and sensor aspect ratio. If the image circle is larger than the sensor, the sensor crops the projection: a lens rated for 2/3" sensors on a 1/2" sensor sees a narrower angle than its datasheet states.
Verify the image circle covers the sensor diagonal, and calculate with your sensor's active dimensions. The Commonlands sensor size and lens compatibility guide covers both failure modes.
Welche Objektive decken Weitwinkel-, Standard- und Engwinkel-Sichtfelder ab?
Focal lengths from 2.6mm to 25mm produce horizontal fields of view from roughly 712mm down to 74mm at 300mm working distance.
Die besten Objektive, sortiert nach Sichtfeldbereich
These five Commonlands lenses span the range at a fixed working distance, ranked widest to narrowest, from the CIL227 190° fisheye to the CIL250 25mm telephoto.
| FOV-Band | Objektiv | Halterung / EFL | Veröffentlichte Berichterstattung | Anwendung zur Best-Fit-Analyse |
|---|---|---|---|---|
| Ultraweitwinkel-Fischauge | CIL227 2,7 mm Fischaugenobjektiv | M12, 2,7 mm | 190° Sichtfeld bei einem Bildkreis von 8,0 mm (äquidistante Projektion) | Halbkugelförmige Abdeckung für Sicherheit, Drohnen und Anwesenheitserkennung |
| Breit | CIL059 6 mm, verzerrungsarm | M12, 6 mm | 76° FOV at an 8.8mm reference circle | Wide coverage; −4% rectilinear needs calibration before measurement |
| Breit | CIL062 6.2mm | M12, 6.2mm | ~347mm at 300mm WD on a 1/1.8" sensor | Budget coverage at −2% rectilinear distortion; calibrate before gauging or alignment |
| Mittel | CIL531 8 mm C-Mount | C-Mount, 8 mm | ~330 mm bei 300 mm Arbeitsabstand auf einem 2/3"-Sensor (~58° horizontales Sichtfeld) | Einstellbare Tiefenregelung mit variabler Blende bei 12-MP-Sensoren im 2/3-Zoll-Format |
| Mittel-Teleobjektiv | CIL250 25-mm-Teleobjektiv | M12, 25 mm | ~74 mm bei 300 mm Arbeitsabstand auf einem 1/2,3-Zoll-Sensor (~14° horizontales Sichtfeld) | Prüfung kleiner Details bei größeren Arbeitsabständen |
Coverage figures come from the 300mm scene-coverage table later in this section or the lens product-page datasheet. The fisheye value is equidistant-projection coverage, not a rectilinear formula result.
Wie die Brennweite den Bildausschnitt bei einem Arbeitsabstand von 300 mm beeinflusst
This Commonlands reference table shows approximate horizontal field of view for rectilinear lenses at 300mm working distance on common sensor formats. All values use active sensor widths.
| Brennweite | Sensorformat | Aktive Breite (mm) | FOV_H bei 300 mm Arbeitsabstand (mm) | Versicherungskategorie |
|---|---|---|---|---|
| 2,6 mm | 1/2,3" | 6.17 | ~712 | Sehr breit |
| 6 mm | 1/2,3" | 6.17 | ~309 | Standard |
| 6 mm | 1/1,8" | 7.18 | ~359 | Standard (größerer Sensor) |
| 8 mm | 2/3" | 8.8 | ~330 | Standard (C-Mount) |
| 25 mm | 1/2,3" | 6.17 | ~74 | Tele / eng |
The C-mount row adds an adjustable iris, so stopping down extends depth of field when a target field of view also carries a depth requirement.
Häufig gestellte Fragen
Was versteht man unter „Sichtfeld“ in der Bildverarbeitung?
Das Sichtfeld (FOV) in der industriellen Bildverarbeitung ist der physikalische Bereich der Szene, den die Kamera bei einem bestimmten Arbeitsabstand erfasst, gemessen in Millimetern in der Objektebene. Ein horizontales Sichtfeld von 120 mm bedeutet, dass die Kamera in diesem Abstand einen 120 mm breiten Streifen erfasst. Das Sichtfeld wird durch die Brennweite, die Abmessungen des aktiven Sensors und den Arbeitsabstand gemeinsam bestimmt.
Wie berechne ich das Sichtfeld eines Bildverarbeitungssystems?
For a rectilinear lens: FOV_H = (sensor width × working distance) / focal length, all in millimeters, a far-conjugate approximation (distance from the entrance pupil in the pinhole model). Use the actual active sensor dimensions, not the nominal format name. A 1/2" sensor has an active width of approximately 6.4mm, not 12.7mm. To find the focal length for a target FOV, rearrange: f = (sensor width × working distance) / target FOV. Fisheye and high-distortion lenses need a projection-corrected calculation.
Warum machen Weitwinkel- und Fischaugenobjektive die einfache Berechnung des Sichtfelds zunichte?
Die Standardformel geht von einer geradlinigen Projektion aus, bei der gerade Linien in der Szene auf gerade Linien auf dem Sensor abgebildet werden. Weitwinkelobjektive mit tonnenförmiger Verzeichnung komprimieren die Bildränder, sodass der nutzbare, unverzerrte Bildausschnitt von der Vorhersage der Formel abweicht. Fisheye-Objektive verwenden ein völlig anderes Projektionsmodell (äquidistant oder äquisolid), sodass die arctan- und tan-Formeln hier überhaupt nicht anwendbar sind.
Was ist der Unterschied zwischen horizontalem, vertikalem und diagonalem Blickwinkel?
Horizontal AoV (HFOV) uses the active sensor width, vertical AoV (VFOV) uses the active sensor height, and diagonal AoV (DFOV) uses the sensor diagonal. For a rectangular sensor, DFOV is the largest of the three. Lens datasheets may quote any axis without saying which, so check before comparing lenses. DFOV can exceed VFOV by more than 30 degrees on a 16:9 sensor.
Wie wähle ich die Brennweite anhand eines gewünschten Sichtfelds aus?
Rearrange the FOV formula, a far-conjugate approximation with distance from the entrance pupil in the pinhole model: f = (sensor width × working distance) / target FOV, all in millimeters. Start from the active sensor width in the camera datasheet, the working distance your system geometry dictates, and the required scene coverage. Round to the nearest available focal length, then verify the resulting FOV with the Commonlands field of view calculator before ordering hardware.
Brauchen Sie Hilfe dabei, ein bestimmtes Sichtfeld zu erreichen?
Commonlands US-based optical engineers can review your sensor, working distance, and inspection geometry and recommend a specific lens. ISO 9001:2015 certified. Orders placed before 12 PM PT ship the same day from San Diego.