실시간 왜곡 시각화 기능을 갖춘 카메라 시야각 계산기

시야각 계산은 어떻게 이루어지나요?

The field of view formula assumes an ideal pinhole camera with rectilinear projection. Use it for low-distortion lenses only, typically telephoto and standard focal lengths. Wide-angle and fisheye lenses deviate significantly from the rectilinear model; fisheye FOV cannot be interpolated from EFL and edge distortion alone. Use this calculator, Commonlands MCP tools, or precomputed product FOV tables for fisheye and distortion-sensitive lenses.

왜곡 시각화 도구는 무엇을 보여주는가?

The distortion visualizer displays a reference grid as it would appear through the selected lens. Barrel distortion (negative coefficients) curves straight lines outward from the image center, a pattern common in wide-angle M12 lenses below 4mm focal length. Pincushion distortion (positive coefficients) curves lines inward, occasionally seen in telephoto designs. The visualizer helps engineers understand the actual image geometry before committing to a lens selection.

시야각에 영향을 미치는 요인은 무엇인가요?

유효 초점 거리(EFL)

The effective focal length determines the angular field of view through the relationship FOV = 2 × arctan(d / 2EFL), where d is the sensor dimension. Shorter focal lengths provide wider coverage; longer focal lengths narrow the field but increase magnification. Browse M12 lenses sorted by focal length from 0.8mm fisheye to 75mm telephoto, or explore C-mount lenses for larger format sensors.

Note: back focal length (BFL) describes the physical distance from the rear lens element to the sensor plane and should not be used for FOV calculations. See our effective focal length calculator for more details on the distinction.

센서 유효 영역

FOV calculations require the active sensor dimensions, not the nominal format name. A "1/2.3 inch" sensor actually measures approximately 6.17 × 4.55 mm. The fraction refers to historical vidicon tube conventions, not physical dimensions. The calculator includes preset dimensions for common Sony, OmniVision, and OnSemi sensors used in machine vision and robotics applications. Browse the full image sensors list for datasheets and active area dimensions.

렌즈 화각

The lens must project an image circle larger than the sensor diagonal to avoid dark corners (vignetting). Most M12 lenses designed for 1/2" format sensors provide approximately 8-10 mm image circles. When using larger sensors, verify coverage in the lens specifications. Our product pages include sensor compatibility information for each lens. For applications requiring precise corner illumination, consider our low-distortion M12 lenses which are optimized for uniform field illumination.

왜곡 및 투영 모델

Barrel distortion in wide-angle lenses maps more angular content to the image periphery than the rectilinear formula predicts. A lens with -15% TV distortion at the image edge may capture 10-20% more angular coverage than the undistorted calculation suggests. Fisheye lenses use specific mathematical projections: equidistant (r = f·θ), equisolid-angle (r = 2f·sin(θ/2)), or stereographic (r = 2f·tan(θ/2)). These produce dramatically different FOV from rectilinear lenses of the same focal length.

For more on how lens characteristics affect image quality, see our technical blog articles covering topics like sensor matching and optical performance.

FOV 결과를 시스템 설계에 어떻게 적용할 수 있을까요?

작동 거리 결정

특정 장면 너비에 필요한 작업 거리를 구하려면 지오메트리를 다음과 같이 재배치하십시오:

Example: To view a 2-meter wide scene with 60° HFOV, the required working distance is approximately 1.73 m. Verify that the depth of field at this distance covers your subject depth using the depth of field calculator.

목표 시야각에 맞는 초점 거리 선택

If you know your required field of view, use our angle of view calculator to determine the target FOV from your scene requirements, then calculate the required focal length:

Example: To achieve 70° HFOV on a Sony IMX477 sensor (6.29 mm width), select a lens with approximately 4.5 mm focal length. Browse M12 lenses filtered by focal length to find matching options, or use our EFL calculator for precise focal length determination.

시야각(FOV) 계산 시 흔히 저지르는 실수는 무엇인가요?

전체 시야(FOV)와 각도 분해능의 혼동

Total field of view indicates the angular extent captured by the sensor. Angular resolution (IFOV, instantaneous field of view) indicates the angle subtended by a single pixel, approximately pixel_pitch / focal_length on axis. Dividing total FOV by pixel count gives only a field-averaged value; on wide rectilinear lenses the per-pixel angle varies noticeably from center to edge. For a 90° HFOV imaged across 1920 pixels at 1 meter working distance, the scene spans 2 meters, roughly 1 mm per pixel on a flat target. This sampling determines whether your system can resolve the features you need to detect in machine vision applications.

활성 영역 대신 명목 형식 사용

Sensor format designations (1/2.3", 1/1.8", etc.) are historical conventions that do not correspond to physical dimensions. A "1/2.3 inch" sensor measuring 6.17 × 4.55 mm has a diagonal of approximately 7.7 mm, not 11 mm (which would be the actual fraction). Always use the active area dimensions from the sensor datasheet. See our CMOS sensor size reference for common sensor specifications.

광각 시스템에서 왜곡 무시하기

For lenses with focal lengths below 4 mm on 1/2" format sensors, barrel distortion typically exceeds -10% at the image corners. This distortion compresses more angular content at the edges, increasing effective FOV beyond the rectilinear prediction. The distortion visualizer shows this effect directly: a heavily distorted grid indicates that the actual FOV exceeds the formula-based calculation.

OpenCV를 사용하여 왜곡 보정을 구현하려면 어떻게 해야 하나요?

This calculator provides initial FOV estimates based on nominal specifications and characterized distortion data. For computer vision applications requiring precise undistortion, you'll need to calibrate your specific lens-sensor combination using physical samples and calibration targets. OpenCV provides two camera models depending on your lens type.

Standard Camera Model (Lenses <120° FOV)

For rectilinear and moderate wide-angle lenses, OpenCV's standard calibration uses the Brown-Conrady distortion model with five coefficients. The cv2.calibrateCamera() function estimates intrinsic parameters (focal length, principal point) and distortion coefficients (k1, k2, p1, p2, k3) from checkerboard images.

# Calibrate using checkerboard images
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(
    objpoints,    # 3D points in world coordinates
    imgpoints,    # 2D points in image plane
    gray.shape[::-1],
    None, None
)

# dist contains [k1, k2, p1, p2, k3]
# Undistort images using the calibration
undistorted = cv2.undistort(img, mtx, dist)

The radial distortion coefficients (k1, k2, k3) model barrel and pincushion distortion, while tangential coefficients (p1, p2) correct for lens-sensor misalignment. For most M12 lenses with focal lengths above 3mm, the standard model provides sub-pixel accuracy after calibration.

어안 카메라 모델 (시야각 >120°인 렌즈)

For ultra-wide and fisheye lenses, the standard model fails at extreme angles. OpenCV's fisheye module implements the Kannala-Brandt equidistant projection model with four distortion coefficients (k1, k2, k3, k4).

# Fisheye calibration for wide-angle lenses
calibration_flags = (
    cv2.fisheye.CALIB_RECOMPUTE_EXTRINSIC +
    cv2.fisheye.CALIB_FIX_SKEW
)

ret, K, D, rvecs, tvecs = cv2.fisheye.calibrate(
    objpoints, imgpoints, gray.shape[::-1],
    None, None,
    flags=calibration_flags
)

# D contains [k1, k2, k3, k4] for equidistant model
# Undistort to rectilinear (crops FOV significantly)
map1, map2 = cv2.fisheye.initUndistortRectifyMap(
    K, D, np.eye(3), K, img.shape[:2][::-1], cv2.CV_16SC2
)
undistorted = cv2.remap(img, map1, map2, cv2.INTER_LINEAR)

교정 워크플로우

비전 시스템에 왜곡 보정 기능을 구현하기 위한 권장 워크플로:

1. Order samples: Select candidate lenses from our M12 or C-mount collections based on FOV estimates from this calculator
2. Capture calibration images: Photograph a checkerboard pattern (typically 9×6 or 7×5 inner corners) at 15-30 different orientations covering the full FOV
3. Run calibration: Use cv2.calibrateCamera() 표준 렌즈의 경우 또는 cv2.fisheye.calibrate() 광각용
4. Evaluate reprojection error: Target <0.5 pixels RMS for precision applications
5. Apply correction: Use cv2.undistort() or pre-compute rectification maps for real-time performance