リアルタイムの歪み可視化機能を備えたカメラ画角計算ツール

視野角の計算はどのように行われるのでしょうか？

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.

ディストーション・ビジュアライザーには何が表示されるのでしょうか？

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.

視野に影響を与える要因は何ですか？

有効焦点距離（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.

センサーの有効領域

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.

レンズの像円

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.

歪みと投影モデル

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の結果をシステム設計にどのように活用すればよいでしょうか？

作動距離の決定

特定のシーン幅に必要な作動距離を求めるには、ジオメトリを再配置します：

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.

対象視野（FOV）に合わせた焦点距離の選定

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.

視野角（FOV）の計算でよくある間違いとは？

全視野角と角度分解能の混同

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.

有効面積の代わりに名目形式を使用する

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.

広角システムにおける歪みの無視

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.

OpenCVを使って歪み補正を実装するにはどうすればよいですか？

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.

魚眼レンズ搭載カメラ（視野角120°以上のレンズ）

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)

校正ワークフロー

ビジョンシステムに歪み補正を実装するための推奨ワークフロー：

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: 使用方法 cv2.calibrateCamera() 標準レンズ用、または cv2.fisheye.calibrate() 広角用
4. Evaluate reprojection error: Target <0.5 pixels RMS for precision applications
5. Apply correction: 使用方法 cv2.undistort() or pre-compute rectification maps for real-time performance