低歪みレンズとは？ マシンビジョンにおける樽型歪み、針刺し型歪み、およびTV歪み
Barrel and pincushion distortion get measured two different ways, TV and optical, and the two numbers do not translate directly. This guide covers what geometric correction actually fixes and when a low distortion lens is enough versus when you need telecentric optics instead.
A low distortion lens is a lens whose optical design minimizes geometric mapping error across the image field, so straight lines in the scene stay straight on the sensor. Distortion is signed and named by convention. Barrel distortion (negative) bows lines outward, and pincushion distortion (positive) bows them inward, though some datasheets publish only an unsigned magnitude. The number is also meaningless without knowing whether it is TV distortion or optical (radial) distortion, since the two metrics report different values for the same lens.
Commonlands low distortion M12 lenses include the CIL036 (−0.7% TV distortion) and the CIL052 at −0.1% optical distortion for precision work; the CIL059 (−4% rectilinear distortion) sits in the 2 to 4% tier that expects calibration first. Those figures use different metrics, so compare within one convention. Low distortion is not telecentricity: it fixes where image points land at a fixed working distance, not whether magnification holds as object distance changes.
低歪みレンズとは何か
Every lens projects a three-dimensional scene onto a flat sensor. The ideal rectilinear projection maps straight scene lines to straight image lines, preserving collinearity; angle and local-shape preservation belongs to the stereographic projection instead. A low distortion lens is one where deviation from that ideal has been reduced through optical design, often with aspherical surfaces or balanced element groups that hold residual distortion to a small, specified percentage of image height.
The Commonlands CIL052 5.2mm M12 lens is specified at −0.1% rectilinear (optical) distortion at its 7.2mm reference image circle. The CIL535 35mm C-mount lens is specified at −0.1% from rectilinear at minimum object distance.
バレル歪み、ピンクッション歪み、テレビ歪みの解説
Barrel and pincushion distortion are opposite-signed forms of the same mapping error: image points land at the wrong radial distance from the ideal rectilinear projection, which reads locally as magnification changing with field height. Third-order theory gives the leading term; wide designs add higher-order terms and can show mustache profiles. Barrel, dominant in short-focal-length machine vision lenses, is reported as a negative percentage; pincushion, more common in telephoto and zoom designs, as positive.
Tangential distortion, a separate non-radial component, comes from elements slightly decentered or tilted during manufacture. It is usually much smaller than radial distortion but can still matter for sub-pixel metrology.
A percentage is meaningless without its metric. TV distortion is a broadcast convention (EIA/IEC) that images a rectangular grid and expresses the bow of a horizontal line near the top of the frame as a percentage of the full picture height. Optical distortion (also called radial or rectilinear) reports the direct percentage displacement of a point from its ideal position, usually at the edge of a stated image circle.
The two methods do not agree numerically for the same lens, so a datasheet reading −3% TV cannot be compared with a competitor's −3% rectilinear. TV distortion samples one line and references picture height rather than the corner, so it usually reports the smaller number, but no fixed ratio converts one into the other.
The ratio between them moves with the TV formula variant, the aspect ratio, the sampled line, the reference projection, and the shape of the distortion curve, which is not a simple radial cubic in mustache designs.
The table lists published distortion for ten Commonlands lenses with each figure's metric and, where stated, its reference image circle. "Display spec" marks a figure published without stating whether it is TV or rectilinear.
| レンズ | マウント | EFL | 歪み（掲載された通り） | メートル法 | 価格 |
|---|---|---|---|---|---|
| CIL018 | M12 | 1.8mm | −14% | ディスプレイの仕様 | $39 |
| CIL023 | M12 | 2.2mm | −5% | テレビ（4:3） | $39 |
| CIL028 | M12 | 2.6mm | −1% | テレビ（4:3） | $39 |
| CIL034 | M12 | 3.25mm | <1% | ディスプレイの仕様 | $39 |
| CIL036 | M12 | 3.3mm | −0.7% | テレビ | $19 |
| CIL038 | M12 | 3.85mm | <1% | TV @7.0mm | $39 |
| CIL052 | M12 | 5.2mm | −0.1% | 直線 @7.2mm | $79 |
| CIL059 | M12 | 5.9mm | −4% | 直線 @8.8mm | $49 |
| CIL062 | M12 | 6.2mm | −2% | 直線的な | $19 |
| CIL535 | Cマウント | 35mm | −0.1% | rectilinear @ MOD より | $149 |
低歪みが実際に解決すること
Commonlands low distortion M12 lenses reduce the displacement of image points from the ideal rectilinear projection. Barcode decoders and character recognition depend on module widths and character proportions staying consistent across the frame, and barrel distortion warps them near the corners, lowering decode and classification rates on dense codes or tightly spaced fonts.
For flat parts imaged at a fixed working distance (PCB panels, labels, gaskets), low distortion optics let tighter tolerances hold without aggressive correction. Stereo depth, robotic pick-and-place, and multi-camera stitching lean on it too, since each feeds distortion coefficients straight into its geometry math.
Distortion is not automatically the dominant error. Part or camera tilt, perspective error from part height, magnification calibration, edge contrast and MTF, thresholding, and illumination uniformity compete for the same budget, so measure before assuming distortion is the limit. Low distortion removes one error source; dimensional accuracy still needs magnification tied to a length standard, controlled perspective, repeatable focus and mounting, and edge localization that holds under the lighting in use.
Software correction can calibrate distortion out, but not for free: warping adds computation and, where resampling is heaviest, softens effective resolution and correlates pixel noise. Starting with low distortion shrinks the residual, so the system degrades less when calibration drifts.
低歪みのM12レンズの選び方
Standard wide-angle M12 lenses can introduce substantial barrel distortion at fields of view above 100 degrees, often double digits when distortion is not deliberately controlled. Wider angles are progressively harder to correct, so a wide field with low distortion takes more elements and tighter tolerances: a 60 degree M12 lens reaches very low distortion with modest design effort, while a 120+ degree design needs dedicated correction.
歪み要件に基づく選定ガイドライン
These tiers are Commonlands application guidance, not an industry standard. No standards body defines a distortion threshold, so treat them as starting points, note the metric and reference image circle behind each number, and convert the percentage into a pixel budget for your own sensor before committing.
- For precision measurement under 0.2%, the CIL052 is the tightest M12 spec in the lineup. The C-mount CIL535 reaches comparable accuracy at a longer focal length.
- For barcode reading and general inspection under 1%, the CIL036 (−0.7% TV) and CIL038 (<1% TV at a 7.0mm circle) meet it in the TV convention without software correction; the CIL028 (−1% TV, 4:3) sits at the line. The CIL034 publishes <1% without a stated metric, so verify it against your pixel budget.
- 2 to 4% with calibration: the CIL062 and CIL059 paired with OpenCV-style calibration suit many robotics and computer vision applications.
- Wide-angle, distortion still controlled: the CIL018 (1.8mm, 128° field of view) stays rectilinear rather than fisheye. Its −14% typically needs calibration. Above 120°, the fisheye distortion guide covers the Kannala-Brandt model that applies instead.
What else to validate
Confirm MTF across the field at the working aperture, chief ray angle (CRA) compatibility with the target sensor, and image circle coverage against the sensor diagonal with margin. A tight distortion number does not guarantee good corner image quality.
Most Commonlands M12 lenses publish a focus range of roughly 50mm to infinity; the reachable near limit in your build is set by the holder, so check the MOD and holder note on each product page. Commonlands C-mount lenses use cam-driven focus, and the focus mechanism and its near-limit behavior are product-specific.
For splash or outdoor exposure the IP67-rated CIL034 variant adds IEC 60529 dust and immersion sealing (not the washdown jet test); not every SKU carries ingress protection. For a wider field than low distortion allows without heavy correction, the field of view guide and calculator show the tradeoff.
歪み率の仕様を実際に読み解く方法
An optical (radial) spec gives the percentage displacement of image height at the edge of a stated image circle; a TV spec reports the bow of a sampled line as a percentage of picture height. Negative is barrel, positive is pincushion, and most machine vision lenses are barrel. Most Commonlands figures carry their metric and reference image circle; the table above marks the rest as display specs.
パーセンテージをピクセルに変換する
Check that displacement against the measurement tolerance and pixel pitch. Also confirm whether the spec was measured at minimum object distance or at a working distance relevant to your setup, since distortion can shift with focus position, particularly at short working distances.
イメージサークルとセンサーサイズ
Distortion is specified at a rated image circle, and in a third-order-dominated design it grows toward the edge of the field. A sensor smaller than that circle captures only the inner portion, where distortion is lower, so the same lens shows more corner distortion on a larger sensor. Match the reference image circle to the sensor in use before comparing published numbers.
ソフトウェアによる歪みの補正
Calibration measures the distortion coefficients of a specific lens-sensor-focus combination. The procedure:
- Mount the lens and camera rigidly, then capture 15-20 images of a checkerboard or dot grid across the full field, including all four corners.
- Run the solver: OpenCV's
calibrateCamera()for rectilinear lenses, orcv2.fisheye.calibrate()with the Kannala-Brandt model above roughly 120 degrees, where the Brown-Conrady tangent term diverges near 90 degrees. - Check reprojection error: under 0.5 pixels is the working target we use, not a guaranteed result. It measures how well the model fits the images you captured, so it moves with the model chosen, target metrology, pose and field coverage, and feature localization, and it says nothing about how the fit holds once focus or temperature shifts.
- Apply the correction to every frame, and recalibrate whenever focus, aperture, or mounting changes.
低歪みレンズとテレセントリックレンズ：適切な選択
Low distortion and telecentricity fix different problems and get confused because both read as "accurate" optics. Distortion is an aberration, a property of the lens elements and how they bend rays onto the sensor. It is fixed and repeatable for a given lens, focus, and aperture, so it can be characterized and corrected in software. Correcting it does not change the lens's projection model: an entocentric lens stays entocentric, and its magnification still shifts when object distance changes.
Perspective-driven magnification change is not an aberration but a geometric consequence of central projection, and it cannot be eliminated within the entocentric class. Only telecentric optics hold magnification nearly constant through the usable depth of field. Software cannot correct it without knowing the 3D position of every scene point, so a lens with zero distortion still changes magnification by roughly h/d (height variation over working distance) when the surface is not flat or working distance varies.
実質的な境界
For a 35mm lens at 500mm working distance, a 5mm height variation across a part produces roughly 1% magnification change between the top and bottom of the feature. If measurement tolerance is 0.5%, a low-distortion lens at −0.1% is well within budget on the distortion axis but already over budget on the perspective axis. Choosing a lower-distortion lens does not help.
For a flat PCB imaged at a fixed working distance with no height variation, a well-corrected low distortion lens with calibration is the cheaper, smaller fix. Telecentric lenses are not a current Commonlands product. They are larger, more expensive, and field-of-view-limited. See the full telecentric lens guide for the entrance-pupil mechanism and when telecentric optics are the correct call.
Commonlandsの低歪みレンズの例
These M12 and C-mount lenses are specified for precision measurement, barcode reading, and inspection.
よくある質問
These answers define the terms used on Commonlands distortion datasheets.
低歪みレンズとは何ですか？
A low distortion lens is a lens whose optical design keeps geometric mapping error small across the image field, typically published under 1% for machine vision M12 lenses and under 0.2% for precision options, against a stated metric and reference image circle. Standard lenses displace image points from their ideal rectilinear positions, bowing straight lines into curves. A low distortion lens minimizes that displacement so scene geometry maps more faithfully onto the sensor.
バレル歪みとピンクッション歪みの違いは何ですか？
樽型歪みは、画像の中心から直線を外側へ湾曲させるもので、負のパーセンテージで表されます。ピンクッション型歪みは、直線を中心に向かって内側に湾曲させるもので、正のパーセンテージで表されます。マシンビジョン分野では、樽型歪みがはるかに一般的です。これは、ほとんどの組み込みカメラが短焦点のM12レンズを使用しており、設計上特に補正されていない限り、通常は樽型（負）の歪みを生じるためです。
テレビの歪みと光学的な歪みの違いは何ですか？
TV distortion and optical (radial) distortion measure the same aberration but produce different numbers for the same lens. Optical distortion is the percentage displacement of an image point from its ideal rectilinear position, usually at the corner.
TV distortion expresses the bow of a sampled horizontal line as a percentage of picture height, so it usually reads smaller, but no fixed ratio converts between them: the TV formula variant, the aspect ratio, the line sampled, and the shape of the distortion curve all move it. A −3% TV figure is not the same as −3% optical.
低歪みとは、テレセントリックと同じことですか？
いいえ。歪みが少ないと、一定の作動距離において幾何学的マッピング誤差が低減されます。テレセントリック性により入瞳の位置が制御されるため、被写体距離が変化しても倍率はほぼ一定に保たれます。歪みが0.2%未満のレンズであっても、作動距離が変化すると倍率に大きな変化が生じることがあります。これら2つの特性は互いに独立しており、歪みの少なさだけではテレセントリック性を補うことはできません。
マシンビジョンにおいて、どの程度の歪みが許容範囲となるのでしょうか？
Acceptable distortion depends on the application, and these tiers are Commonlands starting guidance rather than a standard. Read every figure with its metric (TV or optical) and its reference image circle, then convert it to pixels at your sensor and check it against your error budget. For barcode reading and general computer vision, under 1% often avoids per-deployment calibration. For dimensional measurement, under 0.2% is a common target. Where geometry is inferred loosely, 2-4% can work after a one-time calibration.
ご用途に適した低歪みレンズの選定でお困りではありませんか？
Commonlands engineers can review your sensor format, working distance, and distortion budget to recommend the right lens. Same-day shipping on stocked lenses for orders placed before 12 PM PT.