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
バレル収差対ピンクッション収差、テレビジョン収差対光学収差、幾何学的補正が実際に修正できるもの、そして低収差レンズで十分な場合とテレセントリック光学系が必要な場合
低歪みレンズとは、光学設計によって画像領域全体にわたる幾何学的写像誤差を最小限に抑え、被写体内の直線がセンサー上でも直線のまま写るようにしたレンズのことです。歪みの符号と名称は慣例によって定められており、樽型歪み（負）は直線を外側に湾曲させ、針刺し型歪み（正）は直線を内側に湾曲させますが、一部のデータシートでは符号を付けない絶対値のみが記載されている場合もあります。 また、その数値がテレビ歪みなのか、それとも光学（半径方向）歪みなのかが分からなければ、その数値自体には意味がありません。なぜなら、同じレンズであっても、これら2つの指標では異なる値が報告されるからです。
Commonlands low distortion M12 lenses include the CIL036 (−0.7% TV distortion), the CIL059 (−4% rectilinear distortion), and the CIL052 at −0.1% optical distortion for precision work. Those figures use different metrics, so compare lenses within one convention. Low distortion is not telecentricity: it corrects where image points land at a fixed working distance, not whether magnification holds constant 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 lines in the scene to straight lines in the image, preserving angles and proportions at a given working distance. A low distortion lens is one where the 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 next section covers how that percentage is signed and measured.
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 instances of the same third-order aberration: lens magnification changing with field height instead of staying constant across the frame. Barrel distortion, the dominant type in short-focal-length machine vision lenses, is reported as a negative percentage; pincushion, more common in telephoto and zoom designs, is reported as positive. A third type, tangential distortion, 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.
The sign and magnitude alone do not tell the whole story, because 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. Because TV distortion references picture height rather than the corner, it is the smaller number: for a 4:3 format it runs around a third of the corner optical figure. Check which convention is in use, and at what image circle, before comparing lenses.
The table below lists published distortion for ten Commonlands M12 and C-mount lenses, with the metric each figure uses and, where stated, its reference image circle. "Display spec" marks a figure the product page publishes 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 spatial displacement of image points relative to the ideal rectilinear projection, the one error source distortion control addresses. It matters wherever image geometry feeds a decode or measurement step. Barcode decoders and character recognition depend on module widths and character proportions staying consistent across the frame. Barrel distortion compresses and warps them near the corners, which lowers decode and classification rates on dense codes or tightly spaced fonts.
For flat parts imaged at a fixed working distance (PCB panels, labels, gaskets), distortion is usually the dominant geometric error, and 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.
Software correction can calibrate distortion out, but it is not free: aggressive warping adds computation and, near the edges 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 with temperature or lens seating.
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 reaching double digits when distortion is not deliberately controlled. Wider angles are progressively harder to correct, so reaching a wide field with low distortion takes more lens elements and tighter tolerances. A 60 degree M12 lens can hit very low distortion with modest design effort; 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 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, CIL028, CIL034, and CIL038 meet this without software correction.
- 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. M12 lenses focus from 50mm to infinity, uncorrected, by threading the body in or out. It is a rigid assembly with no internal moving groups, unlike the cam-compensated focus in C-mount lenses.
For washdown or outdoor exposure the CIL034 pairs low distortion with IP67+ sealing, though not every SKU carries ingress protection. If you also need 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
Distortion specs are expressed as a percentage of image height at the edge of a stated image circle. The sign convention matters: negative is barrel, positive is pincushion, and most machine vision lenses are barrel, so negative percentages dominate. Commonlands publishes each distortion figure with its metric and reference image circle, the two qualifiers this section shows you how to read.
パーセンテージをピクセルに変換する
Evaluate whether that displacement fits inside the measurement tolerance and pixel pitch for the application. 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 the rated image circle and generally grows toward the edge of the field. A sensor whose diagonal is smaller than the image circle captures only the inner portion, where distortion is lower, so the same lens shows more corner distortion on a larger sensor than on a smaller one. Match the reference image circle to the sensor in use before comparing a published number against your own: a figure at an 8mm circle describes a smaller portion of the field than one at 9mm.
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 and corrects every frame. The standard 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 a good fit, but trustworthy only if the captured images actually reached the corners.
- 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 are often confused because both are associated with "accurate" machine vision 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. It is a geometric consequence of central projection and 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 divided by 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.
If instead a flat PCB is imaged at a fixed working distance with no height variation, a well-corrected low distortion lens with calibration is the right, cheaper, smaller fix. Telecentric lenses are not a current Commonlands product. They are larger, more expensive, and field-of-view-limited, and they solve a specific class of problem rather than acting as a universal upgrade. 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 where geometric accuracy matters.
よくある質問
Commonlands publishes a distortion profile for each of its low distortion lenses; these answers define the terms on that datasheet.
低歪みレンズとは何ですか？
低歪みレンズとは、光学設計により画像全域にわたって幾何学的写像誤差を小さく抑えたレンズのことです。一般的に、マシンビジョン用M12レンズでは樽型歪みが1%未満、高精度オプションでは0.2%～0.1%未満に抑えられています。標準的なレンズでは、像点が理想的な直線上の位置からずれてしまい、直線が曲線として写像されてしまいます。低歪みレンズは、そのずれを最小限に抑えることで、被写体の形状をより忠実にセンサー上に写像します。
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 horizontal line near the top of the frame as a percentage of the full picture height, so for a 4:3 format it runs around a third of the corner optical figure. 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？
許容される歪みは用途によって異なります。バーコード読み取りや一般的なコンピュータビジョンでは、樽型歪みが1%未満であれば、多くの場合、導入ごとのキャリブレーションが不要となる実用的な閾値となります。寸法測定では、0.2%未満が一般的な目標値です。形状を大まかに推定する用途では、1回限りのキャリブレーションを行った後であれば、2～4%程度まで許容される場合があります。
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のエンジニアが、お客様のセンサー形式、作動距離、歪み許容範囲、および精度要件を確認し、最適なレンズをご提案いたします。太平洋標準時（PST）正午までにご注文いただいた在庫レンズについては、当日発送いたします。