저왜곡 렌즈란 무엇인가? 머신 비전에서의 배럴 왜곡, 핀쿠션 왜곡, TV 왜곡
배럴 왜곡 대 핀쿠션 왜곡, TV 왜곡 대 광학 왜곡, 기하학적 보정이 실제로 해결하는 문제, 그리고 왜곡이 적은 렌즈로 충분한 경우와 텔레센트릭 광학계가 필요한 경우
저왜곡 렌즈는 광학 설계상 이미지 필드 전반에 걸친 기하학적 매핑 오류를 최소화하여, 피사체 속의 직선이 센서 상에서도 직선으로 유지되도록 하는 렌즈입니다. 왜곡의 부호는 관례에 따라 지정되며, 배럴 왜곡(음수)은 선을 바깥쪽으로 휘게 하고, 핀쿠션 왜곡(양수)은 선을 안쪽으로 휘게 하지만, 일부 데이터시트에서는 부호 없이 크기만 표기하기도 합니다. 또한 이 수치는 TV 왜곡인지 광학(방사형) 왜곡인지 알지 못하면 의미가 없는데, 두 측정 기준은 동일한 렌즈에 대해 서로 다른 값을 나타내기 때문입니다.
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.
저왜곡 렌즈란 무엇인가
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.
배럴 왜곡, 핀쿠션 왜곡, TV 왜곡에 대한 설명
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.
| 렌즈 | 마운트 | EFL | 왜곡 (게재된 내용대로) | 미터법 | 가격 |
|---|---|---|---|---|---|
| CIL018 | M12 | 1.8mm | −14% | 디스플레이 사양 | $39 |
| CIL023 | M12 | 2.2mm | −5% | TV (4:3) | $39 |
| CIL028 | M12 | 2.6mm | −1% | TV (4:3) | $39 |
| CIL034 | M12 | 3.25mm | <1% | 디스플레이 사양 | $39 |
| CIL036 | M12 | 3.3mm | −0.7% | TV | $19 |
| CIL038 | M12 | 3.85mm | <1% | TV @7.0mm | $39 |
| CIL052 | M12 | 5.2mm | −0.1% | 직선형 @7.2mm | $79 |
| CIL059 | M12 | 5.9mm | −4% | 직선형 @8.8mm | $49 |
| CIL062 | M12 | 6.2mm | −2% | 직선형 | $19 |
| CIL535 | C-마운트 | 35mm | −0.1% | rectilinear @ MOD에서 | $149 |
저왜곡이 실제로 해결해 주는 문제
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.
왜곡이 적은 M12 렌즈 선택하기
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.
왜곡 요구 사항에 따른 선정 지침
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.
실전에서 왜곡 사양을 해석하는 방법
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.
백분율을 픽셀로 변환하기
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.
이미지 서클 대 센서 크기
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.
소프트웨어를 이용한 왜곡 보정
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.
저왜곡 렌즈 대 텔레센트릭 렌즈: 올바른 선택하기
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.
실질적인 경계
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.
Commonlands의 저왜곡 렌즈 예시
These M12 and C-mount lenses are specified for precision measurement, barcode reading, and inspection where geometric accuracy matters.
자주 묻는 질문
Commonlands publishes a distortion profile for each of its low distortion lenses; these answers define the terms on that datasheet.
저왜곡 렌즈란 무엇인가요?
저왜곡 렌즈란 광학 설계상 이미지 전 영역에 걸쳐 기하학적 매핑 오차를 최소화한 렌즈를 말하며, 일반적으로 머신 비전용 M12 렌즈의 경우 배럴 왜곡이 1% 미만이고, 정밀 사양 제품의 경우 0.2%~0.1% 미만입니다. 표준 렌즈는 이미지 점을 이상적인 직선 위치에서 벗어나게 하여, 직선을 곡선으로 왜곡시킵니다. 저왜곡 렌즈는 이러한 변위를 최소화하여 피사체의 기하학적 형태가 센서에 더 정확하게 매핑되도록 합니다.
배럴 왜곡과 핀쿠션 왜곡의 차이점은 무엇인가요?
배럴 왜곡은 이미지의 중심을 기준으로 직선을 바깥쪽으로 휘게 하며, 음의 백분율로 표시됩니다. 핀쿠션 왜곡은 선을 중심 쪽으로 안쪽으로 휘게 하며, 양의 백분율로 표시됩니다. 머신 비전 분야에서는 배럴 왜곡이 훨씬 더 흔하게 나타납니다. 대부분의 임베디드 카메라가 단초점 M12 렌즈를 사용하기 때문인데, 이러한 렌즈는 설계상 특별히 보정하지 않는 한 일반적으로 배럴(음의) 왜곡을 나타내기 때문입니다.
TV 왜곡과 광학 왜곡의 차이점은 무엇인가요?
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.
저왜곡은 텔레센트릭과 같은 것인가요?
아닙니다. 왜곡이 적으면 고정된 작업 거리에서 기하학적 매핑 오차가 줄어듭니다. 텔레센트릭성은 입사 동공의 위치를 제어하여 피사체 거리가 변해도 배율이 거의 일정하게 유지되도록 합니다. 왜곡이 0.2% 미만인 렌즈라도 작업 거리가 변하면 배율에 큰 변화가 나타날 수 있습니다. 이 두 특성은 서로 독립적이며, 왜곡이 적다고 해서 텔레센트릭성을 대체할 수는 없습니다.
머신 비전 분야에서 어느 정도의 왜곡까지 허용될 수 있나요?
허용 가능한 왜곡 정도는 용도에 따라 다릅니다. 바코드 판독 및 일반적인 컴퓨터 비전의 경우, 배럴 왜곡이 1% 미만이면 배포 시마다 보정을 수행하지 않아도 되는 실용적인 기준이 됩니다. 치수 측정의 경우, 0.2% 미만이 일반적인 목표치입니다. 형상을 대략적으로 추론하는 용도의 경우, 일회성 보정 후 2~4% 정도의 왜곡은 허용될 수 있습니다.
사용 목적에 맞는 저왜곡 렌즈를 선택하는 데 도움이 필요하신가요?
Commonlands 엔지니어들은 고객의 센서 형식, 작동 거리, 왜곡 허용 범위 및 정확도 요구 사항을 검토하여 적합한 렌즈를 추천해 드립니다. 태평양 표준시(PST) 기준 오후 12시 이전에 주문하신 경우, 재고가 있는 렌즈는 당일 발송됩니다.