머신 비전에서의 렌즈 수차: 필드 곡률, 난시, 색수차 및 구면 수차
렌즈가 왜곡 사양을 충족함에도 불구하고 바코드 판독이나 검사 작업에서 실패하는 이유, 그리고 소프트웨어로 보정할 수 있는 수차와 보정할 수 없는 수차는 무엇인지.
렌즈 수차는 이상적인 이미지 형성에서 벗어난 현상으로, 모서리가 흐릿해지거나 방향에 따라 흐려지는 현상, 색 번짐, 또는 중심부와 가장자리 간의 선명도 차이가 발생하는 원인이 됩니다. 왜곡은 선명도를 저하시키지 않으면서 기하학적 형태를 변형시키며, 소프트웨어를 통해 효과적으로 보정할 수 있습니다. 반면, 화각 곡률, 난시, 구면 수차, 색수차는 대비를 저하시키는데, 이러한 현상은 소프트웨어로 완전히 복원할 수 없습니다.
For machine vision, the reliable fix for these blur-causing aberrations is a better-corrected lens, a narrower aperture where illumination allows, or narrowband illumination, not a software patch applied after capture.
머신 비전에서 렌즈 수차란 무엇인가
An ideal lens maps every scene point onto the sensor with perfect sharpness, correct geometry, and no color separation. Real lenses deviate because refraction through a curved surface bends different rays, and different wavelengths, by different amounts. In photography those deviations are often aesthetic. In machine vision they are engineering constraints, where a soft edge can fail a barcode read or push a measurement out of tolerance.
The blur-causing aberrations, field curvature, astigmatism, spherical aberration, and chromatic aberration, lower the contrast of fine detail. Once that contrast is gone, no software step recovers it. Distortion is the exception: it moves image points without softening them, so calibration corrects it to sub-pixel accuracy.
Center sharpness alone does not describe a lens: field curvature, astigmatism, and lateral chromatic aberration grow with field angle. A lens can pass an MTF (modulation transfer function) check at the center yet fail at 70% or 100% field height, where barcodes and part edges sit. The Commonlands MTF curve guide covers sagittal and tangential curves at several field positions.
색수차란 무엇인가요?
Chromatic aberration occurs when a lens focuses different wavelengths to different positions. Glass has a wavelength-dependent refractive index, bending blue light more than red, so a single-glass element cannot bring all colors to one focal point. It appears as focus shift, color fringing at high-contrast edges, and calibration drift when a system switches between visible and NIR illumination.
Two forms exist. Axial, or longitudinal, chromatic aberration focuses wavelengths at different distances along the axis, so no single focus captures all of them. Stopping down reduces the blur but does not correct the dispersion. Lateral chromatic aberration gives wavelengths different magnification, offsetting the color planes across the field, and it ignores aperture because it is a magnification error, not a focus error.
The effect matters more here than in photography because small-pixel sensors amplify any offset between color planes. Switching to 850nm or 940nm NIR shifts focal position, and a lens sharp in visible light can go soft. Commonlands IR-corrected lenses use glass combinations that hold visible and NIR focus close enough to share one position. A monochrome sensor with narrowband illumination avoids the problem, since the lens is corrected at one wavelength.
구면 수차란 무엇인가요?
Spherical aberration occurs when rays through different radial zones of a spherical surface converge at different points along the axis. Paraxial rays near the center focus farther from the lens. Marginal rays near the edge focus closer. No single focal plane catches all rays sharply, so the image looks soft even at best focus, and low distortion does not rule it out.
It is not defocus. Defocus shifts the whole focal plane and refocusing corrects it. Spherical aberration is zone-dependent, so no sensor position gives a fully sharp image. It also differs from field curvature, because it can degrade the on-axis center.
Fast lenses show it most clearly: at a wide aperture the marginal zones with the largest focus offset contribute, and stopping down blocks those rays to improve sharpness, though the lens is restricted, not corrected. For Commonlands M12 lenses, whose aperture is fixed at manufacture, that tradeoff is set at order time. Aspherical elements are the main tool for reducing it. See what is an aspherical lens below.
시야 곡률이란 무엇이며, 왜 난시가 그 축외 왜곡의 동반자인가?
Field curvature is a lens aberration where the surface of best focus is curved rather than flat, so the focal distance changes across the field: the center can be sharp while the corners need a different position. It is sometimes called Petzval field curvature, after Josef Petzval.
A flat sensor meets the curved surface at the center but drifts away toward the periphery, so corners soften and refocusing them pushes the center out. Astigmatism is its off-axis partner: radial and tangential edges focus at different depths, so a line along the radius stays sharp while a perpendicular line at the same position blurs.
Stopping down extends depth of field enough to tolerate the center-to-edge mismatch, but it does not flatten the surface. C-mount lenses with an adjustable iris make that practical, since illumination is usually controllable. M12 lenses typically have fixed apertures.
Field curvature grows with field radius and shifts with working distance, so a lens flat on a 1/3" sensor can soften on a larger format or a short working distance. The sensor size and lens compatibility guide and the working distance guide cover those cases.
비구면 렌즈란 무엇인가요?
A spherical lens surface has one constant radius from center to edge. That shape is simple to make, but it bends marginal rays more strongly than paraxial rays, the direct cause of spherical aberration. An aspherical surface varies its curvature with radius, steering marginal and paraxial rays toward a common focal point and giving the designer one extra degree of freedom per element in a compact housing.
One or two molded glass aspheres can do the work of three or four extra spherical elements, which is why Commonlands compact M12 lenses use them to reach wide apertures without a long stack. Pressed from optical glass at high temperature, they hold their refractive properties across a wider temperature range than plastic-molded aspheres, which matters outdoors and in industrial heat.
An asphere is primarily a spherical-aberration tool. It does not automatically fix distortion, chromatic aberration, or field curvature. Those are set by the full prescription, so verify distortion, chromatic behavior, and field MTF independently.
실제 비전 시스템에서 각 수차가 어떻게 보이는지
This Commonlands reference table maps each aberration to its visual signature, the applications it affects most, and whether software correction helps.
| 수차 | 어떤 모습인지 | 가장 큰 영향을 받은 애플리케이션 | 소프트웨어로 수정 가능한가요? |
|---|---|---|---|
| 왜곡 | 직선이 안쪽으로 휘어지거나(핀쿠션) 바깥쪽으로 휘어집니다(배럴); 기하학적 구조는 틀렸지만 선명합니다 | 치수 측정, 로봇 안내, 필드 가장자리에서의 바코드 판독 | Yes, to sub-pixel accuracy with geometric calibration. |
| 화면 곡률 | 한 가지 초점 설정에서는 중앙은 선명하고 모서리는 흐릿하며, 초점을 다시 맞추면 모서리가 흐릿해지고 중앙은 선명해진다. | 평면 대상물 검사(PCB, 라벨, 평면 부품 표면), 전체 센서 바코드 판독 | No; stopping down helps tolerance but adds diffraction. |
| 난시 | 축외 가장자리는 한 방향에서는 선명하지만 수직 방향에서는 흐릿하며, 시상/접선 방향 MTF가 서로 다른 양상을 보인다 | 텍스트 OCR, 모서리 기반 측정, 모서리 부분의 바코드 판독 | No; MTF data reveals its severity. |
| 구면 수차 | 명암 대비가 강한 가장자리 주변에 부드러운 헤이즈 현상이 나타나며, 낮은 F/#에서 가장 심하고, 조리개 값에 따라 초점 위치가 변동한다. | 고해상도 검사, 미세 픽셀 피치 센서, 저조도 이미징 | No; stopping down or an asphere reduces it optically, but software cannot restore the lost contrast. |
| 색수차 (축방향) | 명암 대비가 강한 가장자리에서 나타나는 색상 후광; 동일한 초점 거리에서도 채널마다 선명도가 다름 | 색상 결함 감지, 가시광선/근적외선 주야간 시스템 | No; narrowband illumination avoids it optically. |
| 색수차 (횡방향) | 화면 가장자리에 색 번짐 현상; RGB 채널 간에 상대적인 위치가 어긋남 | 센서 전체 폭에 걸친 색상 검사, 색상 경계 감지 | Partially; per-channel calibration helps. |
소프트웨어로 해결할 수 있는 것과 해결할 수 없는 것
Geometric distortion is the one aberration software handles well. Calibration computes radial and tangential distortion coefficients from a checkerboard target and corrects the image to sub-pixel accuracy in real time. Lateral chromatic aberration can be partly corrected by aligning per-channel maps in post-processing, at some cost.
Field curvature, astigmatism, spherical aberration, and axial chromatic aberration lower the contrast of fine detail. Once it is gone, processing cannot recover it. Deconvolution can partly restore well-characterized blur, but it needs a point-spread-function model for every field position and focus distance, so in production it is rarely practical. For soft corners or color fringing, change the lens or the illumination.
Stopping down helps by two mechanisms: it blocks the outer zones that drive spherical aberration, and it shrinks the blur circle for astigmatism and axial chromatic aberration. On a C-mount lens with an adjustable iris this is practical, limited by diffraction. The depth of field guide and the f-number guide cover the tradeoff. M12 apertures are fixed, so it is not a field correction there.
커먼랜드 렌즈의 예시와 수차 간의 상충 관계
Every lens design makes aberration tradeoffs. These three Commonlands lenses show how the priorities shift with format, focal length, aperture, and construction.
| 렌즈 | Mount and image circle | 조리개 | Aberration the design prioritizes |
|---|---|---|---|
| CIL062 | M12, 9.0mm image circle | F/2.8, fixed at manufacture | Low distortion (-2%) |
| CIL122 | M12, 9.3mm image circle | F/2.4, fixed at manufacture | Axial chromatic aberration across visible and NIR |
| CIL514 | C-mount, 17.6mm image circle | F/2.8 to F/16, adjustable iris | Field curvature and lateral chromatic aberration on a 1.1" format |
The CIL062 is a $19 M12 lens with -2% distortion. At F/2.8 fixed, verify edge MTF before using its full 9.0mm image circle on a larger sensor.
The CIL122 holds visible and NIR focus close enough to share one position, addressing axial chromatic aberration directly. The CIL514 covers a 17.6mm, 1.1" image circle where field curvature and lateral chromatic aberration are hardest to hold, and its F/2.8 to F/16 iris trades aperture for depth-of-field tolerance.
구매 주문서에서 수차 허용 오차 명시하기
Most machine vision purchase orders name focal length, mount, resolution, and F/#, then stop. That selects a lens family but does not pin down corner and off-axis performance. A complete Commonlands aberration specification names four things, each on its own line.
| Requirement | What to state | Why it matters | Example line |
|---|---|---|---|
| Field positions | Where in the frame performance is required | Brackets where barcodes, labels, and part edges sit | Center, 70%, and 100% of image height |
| 미터법 | MTF at a stated spatial frequency, not a single resolution number | Ties the requirement to the sensor's pixel pitch | MTF at 100 lp/mm |
| 조건 | Aperture and working distance the measurement is taken at | Spherical aberration and aberration balance change with both | F/1.8 at 300mm working distance |
| Band | Illumination wavelength or band | Axial chromatic aberration shifts focus between visible and NIR | 850nm or 940nm NIR |
Give distortion, chromatic aberration, field curvature, and astigmatism their own tolerance lines, not one blanket image-quality requirement. A lens can meet ±1% distortion and still fail on field curvature. For volume programs, a measured test report per batch, tied to a lot or serial range, turns a subjective complaint into a quantified MTF comparison. A Commonlands Trioptics ImageMaster HR2 report provides that data.
자주 묻는 질문
Commonlands publishes distortion data for its lenses, and these answers name the aberrations behind those numbers.
머신 비전에서 렌즈 수차란 무엇인가요?
Lens aberrations are deviations from ideal image formation caused by light refracting through real glass or plastic elements. In machine vision they produce repeatable defects: soft corners, orientation-dependent blur, color fringing, or center-to-edge sharpness mismatch. The patterns follow field position, wavelength, and aperture, not random noise.
렌즈의 색수차란 무엇인가요?
Chromatic aberration comes from the wavelength-dependent refractive index of glass. A lens bends short wavelengths more than long ones, so colors focus at different distances (axial) and different magnifications (lateral). The result is focus shift, color fringing at high-contrast edges, and calibration drift when a system switches between visible and NIR illumination.
렌즈의 구면 수차란 무엇인가요?
Spherical aberration is where rays through different radial zones of a spherical surface converge at different points along the optical axis. Marginal rays near the edge focus closer than paraxial rays near the center. No single focal plane captures all rays sharply, so the image is soft even at best focus.
렌즈의 필드 커브러처란 무엇인가요?
Field curvature is where the surface of best focus is curved rather than flat. On a flat sensor viewing a flat target, the center can be sharp while the corners are soft, or the reverse, even when focus is otherwise correct. It is sometimes called Petzval field curvature, after Josef Petzval.
비구면 렌즈란 무엇인가요?
An aspherical lens uses one or more surfaces whose curvature varies with radius, rather than a constant spherical radius. That steers marginal and paraxial rays toward a common focal point, reducing spherical aberration with fewer elements. It is a design tool, not a guarantee against every aberration: it does not automatically fix distortion, chromatic aberration, or field curvature.
소프트웨어로 렌즈 수차를 보정할 수 있나요?
Software corrects geometric distortion well because the pixel data is present, just mispositioned. It cannot reliably restore contrast lost to field curvature, astigmatism, spherical aberration, or axial chromatic aberration. Where the lens MTF has fallen to zero, that information is gone. Deconvolution can partly recover attenuated detail but is rarely practical in production. Lateral chromatic aberration responds partly to per-channel calibration, but production systems should fix blur-causing aberrations at the lens or illumination level.
수차에 민감한 이미징용 렌즈를 선택하는 데 도움이 필요하신가요?
Commonlands는 머신 비전용 M12 및 C-마운트 렌즈를 제조하며, Trioptics ImageMaster HR2 시스템으로 측정된 MTF 테스트 보고서를 제공합니다. 샌디에이고 엔지니어링 팀( engineering@commonlands.com)으로 센서 모델, 작동 거리 및 검사 요구 사항을 보내 주시기 바랍니다. 태평양 표준시(PST) 기준 정오 이전에 주문하시면 당일 발송됩니다.