マシンビジョンにおけるレンズ収差：像面湾曲、非点収差、色収差、球面収差
なぜレンズが歪曲収差の仕様を満たしていても、バーコード読み取りや検査タスクに失敗することがあるのか、また、ソフトウェアで補正できる収差とできない収差について。
レンズの収差とは、理想的な像形成から逸脱した現象であり、画像の隅がぼやけたり、向きによってぼやけ方が変わったり、色にじみが生じたり、中心部と周辺部のシャープネスに差が生じたりする原因となります。歪曲は、シャープネスを損なうことなく像の形状を変えるものであり、ソフトウェアで十分に補正可能です。一方、像面湾曲、非点収差、球面収差、色収差は、ソフトウェアでは完全に回復できない形でコントラストを低下させます。
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.
マシンビジョンにおけるレンズ収差の意味
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.
色収差とは何ですか？
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.
球面収差とは何ですか？
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.
像面湾曲とは何ですか？また、なぜ非軸上の像面湾曲には像面収差が伴うのでしょうか？
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.
非球面レンズとは何ですか？
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.
実際の視覚システムにおいて、各異常がどのように見えるか
This Commonlands reference table maps each aberration to its visual signature, the applications it affects most, and whether software correction helps.
| 収差 | その様子 | 最も影響を受けたアプリケーション | ソフトウェアで修正可能か？ |
|---|---|---|---|
| 歪み | 直線部分が内側に（ピンクッション）または外側に（バレル）湾曲している。幾何学的形状は不正確だが、シャープである。 | 寸法測定、ロボット誘導、フィールドエッジでのバーコード読み取り | Yes, to sub-pixel accuracy with geometric calibration. |
| 像面湾曲 | 1つの焦点設定では、中央はシャープで四隅はソフトになる。再ピント合わせを行うと、四隅がソフトになり、中央がソフトになる。 | 平面対象物の検査（PCB、ラベル、平面部表面）、センサーによるバーコードの全範囲読み取り | No; stopping down helps tolerance but adds diffraction. |
| 乱視 | 軸外のエッジは、ある方向では鮮明だが、その垂直方向ではぼやけており、矢状方向と接線方向のMTFが異なる | テキストのOCR、エッジベースの計測、角部のバーコード読み取り | No; MTF data reveals its severity. |
| 球面収差 | コントラストの高いエッジの周囲に柔らかなヘイズが生じ、F値が小さいほど顕著になる。また、絞り値によってピント位置がずれる。 | 高解像度検査、微細ピクセルピッチのセンサー、低照度撮影 | No; stopping down or an asphere reduces it optically, but software cannot restore the lost contrast. |
| 色収差（軸上） | コントラストの高いエッジに色ハローが生じる；同じ焦点距離でもチャンネルごとに鮮明度が異なる | 色欠陥検出、可視光・近赤外（VIS/NIR）昼夜兼用システム | No; narrowband illumination avoids it optically. |
| 色収差（横方向） | 画像の端に色にじみが生じている；RGB各チャンネルの位置が互いにずれている | センサー全幅での色検査、色のエッジ検出 | Partially; per-channel calibration helps. |
ソフトウェアで解決できること、できないこと
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.
コモンランドレンズの例と収差のトレードオフ
Every lens design makes aberration tradeoffs. These three Commonlands lenses show how the priorities shift with format, focal length, aperture, and construction.
| レンズ | Mount and image circle | 絞り | 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.
発注書における収差許容値の指定
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 |
| メートル法 | 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 |
| 条件 | 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.
よくある質問
Commonlands publishes distortion data for its lenses, and these answers name the aberrations behind those numbers.
マシンビジョンにおけるレンズ収差とは何ですか？
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.
レンズにおける色収差とは何ですか？
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.
レンズにおける球面収差とは何ですか？
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.
レンズにおけるフィールドカーブとは何ですか？
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.
非球面レンズとは何ですか？
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.
ソフトウェアでレンズの収差を補正することはできますか？
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.
収差に敏感な撮影用のレンズ選びについて、アドバイスが必要ですか？
Commonlands社は、マシンビジョン用のM12およびCマウントレンズを製造しており、Trioptics ImageMaster HR2システムで測定したMTF測定レポートを提供しています。センサーの型番、作動距離、検査要件を、engineering@commonlands.com まで、当社のサンディエゴのエンジニアリングチームまでお送りください。太平洋標準時（PST）正午までにご注文いただいた場合は、当日発送いたします。