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
A lens can pass its distortion spec and still fail a barcode or inspection task. This guide covers which aberrations software can fix and which ones it cannot.
Lens aberrations are deviations from ideal image formation that produce soft corners, orientation-dependent blur, color fringing, or center-to-edge sharpness mismatch. Distortion changes geometry without reducing sharpness, and calibration reaches a sub-pixel residual when target, model, and poses support it, though the correction resamples the image and costs a little corner contrast. Field curvature, astigmatism, spherical aberration, and chromatic aberration reduce contrast in ways software cannot fully recover.
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. Where the transfer function reaches zero that detail is gone; where it is only attenuated, deconvolution recovers part of it, at the cost of amplified noise. Distortion is the exception: it moves image points without softening them, so calibration removes most of it.
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 under narrowband illumination sidesteps it entirely.
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. In a simple positive lens the marginal rays near the edge typically focus closer than the paraxial rays near the center, though the sign of the shift depends on the lens form, powers, and conjugates (Kingslake, Lens Design Fundamentals, 2nd ed.). 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, which shifts the whole focal plane and is corrected by refocusing. 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. 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 Petzval surface, named after Josef Petzval, is the astigmatism-free reference: with astigmatism present the sagittal and tangential focal surfaces split away from it, and best focus lands between them.
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.
Stopping down extends depth of field enough to tolerate the center-to-edge mismatch, but it does not flatten the surface.
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.
An aspheric surface can absorb correction that would otherwise take extra spherical elements, which is why Commonlands compact M12 lenses use them to reach wide apertures without a long stack. How many elements that saves depends on the prescription, field, aperture, band, and tolerances.
The aspheres are molded in glass or plastic depending on the SKU, and several high-volume compact designs are hybrid glass-plastic stacks. A molded glass asphere drifts less in index with temperature than an optical plastic, but that is one term in the thermal budget: what a camera sees is the combined shift of the element powers and of the barrel, spacers, adhesives, and sensor housing, so ask for the modeled or measured focus shift across your range.
Spherical aberration is the classic job for an asphere, but each aspheric surface adds coefficients that act on distortion and field curvature, and in wide-angle M12 designs they are a primary handle on both.
Color is a weaker lever for shape alone: axial and lateral chromatic aberration follow from glass dispersion, so material choice does most of that work. Shape still takes part: an asphere sets how each aperture zone focuses, which enters the spherochromatism balance, and a diffractive surface on an aspheric substrate corrects color directly. Verify distortion, chromatic behavior, and field MTF against the full prescription.
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 signature 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; geometric calibration reaches sub-pixel residuals when target, model, and poses support it, and the remap costs some corner MTF. |
| 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 | Soft haze around high-contrast edges, worst at a low F#; focus position shifts with aperture | 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 | Only partly; stopping down or an asphere reduces it optically, and deconvolution recovers limited detail. |
| 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 in real time. Sub-pixel residuals are achievable rather than automatic: they need a metrology-grade target, enough poses across the field, a model that matches the lens, and stable focus, temperature, and assembly.
Undistortion is not free: the remap resamples every pixel, so local MTF drops where the correction stretches the field hardest, usually the corners, and the noise in neighboring pixels becomes correlated.
Field curvature, astigmatism, spherical aberration, and axial chromatic aberration lower the contrast of fine detail. Where the MTF has reached zero, that information is gone. Below that, deconvolution can partly restore well-characterized blur, but it needs a point-spread-function model for every field position and focus distance and it amplifies noise, so in production it is rarely practical.
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
These three Commonlands lenses show how aberration 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. 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 | A minimum MTF value at a stated spatial frequency, sagittal and tangential, not a single resolution number | Ties the requirement to the sensor's pixel pitch | MTF ≥ 0.30 sagittal and tangential 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 |
A frequency by itself is not a tolerance: it needs a minimum MTF value, the sagittal and tangential orientations, the aperture, the wavelength, and the conjugate beside it.
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
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. In a simple positive lens the marginal rays near the edge typically focus closer than the paraxial rays near the center, though the sign depends on the lens design. 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. The astigmatism-free reference surface is the Petzval surface, named after Josef Petzval; with astigmatism present the sagittal and tangential focal surfaces split away from it.
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. Each aspheric surface also adds degrees of freedom the designer can spend on distortion and field curvature, which wide-angle designs rely on. Chromatic aberration is a weaker lever for surface shape, since axial and lateral color follow from glass dispersion, so check the full prescription rather than assuming one surface covered everything.
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, though the remap resamples the image and costs some corner MTF. 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 manufactures M12 and C-mount lenses for machine vision and offers MTF test reports measured on a Trioptics ImageMaster HR2 system. Send our San Diego engineering team your sensor model, working distance, and inspection requirement at engineering@commonlands.com. Orders placed before 12 PM PT ship same day.