テレセントリックレンズとは？ 被写体空間におけるテレセントリック性、遠近誤差、およびマシンビジョンにおける代替手段
物体空間のテレセントリック性、像空間のテレセントリック性、および透視誤差に関する解説に加え、標準的なM12マウントやCマウントの光学系が適切な選択肢となる場合についても解説します。
A telecentric lens is a lens in which the chief rays on at least one side of the system run parallel to the optical axis instead of converging toward a finite point. In the object-space form used for machine vision metrology, the entrance pupil sits at optical infinity, so apparent object size stays constant as the object shifts slightly in depth.
Telecentric lenses are not a Commonlands product. This page explains the concept so engineers can decide whether they need one or whether a standard M12 or C-mount lens already solves the problem.
「物体空間テレセントリック性」とは何ですか？
被写体空間テレセントリック性とは、入射瞳が被写体側の光学無限遠に位置するレンズの特性である。各視野点からの主光線は、レンズに入る前に光軸と平行に進むため、被写体がレンズに対してわずかに近づいたり遠ざかったりしても、同じ焦点距離の標準レンズの場合に比べて、倍率がはるかに安定して保たれる。
The entrance pupil is the image of the aperture stop seen from the object side. In a standard lens it sits at a finite distance, so a chief ray's angle of arrival changes when the object moves axially, and apparent size changes with it. Placing the aperture stop at the rear focal plane of the front group maps that pupil to infinity and holds the object-side chief rays parallel.
No lens is perfectly telecentric across the full field at every distance. Telecentric error is specified as a maximum chief-ray angle in degrees, milliradians, or arc-minutes, and checked against the measurement tolerance for tight metrology work.
Pupil location and aperture size are independent. The entrance pupil position sets telecentricity. F-number sets depth of field and light throughput. An object-space telecentric lens can be built with a wide or narrow aperture. The stop location, not its diameter, is what makes the design telecentric.
The geometry also costs size: the front element must be at least as large as the object field, so a lens covering a 50mm field needs a front element of at least 50mm, and these systems often run stopped down with bright LED illumination.
Object-space telecentricity does not increase depth of field. At a given magnification, depth of field is set by f-number and pixel pitch, the same as any lens (estimate it with the depth-of-field calculator). What it changes is how reliably an object measures the same size across that depth of field, which is what dimensional measurement needs and detection does not.
画像空間のテレセントリック性とは何ですか？
像空間テレセントリック性とは、出瞳が像側の光学無限遠に位置するレンズの特性である。主光線は、隅に向かって徐々に角度が急になるのではなく、画角全体にわたってセンサーに対してほぼ垂直に到達する。これはセンサー結合の特性であり、測定精度の特性ではない。また、被写体距離に対する倍率を安定させるものではない。
Both pupils are images of the same aperture stop. In most lenses they sit at finite distances, so the chief ray angle (CRA) at the sensor increases with field position, reaching 20°–30° at the corners of some large-format designs. Placing the aperture stop at the front focal plane of the rear group sends the exit pupil to infinity instead.
The benefit is at the sensor. CMOS sensors use microlenses shifted progressively from center to corner to match an expected CRA. If the actual angles exceed what that design expects, corner pixels lose fill factor. That produces shading, and on color sensors, it also shifts corner color. Holding incidence near zero removes the gradient. That matters most for large-format sensors (1" and above) with strict CRA specs and much less for small formats with relaxed tolerance.
像空間のテレセントリック性は、被写体距離に対する倍率が一定であることを保証するものではなく、また、被写体空間のテレセントリック性は、センサーへの主光線がほぼ垂直に照射されることを保証するものではありません。これらは互いに独立した特性であり、それぞれ異なる問題を解決するものです。両方の特性が必要な用途では、バイテレセントリックレンズが必要となります。
Image-space telecentricity does not fix distortion or MTF. A lens can still show barrel distortion or poor full-aperture MTF, so evaluate those separately. To decide whether you need it, compare the sensor's maximum CRA spec at the image corner to the lens's expected CRA there. Commonlands M12 and C-mount lenses target the small- and medium-format sensors common in embedded vision, where relaxed CRA tolerance usually makes it unnecessary.
遠近法の誤差とは何ですか？
遠近法誤差とは、従来の内中心レンズが角度視野を通じて被写体を観察する際に生じる測定誤差のことです。すべての主光線は有限の距離にある単一の入射瞳に向かって収束するため、ある作動距離にある被写体は、レンズからわずかに近い位置または遠い位置にある同じ被写体とは異なる角度をなしており、測定される大きさも異なります。これは投影幾何学に起因するものであり、レンズの収差ではありません。
This is why perspective error and lens distortion are different problems. Distortion is a fixed optical aberration that misplaces image points relative to an ideal rectilinear grid. It is repeatable and can be characterized and removed through calibration. Perspective error depends on the 3D position of each scene point, which changes from part to part, so no fixed calibration removes it. A lens can measure less than 0.1% distortion and still produce substantial perspective error if part height or working distance varies.
| エラーの種類 | 根本原因 | 変更点 | 一般的な対処法 |
|---|---|---|---|
| レンズの歪み | レンズ要素における光学収差 | 画像上の点の位置と理想的な直線格子との比較 | 低歪みレンズ；ソフトウェアによるキャリブレーション |
| 遠近法の誤り | 角度視野、中心投影法 | 被写体までの距離が変わったときの倍率 | 物体空間テレセントリックレンズ；一定の作動距離における固定された平面被写体 |
| 視差誤差（関連） | Central projection through a finite entrance pupil, combined with scene depth | 身長によって、特徴が横方向にずれて見える | Object-space telecentric lens; controlled, fixed working distance |
For a rough estimate, the magnification change across a height variation h at working distance d is approximately h/(d - f), which simplifies to h/d when the working distance is large relative to focal length. A 5mm tall part at 200mm introduces roughly 2.5% variation between its near and far faces. Whether that is acceptable depends on the tolerance, and for sub-pixel metrology it usually is not. Use the field-of-view calculator to check magnification at your working distance.
It shows up most in tall or tilted parts and in setups with variable working distance, and is largely irrelevant for flat parts at a fixed working distance or for presence/absence checks.
A related effect is parallax error: the same projection that changes apparent size with depth also shifts an off-axis feature laterally in proportion to its height. Both are addressed the same way, by fixing working distance mechanically where possible and moving to object-space telecentric optics when fixturing cannot hold depth inside the tolerance budget. Software distortion correction is not a substitute, because that error depends on each part's geometry, not a fixed lens property.
「エントセントリックレンズ」とは何ですか？
An entocentric lens is a conventional lens in which all chief rays converge toward a single entrance pupil at a finite distance inside the optical system. Objects farther from the lens appear smaller in the image. This central projection is the standard behavior of ordinary lenses, and the term entocentric simply describes it. It does not imply lower quality. Most M12 and C-mount lenses used in machine vision are entocentric unless a product page explicitly states telecentric.
The thin-lens relationship shows why magnification tracks distance: image height equals focal length times object height, divided by (object distance minus focal length). Focused at one working distance, magnification is fixed there, but if the object shifts even a few millimeters, image height changes proportionally. For a 50mm lens at a 500mm working distance, a 5mm shift changes magnification by roughly 1.1%, which can matter for a system targeting sub-1% accuracy.
Entocentric lenses remain the right default for most machine vision work. Commonlands supplies M12 and C-mount entocentric optics for general inspection, assembly verification, robotic guidance, and barcode or QR reading. They also cover flat or nearly flat parts imaged at a consistent working distance, and wide fields of view where a telecentric front element would grow large and expensive.
Entocentric lenses can still support dimensional measurement when scene geometry is favorable, with careful calibration. The limiting factor is whether depth variation in the scene stays inside the measurement tolerance. Treating entocentric as a lesser category misreads the term: it describes projection geometry, not image quality.
テレセントリックレンズとエントセントリックレンズ：主な違い
The three telecentric configurations are easy to conflate. This table separates them by which pupil sits at infinity and which problem each one solves, including where a standard entocentric lens fits.
| 設定 | 無限遠の瞳孔 | 制御されたままのもの | 肝心なところ |
|---|---|---|---|
| 被写体空間テレセントリック | 入射瞳 | 倍率と被写体距離の関係 | 寸法測定、ゲージ測定、高さが変動する部品 |
| 画像空間テレセントリック | 出射瞳 | センサーにおける主光線角 | CRA公差が厳格に規定された大判センサー |
| 双テレセントリック | 両方とも | 上記の両方を同時に | 均一なセンサー結合も求められる高精度計測 |
| 内中心（標準） | どちらでもない | 明示的な制約はない | 一般的な検知・検査、ロボット工学、バーコード読み取り |
When a machine-vision catalog says "telecentric" without qualification, it means the object-space form unless stated otherwise. If a vendor lists "bi-telecentric," verify it against the exit pupil specification. Telecentricity, MTF, and distortion are independent specifications, and none substitutes for the others. When the tolerance budget allows a standard lens, Commonlands M12 and C-mount entocentric optics cover the same inspection work at lower cost and size.
Telecentric or standard: how to choose
Telecentric lenses solve one problem: magnification stability when object depth cannot be perfectly controlled. The clearest cases are precision dimensional gauging to fractions of a millimeter where parts cannot sit at a fixed distance, height-variation inspection where thickness differences or board warp would shift apparent dimensions into false accepts or rejects, and metrology that must hold calibration over long runs despite small drift along the Z axis.
The common factor is depth variation that cannot be removed mechanically. Telecentric optics earn their place when perspective error is a significant fraction of tolerance, not because telecentricity reads as a premium feature.
Most applications do not clear that bar, and a standard low-distortion lens is the right answer more often than engineers assume:
- Detection, presence-absence, and classification, where tight dimensional measurement is not required.
- Parts fixtured accurately enough that depth variation stays small relative to working distance.
- Setups needing working-distance flexibility, since standard lenses focus over a range and telecentric lenses have a fixed conjugate.
- Deployments where size, weight, or cost rules out a large telecentric front element.
Check magnification with the field-of-view calculator and focal length with the EFL calculator. Commonlands does not stock telecentric lenses, but its engineering team can help run that tolerance math for a standard M12 or C-mount alternative.
テレセントリックレンズのメーカー：購入先
Commonlands does not stock telecentric lenses. The manufacturers below are established sources for object-space and bi-telecentric optics in industrial machine vision, each a lens maker with a catalog telecentric line, listed with where it is based and what it is known for.
| 製造元 | 本部 | 注目の製品 | よく知られているのは |
|---|---|---|---|
| オプト・エンジニアリング | イタリア | 専用テレセントリック光学系およびマシンビジョン用光学系 | 物体空間およびバイテレセントリックラインを網羅した幅広いテレセントリック製品カタログ |
| エドマンド・オプティクス | アメリカ | 光学製品およびマシンビジョン用レンズのカタログ | TECHSPEC テレセントリック製品群、豊富な在庫、迅速な発送 |
| VSテクノロジー | 日本 | マシンビジョン用レンズ | テレセントリックおよび高解像度の産業用レンズ |
| モリテックス | 日本 | マシンビジョン用光学系および照明 | テレセントリックレンズと、それに適合した照明の組み合わせ |
| シル・オプティクス | ドイツ | テレセントリック光学系、スキャン光学系、およびf-θ光学系 | テレセントリック測定レンズおよびカスタム設計 |
| コンピュター | 日本 | マシンビジョンおよびCCTV用レンズ | 標準レンズと並んで展開されるエントリーレベルのテレセントリックレンズシリーズ |
Commonlandsの標準レンズの代替品
These are entocentric lenses, not telecentric ones. They fit when controlled fixturing, working distances long relative to part height, or a tolerance budget that absorbs residual perspective error mean telecentricity is not required. Each offers low geometric distortion, which addresses in-plane accuracy, a separate property from magnification stability across depth.
The M12 vs. C-mount guide covers the mechanical differences between the two mount families. The choice turns on sensor format, working distance, and whether adjustable-iris depth-of-field control is needed, not on telecentricity.
よくある質問
テレセントリックレンズとは何ですか？
A telecentric lens is one whose chief rays, on at least one side of the system, run parallel to the optical axis instead of converging toward a finite point. The common object-space form places the entrance pupil at optical infinity, so apparent object size stays constant across the usable depth range.
「物体空間テレセントリック性」とは何ですか？
Object-space telecentricity means the entrance pupil sits at optical infinity on the object side. Chief rays from every field point travel parallel to the axis, so magnification stays much more constant as the object shifts slightly in depth. This is the form used for dimensional measurement.
画像空間のテレセントリック性とは何ですか？
Image-space telecentricity means the exit pupil sits at optical infinity on the image side, so chief rays arrive near-perpendicular to the sensor across the field. It improves coupling with sensor microlenses and can reduce corner shading, but it does not stabilize magnification versus object distance.
テレセントリックレンズは、低歪みレンズと同じものですか？
No. Low distortion describes how faithfully a lens maps straight lines within a plane. Telecentricity describes chief-ray direction and whether magnification is stable versus depth. A lens can have very low distortion and still show perspective error. They correct different problems.
検査システム用のレンズをお選びですか？
テレセントリック光学系はCommonlands社の製品ではありませんが、標準的なM12およびCマウントレンズであれば、マシンビジョン用途の大部分をカバーできます。無料の計算ツールを使用して、ご使用の作動距離における視野角や被写界深度を確認するか、特定の測定公差についてご相談の際は、エンジニアリング部門までお問い合わせください。