머신 비전을 위한 초점 거리 선택 방법: 공식, 센서 크기 및 선택 단계
초점 거리는 각 설정마다 구체적인 답이 있는 기하학 문제입니다. 이 가이드에서는 공식, 유효 초점 거리의 실제 의미, 전체 선택 절차, 그리고 망원 렌즈가 적합한 경우를 다룹니다.
To choose a focal length for machine vision, start from three measured numbers: the scene width the camera must cover, the working distance from the front of the lens to the target, and the active width of your sensor. The required focal length is EFL = (WD × sensor_width) / FOV_width for rectilinear lenses, a far-conjugate approximation that holds closely at normal machine vision working distances, where the distance is long compared with the focal length.
가장 가까운 표준 초점 거리를 선택한 다음, 주문하기 전에 왜곡, 피사계 심도, 이미지 서클을 확인하세요. 시야각 계산기를 사용하면 어떤 렌즈와 센서 조합이든 몇 초 만에 확인할 수 있습니다.
필요한 초점 거리는 어떻게 계산하나요?
필요한 초점 거리는 유효 센서 폭에 작업 거리를 곱한 값을 필요한 장면 폭으로 나눈 값과 같습니다. 1/2.7인치 센서(유효 폭 5.37mm)가 400mm 거리에서 폭 120mm인 부품을 촬영할 경우, 필요한 초점 거리는 (5.37 × 400) / 120 = 17.9mm가 되므로, 16mm와 21.8mm 렌즈가 고해상도용으로 실용적인 후보 렌즈가 됩니다.
This geometry is a far-conjugate approximation, exact only in a pinhole ray model; real finite-conjugate imaging follows Gaussian conjugates measured from the principal planes, and the error grows with magnification. Covering a 100mm scene from 300mm with a 14.1mm-wide sensor (m ≈ 0.14), the formula gives 42.3mm, while the thin-lens form (Hecht, Optics, 5th ed., §5.2) f = WD × m / (1 + m) gives about 37mm. Fisheye and F-theta lenses use different projections; use datasheet FOV values for those.
유효 초점 거리는 무엇인가요?
Effective focal length (EFL) is the distance from a lens's rear principal plane to its focal point when the lens is focused at infinity. With the sensor size and the object and image conjugates, it sets field of view and magnification; the mm value printed on a lens listing (6mm, 12mm, 35mm) is the EFL. Nominal EFL does not change with working distance: a 12mm lens stays a 12mm lens at 500mm or 100mm. The effective value drifts slightly with focus breathing in internal-focus designs.
| 용어 | 이것이 무엇인지 | 제어 대상 |
|---|---|---|
| EFL (유효 초점 거리) | 처방된 렌즈의 광학적 매개변수 | Field of view and magnification, with sensor and conjugates |
| BFL / MBFL (후초점거리) | 렌즈별 후면 간격 치수 | 홀더 및 어댑터 간 간격 (렌즈가 초점을 맞출 수 있는지 여부) |
| FFD (플랜지 초점 거리) | 마운트 표준 사양 | 렌즈 호환성 (17.526mm C-마운트, 12.526mm CS-마운트, M12는 호환 불가) |
The EFL calculator runs the rectilinear math for common sensor formats and flags where the wide-angle caution applies.
머신 비전 렌즈는 단계별로 어떻게 선택하나요?
- 시야 범위를 정의하십시오. 대상 평면에서의 장면 크기를 밀리미터 단위로 기재하고, 배치 오차에 대비해 10~20%의 여유를 더하십시오. 폭이 200mm인 보드는 240mm의 설계 영역이 됩니다.
- Measure the working distance. Working distance runs from the front of the lens to the target. Early in a project it is a design variable; once the mechanical design commits, it hardens into a number you measure rather than choose. Most Commonlands M12 lenses publish a focus range of roughly 50mm to infinity; the reachable near limit in your build is set by the holder, so check the MOD and holder note on each product page. C-mount working distance varies by product, typically 100mm to infinity. The working distance guide covers this hardening.
- 센서의 유효 영역 치수를 확인하십시오. 센서 데이터시트에서 픽셀 수 × 픽셀 피치를 참조해야 하며, 절대 명목상 포맷 표기를 기준으로 삼아서는 안 됩니다. 이미지 센서 데이터베이스에는 일반적인 부품의 유효 영역이 기재되어 있습니다.
- Set the smallest feature to resolve. Divide scene width by horizontal pixel count for ground sampling distance (mm/pixel). Sensor Nyquist is a sampling ceiling, 1000/(2 × pixel_pitch_um) lp/mm, or two samples per line pair. Two pixels across the smallest feature is a separate inspection rule of thumb, and the headroom you need above it depends on contrast, the algorithm, and your inspection or decoder vendor's minimum sampling spec. The spatial resolution guide covers the math.
- 초점 거리를 계산합니다. EFL = (WD × 센서_폭) / FOV_폭, 그런 다음 가장 가까운 표준 값을 선별합니다. EFL 계산기는 이 과정을 한 번에 처리해 줍니다.
- Choose the mount family. M12 fits compact, light, board-level builds. C-mount fits larger sensors and an adjustable iris; Commonlands C-mount lenses use cam-driven focus, and the focus mechanism and its near-limit behavior are product-specific, so check the product page. CS-mount sits between the two. The lens mount guide compares thread, flange, and coverage in detail.
- Verify image quality. Run four checks: image circle at least as large as the sensor diagonal, distortion against the application's position-error budget, depth of field spanning the object height range (run the depth of field calculator), and lens MTF at the feature's spatial frequency (see the MTF curve guide).
초점 거리는 짧게, 중간으로, 아니면 길게 선택해야 할까요?
Commonlands M12 lenses span all three focal length bands, and a medium range near 5mm to 16mm fits most factory inspection setups. Treat the bands as rough groupings, not hard thresholds. Shorter lenses tend to buy scene coverage and depth of field from close range; longer lenses tend to buy pixel density at the cost of shallower depth of field. Distortion follows the lens projection and correction, not focal length alone. Start medium unless the geometry forces you elsewhere. The depth of field guide covers the long-lens trade.
| 초점 거리 범위 | 시야각 (상대적) | Distortion (design-dependent) | 피사계 심도 | 목표치에 부합하는 픽셀 밀도 | 일반적인 용도 |
|---|---|---|---|---|---|
| Short (<5mm) | 넓은 | Design- and field-dependent | 깊은 | 아래로 | Wide coverage, navigation, autonomous mobile robots (AMRs) |
| 중간 (5–16mm) | 보통 | Varies | 보통 | 보통 | 종합 점검, 바코드 판독 |
| 긴 (>16mm) | 좁은 | Design- and field-dependent | 얕은 | 더 높은 | 정밀 특징 검출, 계측학 |
The field of view column is relative, with no degree ranges, because the angle depends on the sensor as much as the lens: the same 12mm lens reads 25.2° on a 1/2.7" sensor and 33.3° on a 1/1.8" sensor. Compute the actual angle for your lens with the angle of view calculator before classifying a candidate as wide or narrow.
어떤 M12 초점 거리가 대부분의 용도에 적합할까요?
Three stock M12 lenses span the working range for most machine vision setups: 3.3mm for wide coverage, 6.2mm as the general-purpose default, and 12.5mm where pixel density matters. The full M12 catalog runs 0.8mm fisheye to 100mm telephoto.
Commonlands stocks roughly 70 M12 lens models in the US, most offered in several aperture and filter variants. Orders placed before 12 PM PT ship the same day from San Diego, CA.
Commonlands M12 lens options by focal length. Field-of-view angles are diagonal (DFOV), quoted across each lens's full image circle; horizontal coverage on a given sensor is narrower, so confirm it with the angle of view calculator.
| 렌즈 | EFL | 센서 형식 | FOV (diagonal) | 왜곡 | 가격 | 다음에 가장 적합합니다 |
|---|---|---|---|---|---|---|
| CIL036 | 3.3mm | 1/2.7인치 | 6.4mm 화각에서 89° | -0.7% TV | $19 | 좁은 설치 공간에서도 왜곡이 적은 넓은 시야각 |
| CIL062 | 6.2mm | 최대 1/1.8" | 7.2mm 화각에서 60° | -2% 광학 | $19 | 균형 잡힌 종합 점검과 기본 출발점 |
| CIL125 | 12.5mm | 최대 1/2" | 7.9mm 화각에서 35° | -1.4% 광학 | $39 | 더 높은 픽셀 밀도를 갖춘 더 촘촘한 영역으로, 미세한 특징과 레이블을 표현합니다. |
TV distortion is measured as the image-height deviation at the frame edge, optical distortion against the paraxial ideal ray height, and F-theta distortion against the r = f·θ reference. Because the references differ, the percentages are not directly comparable row to row.
어떤 경우에 망원 머신 비전 렌즈를 선택해야 할까요?
Choose a telephoto machine vision lens when the target is small or distant and the camera cannot move closer. As a rough guide, that means the target fills only a small fraction of the frame with the lens you have. Commonlands telephoto M12 options run 12.5mm to 50mm, with 75mm and 100mm models at the long end of the catalog. All of them trade scene coverage for magnification, tighter focus tolerance, and higher vibration sensitivity.
In machine vision, "telephoto" is used loosely for any long-EFL lens. Strictly it names a construction shorter than its focal length, so a long-focus lens is not necessarily telephoto (Smith, Modern Optical Engineering, 4th ed.). Doubling the EFL halves the linear field of view at the same working distance and doubles the apparent target size. Typical applications are aerial inspection from drones, traffic monitoring at distance, overhead conveyor lines, and barcode or OCR reading at long standoff.
Long lenses are less forgiving than short ones. Depth of field shrinks rapidly as focal length grows, so a focus setting easy at 6mm becomes critical at 35mm, and image shift from platform wobble scales with focal length. Plan stiffer mounts, lock focus, and re-verify after mechanical service. The focusing guide covers the procedure.
Telephoto is also often the wrong answer: to monitor a wide area or run on a vibration-heavy platform, a shorter focal length tolerates the pointing error and motion that would push a narrow frame off target.
Near-focus behavior differs by mount. Commonlands C-mount telephotos use cam-driven focus; the mechanism and its near-limit behavior are product-specific, so check the minimum object distance on each product page. M12 telephotos are rigid barrels focused by thread rotation: thread engagement, the barrel shoulder, and rear-element clearance set hard near-focus limits, so short standoffs demand deep holders, and close-range sharpness falls to conjugate-dependent aberrations such as field curvature, not center focus alone.
Selected telephoto M12 lenses reach 1/1.7" sensor coverage in a fixed-aperture board-lens package, the right fit for drones, embedded systems, and weight-limited payloads. Move to C-mount when the sensor is larger, when you need an iris to stop down for depth of field, or when lighting is too dim to fix at a fixed aperture. The low-light section of the f-number guide covers that trade.
Commonlands telephoto M12 lenses from 12.5mm to 50mm, ordered by focal length.
| 부분 | EFL | 서식 | 결의안 | 조리개 | 가격 |
|---|---|---|---|---|---|
| CIL125 | 12.5mm | 최대 1/2" | 12MP | 수정됨 | $39 |
| CIL121 | 21.8mm | 최대 1/1.7인치 | 12MP+ | 수정됨 | $70 |
| CIL350 | 35mm | 1/1.7인치 | 8~10MP | 수정됨 | $59 |
| CIL051 | 50mm | 최대 1/1.8" | 12MP | 수정됨 | $79 |
The resolution column names the sensor class each design targets. MP ratings are unstandardized labels with no aperture, field, spectrum, or contrast conditions attached; confirm against the measured MTF data and pixel-pitch pairing on each product page.
계산된 초점 거리가 존재하지 않는다면 어떻게 될까요?
Round to the nearest stock focal length and recompute the field of view. Rounding shorter gives extra coverage you can crop, the safe default when installation geometry is not locked. Rounding longer gives less coverage and is only acceptable once you confirm the scene still fits the sensor, the call when the feature is small and resolution outweighs coverage. If neither works, a 10–20% working distance change is a starting point we use, provided magnification, clearance, perspective, and lighting allow.
Commonlands stocks M12 focal lengths in discrete steps (2.6mm, 3.3mm, 3.6mm, 6.2mm, 8mm, 12.5mm, 14.2mm, 16mm, 18mm, 19mm, 21.8mm, 25mm, and up), so a calculated value will often land between them. The steps cluster tightly from 12mm to 25mm, where the nearest option usually sits within about 10% of the calculated value. Some intermediate steps, including the 18mm and 19mm options, are lower-resolution designs rated for 2MP sensors and below, so check the resolution rating before shortlisting.
Whatever the rounding decision, validate with physical test images before locking the design: mount the lens at the planned distance, image a calibration target or the real part, and confirm the features resolve and the scene fits. Test images catch corner vignetting, focus error at the target plane, and distortion in the actual part geometry that the math does not.
자주 묻는 질문
The Commonlands FOV calculator runs these formulas for any sensor; the answers below explain the math behind it.
시야각과 작업 거리를 바탕으로 초점 거리를 어떻게 계산하나요?
유효 센서 폭에 작동 거리를 곱한 다음, 필요한 장면 폭으로 나눕니다: EFL = (WD × 센서_폭) / FOV_폭. 400mm 작동 거리에서 120mm 장면을 촬영하는 1/2.7" 센서(유효 폭 5.37mm)의 경우 (5.37 × 400) / 120 = 17.9mm가 필요하므로, 따라서 16mm와 21.8mm가 고해상도 표준 렌즈 후보입니다(18mm 및 19mm 옵션은 2MP 이하 센서용 저해상도 설계로 존재합니다). EFL 계산기는 이를 직접 계산해 줍니다.
유효 초점 거리는 무엇인가요?
Effective focal length (EFL) is the distance from a lens's rear principal plane to its focal point when the lens is focused at infinity. With the sensor size and the object and image conjugates, it sets field of view and magnification. The mm value on a machine vision lens listing (6mm, 12mm, 35mm) is the EFL, not the back focal length and not the flange focal distance.
머신 비전 렌즈를 선정할 때 어떤 단계를 거쳐야 할까요?
Machine vision lens selection runs in a fixed order: define the required field of view, measure the working distance, and pull active sensor dimensions from the sensor datasheet. Then set the smallest feature to resolve, calculate focal length with EFL = (WD × sensor_width) / FOV_width, and choose the mount family. The final step is to verify image circle, distortion, depth of field, and MTF.
망원 머신 비전 렌즈란 무엇인가요?
망원 머신 비전 렌즈는 긴 초점 거리를 갖도록 설계되어, 주어진 작업 거리에서 좁은 시야와 더 높은 배율을 제공합니다. 일반적인 M12 망원 렌즈의 초점 거리는 12.5mm에서 50mm까지이며, 초점 및 진동 허용 오차가 더 엄격하다는 단점이 있지만, 작거나 멀리 있는 대상(항공 검사, 교통 모니터링, 원거리 바코드 판독 등)을 촬영하는 데 사용됩니다.
만약 내 이상적인 초점 거리가 존재하지 않는다면 어떻게 될까요?
Choose the nearest stock focal length and recompute the field of view. Rounding shorter adds coverage you can crop in software, which is the safer direction. Rounding longer cuts coverage and requires confirming the scene still fits the sensor. A 10–20% working distance change is a starting point we use when magnification, clearance, perspective, and lighting allow. Verify any candidate with the field of view calculator before ordering.
적합한 초점 거리 추천 받기
Send your working distance, scene size, and sensor part number to the Commonlands engineering team in San Diego and they will run the numbers with you. Orders placed before 12 PM PT ship the same day.