MTF 곡선 해석 방법: 머신 비전을 위한 명암비, 공간 주파수 및 센서 매칭
MTF는 공간 주파수에 대한 콘트라스트 전달도를 나타냅니다. 이 가이드에서는 두 가지 차트 형식, 시상 곡선과 접선 곡선, 필드 위치 데이터, 픽셀 피치별 센서 매칭, 그리고 설계 MTF와 측정 MTF의 차이점을 모두 다룹니다.
An MTF curve plots how much contrast a lens transfers from scene to sensor, on a scale of 0 to 1, against spatial frequency in line pairs per millimeter (lp/mm).
To read one: calculate the Nyquist frequency of your sensor, read the lens contrast across the frequency band your task actually samples, which we start at 0.5× to 0.7× of that frequency, at the field positions your algorithm uses, and check that the sagittal and tangential curves stay close together. A lens that looks strong at the center can still fall short at the edge of the image circle, so field-position data matters as much as the on-axis curve.
MTF란 무엇인가요?
MTF, the modulation transfer function, is the ratio of image contrast to object contrast as a function of spatial frequency, measured in line pairs per millimeter (lp/mm). An MTF of 1.0 means the lens transfers full contrast at that frequency, while 0.3 means only 30% survives. Every MTF value is tied to a specific frequency, field position, and test condition.
One line pair is one dark bar plus one adjacent bright bar. A spatial frequency of 50 lp/mm packs 50 such pairs into one millimeter on the sensor, so higher lp/mm means finer detail. A 10µm line width in a periodic pattern, 20µm per pair, is 50 lp/mm; a 5µm line width is 100 lp/mm. An isolated feature has no single frequency and does not convert this way.
MTF is field-dependent: the same lens usually measures higher at the center than at the edge, so a full characterization reports curves at several image heights.
MTF 곡선은 어떻게 해석하나요?
Identify the plot format first. MTF vs spatial frequency fixes the field position and sweeps detail fineness. MTF vs image height fixes the frequency and sweeps from center to corner. Read contrast at the frequencies your sensor samples and the field positions your algorithm uses, on both curves.
A datasheet with only one format is half a specification. Commonlands publishes both for its measured M12 lenses.
주파수 축 읽기
On an MTF vs spatial frequency chart, the x-axis runs in lp/mm and the y-axis runs from 0 to 1.0, or 0 to 100% on some datasheets. The information is in how fast the curve falls and where it sits at the frequencies you care about.
Datasheets usually overlay curves for several field positions: on-axis, around 0.7 field (70% of the lens's specified maximum image height), and full field. That maximum is the image-circle radius, not necessarily half the sensor diagonal. Each position carries sagittal and tangential traces. Higher and flatter is better across the band your application samples. The sensor-matching section derives that band from pixel pitch.
시상면 및 접선면 MTF 곡선은 무엇을 의미하나요?
Sagittal curves plot contrast for features oriented radially, along the line from the image center outward. Tangential curves plot contrast for features perpendicular to that radius. The two are identical on-axis for a perfectly centered, rotationally symmetric design.
A wheel makes it concrete: sagittal features run like spokes; tangential features run like the rim. Off-axis in an astigmatic lens, spoke-oriented and rim-oriented detail focus at slightly different distances, so one orientation is sharp while the other is soft at a single focus setting.
The separation is a diagnostic signal. On-axis, an S-T split points to assembly asymmetry such as decenter or tilt, though test-fixture misalignment can produce the same signature. Off-axis, a widening gap indicates astigmatism building toward the image boundary: round holes image as ellipses near the corners, and edge thresholds tuned at one orientation misfire at another. When feature orientation is fixed, verify the lower of the two curves at your operating frequency.
MTF 대 필드 위치 곡선은 어떻게 해석하나요?
An MTF vs field curve plots contrast at a fixed spatial frequency against image height, the distance from the optical axis in millimeters. The center sits at 0mm, while the maximum is the image height the lens is specified to cover, the radius of its image circle. Only a matched format puts the sensor half-diagonal at that endpoint. A flat curve means uniform performance. A steep drop usually marks where correction runs out.
Convert your sensor geometry to image height before reading. A 1/1.7" sensor has a diagonal of about 9.4mm, so its corner sits near 4.7mm image height. Format names do not map exactly to millimeters, so take the diagonal from the sensor datasheet, not the format label. The sensor size and lens compatibility guide covers image circle coverage and format math.
Two shapes call for different responses. A smooth, moderate decline that still clears your contrast threshold at the corner is normal for a well-corrected design. A cliff at a specific radius usually marks a design boundary, and no focus adjustment fixes the soft corners a sensor gets by reaching past it.
Confirm the cause before you accept that reading: defocus, field curvature, vignetting, sensor or target tilt, fixture misalignment, and assembly decenter bend a field curve the same way, and a through-focus sweep separates them. Wide-angle designs face the hardest field demands, so a 4mm lens covering 98° needs field MTF verified at several image heights, not a center measurement extrapolated outward.
렌즈의 MTF를 센서의 픽셀 피치와 어떻게 일치시키나요?
Calculate the sensor's Nyquist frequency, 1000 divided by twice the pixel pitch in µm, then read the lens MTF at every field position your algorithm uses. Commonlands starts at 0.5× to 0.7× of Nyquist and at an MTF near 0.3. Both are heuristics, not standards, so validate them against your task: the band that matters follows from your feature size and contrast, and whether the lens limits the system depends on the whole chain of sampling, sensor, ISP, noise, and task tolerance.
That band sits below Nyquist because the sampled response there is set by more than the lens: pixel aperture, a color filter array and its demosaic, an optical low-pass filter, sampling phase, noise, and the ISP. A monochrome sensor with no OLPF holds contrast much closer to Nyquist, at the price of aliasing.
For a 1.85µm sensor, that band spans roughly 135 to 190 lp/mm. Against the 0.3 starting point, a lens that clears it there carries contrast the sensor can digitize, while one near 0.2 at half-Nyquist leaves those extra pixels resolving less detail than their count implies. Both readings are starting calls, not verdicts.
명암 대비 임계값 설정
No universal MTF threshold guarantees reliable machine vision, and an application name alone does not fix an image-plane frequency. That comes from the smallest feature the task reads, carried into the image plane by magnification, and it shifts with field position, spectrum, and scene contrast. Fix those first. The rows below are Commonlands starting heuristics, not published engineering standards; derive your own from feature size, magnification, field, wavelength, aperture, and a task acceptance criterion.
| 신청 | Typical image-space frequency (lp/mm at the sensor) | MTF 목표 시작 | 참고 사항 |
|---|---|---|---|
| 1차원 바코드 판독 | 10–40 lp/mm | 좁은 바 주파수에서 0.4 | 넓은 바는 오류에 대한 허용 범위가 넓지만, 고밀도 Code 128의 좁은 바는 그렇지 않습니다. |
| OCR | 40–80 lp/mm | 스트로크 주파수에서 0.3 | 인쇄된 글자의 획은 일반적으로 글자 크기와 인쇄 공정에 따라 물체 위에서 대략 100~400µm 정도를 차지합니다. |
| 표면 결함 검사 | 최소 결함 크기로 설정 | 결함 주파수에서 0.3 | 결함 크기 × 배율을 곱하면 센서상의 특징 크기가 나오며, 이를 통해 주파수를 구할 수 있다. |
| 치수 측정 | 50–150 lp/mm | 나이퀴스트 주파수의 절반에서 0.4, 전 영역에 걸쳐 균일함 | 서브픽셀 에지 감지 시에도 왜곡 허용 한도를 별도로 확인해야 합니다. |
| AI / CNN 기반 물체 탐지 | 20–60 lp/mm | 중주파수 대역에서 0.3, 전계 균일 | CNN은 에지 기반 코드보다 소프트 옵틱스를 더 잘 수용하지만, 훈련 및 배포 시 사용되는 옵틱스는 일치해야 합니다. |
이미지 공간의 주파수와 장면 내 특징 크기의 상관관계
MTF is specified in the image plane, so object-space features must be converted through magnification. Image-space frequency equals object-space frequency divided by the magnification m (image size over object size). At m = 0.1, a 10 lp/mm pattern in the scene lands at 100 lp/mm on the sensor, so that is the frequency to read. The field of view calculator gives the magnification for your geometry.
Aperture belongs in the same calculation: stopping down one to two stops often lifts off-axis MTF as aberrations shrink faster than diffraction grows. On the fixed-aperture M12 lenses Commonlands measures, that operating point is set at purchase. A C-mount iris can be tuned at the fixture.
설계 MTF와 측정 MTF의 차이점은 무엇인가요?
Design MTF is computed from the lens prescription in optical design software, with every element at its nominal position. Measured MTF is instrument data from a physical lens. It includes the decenter, tilt, spacing error, and glass variation a real build carries, so as-built MTF is typically lower than the design curve. Tolerance analysis predicts a distribution rather than one line. Two units of the same design measure differently, so acceptance should use measured data.
A standard report covers MTF vs spatial frequency and MTF vs field at 9 field points across 3 azimuths, plus EFL and distortion at 21 points. It also covers lateral and longitudinal chromatic aberration at 480nm, 546nm, and 644nm. Astigmatism and field curvature are included, with through-focus MTF on request.
Curves are measured on a Trioptics ImageMaster HR2, with calibration documentation available on request, so a report can back incoming inspection and lot acceptance. The $199 report is open to customer-supplied lenses, and near-infrared users can request 850nm and 940nm. Current scope and pricing are on the MTF testing service page.
F/2.0, 무한대 초점, 546nm 조건에서 측정된 곡선을 F/5.6, 500mm 공액, 광대역 백색광 조건에서 측정된 곡선과 직접 비교할 수는 없습니다. 두 측정값 모두 서로 다른 작동 지점에 대한 유효한 측정값입니다. 특정 파장에서 조리개를 최대로 연 상태의 중심 MTF만 제시하는 공급업체는 가장 유리한 수치만을 보여주고 있을 뿐, 귀하의 장비가 실제로 관측하게 될 수치는 아닙니다.
MTF 측정 옵션 비교
Three routes produce MTF data, and they do not measure the same thing. Pick the cheapest route that isolates the variable you need to qualify.
| 접근 방식 | 측정 항목 | 상대적 비용 | 가장 적합한 |
|---|---|---|---|
| 사내 경사 모서리 측정 (ISO 12233 차트 및 분석 소프트웨어) | 시스템 수준의 MTF: 렌즈, 센서 및 ISP를 종합한 값으로, 작업 거리 기준 | 가장 저렴한 방법: 이미 보유하고 있는 하드웨어에 인쇄된 타깃과 소프트웨어를 활용하는 것 | 자사 생산 라인에서 합격/불합격 검사 실시 |
| Commonlands MTF testing on the Trioptics ImageMaster HR2 | 교정된 시험대에서 측정된 부품 수준의 렌즈 MTF: 3개의 방위각에 걸쳐 9개 위치에서 주파수 및 시야에 따른 비교 | 렌즈당 199달러, 초기 투자 비용 없음 | Incoming inspection or lot acceptance without owning a bench |
| Trioptics 또는 Optikos에서 제공하는 전용 실험 장비 또는 실험대 사용 시간 | 처리량에 맞춰 조정된 구성 요소 수준의 MTF 및 광범위한 광학 계측 | 최고; 자본 설비 또는 시간당 작업대 서비스 | 대량 입고 검사 또는 사내 계측 실험실 |
MTF 테스트를 거친 렌즈 및 MTF 테스트 서비스
Commonlands measures lens designs on the Trioptics ImageMaster HR2, so selection decisions can rest on measured curves rather than design plots. Three MTF-tested options cover the demand space: the CIL560 4mm C-mount for wide-field coverage, the CIL561 6mm C-mount for a tighter field on the same 1/1.7" format, and the CIL122 IR-corrected 12mm M12 for near-IR work. The test service applies the same instrument to lenses you supply.
Commonlands stocks a broad range of M12 lens variants in the US, with C-mount and filter inventory alongside. Orders placed before 12 PM PT ship same day from San Diego, CA. ISO 9001:2015 certified.
자주 묻는 질문
렌즈에서 MTF란 무엇인가요?
MTF, the modulation transfer function, is the ratio of image contrast to object contrast at a given spatial frequency, expressed in line pairs per millimeter (lp/mm). An MTF of 1.0 means full contrast transfer, while 0.3 means only 30% survives. It is a curve across frequency and field position, not a single sharpness score.
MTF 차트는 어떻게 읽나요?
먼저 형식을 파악하십시오. MTF 대 공간 주파수 그래프는 고정된 시야 위치에서 lp/mm를 기준으로 대비를 나타내는 반면, MTF 대 이미지 높이 그래프는 고정된 주파수에서 시야 위치를 기준으로 대비를 나타냅니다. 센서가 샘플링하는 주파수 대역과 알고리즘이 사용하는 시야 위치에서 대비 값을 확인하고, 난시에 대해서는 시상 곡선과 접선 곡선을 비교하십시오.
MTF 그래프에서 ‘시상(sagittal)’과 ‘접선(tangential)’은 각각 무엇을 의미하나요?
Sagittal curves describe contrast for features oriented radially, like spokes pointing at the image center. Tangential curves describe features perpendicular to the radius. They are identical on-axis for a centered design. On a measured unit, an on-axis split points to asymmetry in the assembly such as decenter or tilt, though test-fixture misalignment can produce the same signature. A large gap off-axis indicates astigmatism: round objects image as ellipses, and edge sharpness depends on orientation at that field height.
MTF를 픽셀 피치에 어떻게 맞추나요?
Calculate the Nyquist frequency: 1000 / (2 × pixel pitch in µm). A 1.85µm pixel gives 270 lp/mm. A 3.45µm pixel gives 145 lp/mm. Then check lens MTF across the band your task samples, at the field positions your algorithm uses. Commonlands starts near 0.5× to 0.7× Nyquist and at an MTF near 0.3; both are heuristics to validate against your task, not standards, and final resolution depends on the whole imaging chain.
설계 MTF와 측정 MTF의 차이점은 무엇인가요?
설계 MTF는 설계 소프트웨어에서 광학 처방에 따라 예측된 값으로, 모든 요소가 완벽하게 제작되고 배치된 상태를 반영합니다. 측정된 MTF는 실제 렌즈를 측정 기기로 테스트하여 얻은 값으로, 중심 이탈, 기울기, 간격 오차와 같은 제조 공차 등이 포함됩니다. 실제 제작된 렌즈는 일반적으로 설계 곡선보다 낮은 수치를 보이기 때문에, 합격 여부 판단 시에는 측정된 데이터를 사용해야 합니다.
특정 렌즈에 대한 MTF 데이터가 필요하신가요?
Send the Commonlands engineering team your sensor, pixel pitch, working distance, and the field positions your algorithm uses. We will pull measured curves or run a Trioptics HR2 report on the lens in question.