머신 비전의 공간 분해능: 픽셀당 mm, 최소 감지 가능 크기, 그리고 회절 한계
Field of view, pixel count, lens resolving power, and aperture combine to set the smallest feature a camera system can detect.
Spatial resolution is the real-world size one pixel samples at the working distance: the sampling interval, not the smallest feature the system can resolve. Divide the field of view by the pixel count across it: a 100mm wide FOV on 2592 horizontal pixels gives 0.039mm per pixel. The smallest reliably detectable feature must span several pixels, typically 3 to 5 for detection and 10 or more for measurement.
Pixel math sets the ceiling, not the result. The lens must resolve the spatial frequency the pixel pitch demands (the Nyquist rule, lp/mm = 1 ÷ (2 × pixel pitch in mm)), and the aperture controls the diffraction Airy disk (d = 2.44 × λ × F#): once the disk grows past roughly two pixel pitches, diffraction erodes fine detail gradually. This guide covers all four layers: pixel math, angular sampling (IFOV), lens resolving power, and diffraction.
What Is Spatial Resolution in Machine Vision?
Spatial resolution is the real-world size one pixel samples at the working distance, written as mm per pixel: a sampling interval (strictly, the object-space sampling distance; ground sample distance in remote sensing), not the smallest feature the system resolves. Two numbers set it: field of view and pixel count along that axis. A 12MP camera (4032 × 3024) on a 600mm wide tote has 0.149mm per pixel; on a 60mm connector it has 0.0149mm per pixel, ten times finer. Only the field of view changed.
If one pixel covers 0.1mm, a 0.05mm scratch is sub-pixel and usually lost unless its contrast is high; a 0.4mm scratch spans four pixels and is detectable. Its distance-independent counterpart is the per-pixel angle, covered in the IFOV section. A megapixel count is only a pixel budget, so this guide also covers resolving power and diffraction, with Commonlands M12 and C-mount examples.
How Do You Calculate mm per Pixel?
Divide the field of view by the pixel count along the same axis. A 100mm wide scene on 2592 horizontal pixels gives 0.0386mm per pixel. The reciprocal is pixels per mm.
Use mm per pixel for inspection sizing. Lens resolving power is quoted in lp/mm at the image plane, a different plane from object-space pixels per mm: divide an object-space frequency by the magnification to compare, or work in image space, where one line pair needs two pixels (lp/mm = 1 ÷ (2 × pixel pitch in mm)). Model any sensor, focal length, and working distance with the Commonlands FOV calculator. With noticeable distortion, the average does not hold at the frame edges.
What Is the Minimum Detectable Size in Machine Vision?
Minimum detectable size is the smallest feature a system reliably identifies. Multiply spatial resolution by the pixel coverage the task needs: minimum size = (FOV ÷ pixel count) × required pixels. Two pixels is the theoretical sampling floor, a Nyquist figure for periodic patterns that noise or blur erases; a high-contrast sub-pixel particle can still be detected, but not sized. Production inspection typically needs 3 to 5 pixels across a defect, and measurement 10 or more; both are starting heuristics moved by contrast, SNR, and algorithm.
| 과제 | 전체 화면에 걸친 픽셀 | 참고 사항 |
|---|---|---|
| 이론적 표본 하한 | 2 | 서브 픽셀 정렬과 거의 완벽한 명암비에 달려 있으며, 디자인상의 고려 사항은 아닙니다. |
| 명암 대비가 뚜렷한 유무 | 3–5 | 조명이 제어된 환경에서 밝은 배경 위의 어두운 균열에 대한 유효 마진 |
| 형태 또는 방향 분류 | 5–10 | 원형 특징과 길쭉한 특징을 구분할 수 있을 만큼 충분한 세부 정보 |
| 명암 대비가 낮거나 질감이 있는 결함 | 8–15 | 더 많은 픽셀이 노이즈 플로어 이상의 충분한 신호를 축적합니다 |
| 치수 측정 | 10+ | 서브픽셀 알고리즘은 약 0.1~0.3 픽셀까지 정밀도를 높이지만, 이는 해상도가 높은 경계에서만 적용됩니다. |
Target: detect a 0.2mm scratch with 5 pixels of coverage. Required spatial resolution = 0.2 ÷ 5 = 0.04 mm/pixel. On a 2448-pixel-wide sensor, the maximum horizontal FOV = 0.04 × 2448 = 98mm. Find the focal length that produces a 98mm FOV at your working distance.
Motion Blur Eats the Pixel Budget
A part moving at velocity v during exposure t smears the image by v × t. Keeping that smear under half a pixel at your spatial resolution is a common heuristic; past it, features near the minimum detectable size start disappearing.
What Is IFOV in Machine Vision?
Instantaneous field of view (IFOV) is the angle a single pixel subtends. It is a sampling quantity, not optical angular resolution: separating two points is a Rayleigh or MTF question, and a system can sample finer than its optics resolve. IFOV = FOV ÷ pixel count gives the frame average, since the per-pixel value varies with field position. An 80° FOV across 3840 pixels averages 0.021° per pixel, or 48 pixels per degree. Multiplied by the working distance, that becomes the pixel footprint on the object.
| 렌즈 | FOV (axis named) | IFOV on a 4K frame | 도당 픽셀 수 |
|---|---|---|---|
| CIL250 25mm 망원 M12 | 20° diagonal @ 8.8mm image circle (sensors up to 1/1.7") | 0.0045° (diagonal) | ~220 (diagonal) |
At fixed sensor resolution, wide coverage and fine angular sampling are in direct tension. Because real-world contrast, noise, and blur are worse than on the bench, many teams carry a 2× to 3× design margin over the theoretical minimum pixel count; the factor depends on MTF, task contrast, sensor noise, and the detector or decoder's minimum-sampling spec.
What Does a Megapixel Rating Mean on a Machine Vision Lens?
렌즈에 표기된 메가픽셀 수치는 광학 분해능이 아니라, 해당 렌즈가 지원하도록 설계된 센서 등급(픽셀 피치와 포맷의 조합)을 나타냅니다. 분해능은 이미지 평면에서 밀리미터당 라인 페어(lp/mm) 단위로 측정되며, 나이퀴스트 법칙에 따라 다음과 같은 요건이 정해집니다: lp/mm = 1 ÷ (2 × 픽셀 피치(mm)).
| 픽셀 피치 | 필요 lp/mm (나이퀴스트) | 센서 예시 |
|---|---|---|
| 5.0µm급 | 100 lp/mm | 더 큰 픽셀 크기를 가진 글로벌 셔터 센서 |
| 3.45µm | 145 lp/mm | 소니 프레지우스 IMX250, IMX264 (5MP), IMX253, IMX304 (12MP) |
| 2.74µm | 182 lp/mm | 소니 프레지우스 S IMX547 (5.1MP), IMX546 (8.1MP), IMX541 (20.4MP) |
| 2.0µm | 250 lp/mm | 소니 IMX678(8MP, 1/1.8") 및 이와 유사한 임베디드 센서 |
| 1.55µm | 323 lp/mm | 고밀도 내장형 및 스마트폰급 센서 |
Coverage is the second requirement: the lens image circle must be at least the sensor diagonal, or the corners vignette. The MTF check evaluates contrast near 0.5 to 0.7× the Nyquist frequency the pixel pitch sets, a Commonlands starting band rather than a standard (validate against your task), held out to the corners. Nyquist itself is a sampling ceiling, not an MTF target; a cutoff above it does not guarantee contrast holds that far. If either check fails, the lens limits the system regardless of megapixel labels.
What Is the Diffraction Limit in Machine Vision?
The diffraction limit is the minimum blur spot a lens can produce at a given aperture, set by the wave nature of light, not manufacturing quality. Stopping down shrinks aberrations but grows the Airy disk linearly with F#, so a smaller aperture eventually caps resolution.
The MTF of a diffraction-limited lens falls to zero at a cutoff frequency of 1 ÷ (λ × F#). At 550nm and F/8, that cutoff is roughly 227 lp/mm. At F/16, still at 550nm, it drops to 114 lp/mm, below the 145 lp/mm a 3.45µm sensor needs. "Diffraction-limited" is not a defect label: the lens is corrected well enough that diffraction, not residual aberration, decides image quality at that aperture.
What Is an Airy Disk?
The Airy disk is the bright central spot of the diffraction pattern from a point source imaged through a circular aperture. The first dark ring bounds it; about 84% of the pattern's energy falls inside (Hecht, Optics, 5th ed.). No lens can focus light to a smaller spot at that aperture and wavelength.
| F# | 550nm에서 관측된 에어리 원반 | 3.45µm 픽셀에 걸친 범위 | 2.74µm 픽셀에 걸친 범위 | 1.55µm 픽셀에 걸친 범위 |
|---|---|---|---|---|
| F/1.9 | 2.5µm | 0.7 픽셀 | 0.9 픽셀 | 1.6 픽셀 |
| F/2.8 | 3.8µm | 1.1 픽셀 | 1.4 픽셀 | 2.4 픽셀 |
| F/4 | 5.4µm | 1.6 픽셀 | 2.0 픽셀 | 3.5 픽셀 |
| F/5.6 | 7.5µm | 2.2 픽셀 | 2.7 픽셀 | 4.8 픽셀 |
| F/8 | 10.7µm | 3.1 픽셀 | 3.9 픽셀 | 6.9 픽셀 |
| F/11 | 14.8µm | 4.3 픽셀 | 5.4 픽셀 | 9.5 픽셀 |
| F/16 | 21.5µm | 6.2 픽셀 | 7.8 픽셀 | 13.9 픽셀 |
Wavelength scales the disk linearly. At 850nm the Airy disk is about 55% larger than at 550nm for the same F#, so NIR systems hit diffraction at wider apertures than visible-light systems. See the NIR imaging guide for wavelength-specific notes.
Pixel-Pitch Matching: When the Sensor Out-Resolves the Lens
Compare the Airy disk to twice the pixel pitch as a marker, not a cliff: diffraction contrast falls off gradually, so useful detail survives past it. At 550nm and far conjugates, that marker lands near F/5.1 for 3.45µm pixels, F/4.1 for 2.74µm pixels, and F/2.3 for 1.55µm pixels; close in, substitute the working f-number.
With aperture and format equal, a 2.74µm 20MP sensor samples finer detail than a 3.45µm 12MP one while lens MTF keeps up; past the 2.74µm marker, diffraction erases that edge first, so the full system, not pixel count, decides.
Opening from F/11 to F/5.6 admits roughly 4× the light and halves the Airy disk. Brighter or strobed light buys back the exposure lost to a stopped-down aperture; deconvolution can partially restore diffraction-attenuated contrast, at a noise cost; nothing recovers detail past the cutoff. Pick the aperture from the depth of field your scene needs with the depth of field calculator, then check the Airy disk against twice the pixel pitch and the MTF there. The Commonlands f-number guide covers the full tradeoff.
Lens Examples Across the Resolution Range
These Commonlands lenses are a shortlist for each resolution tier. Here, supported means the published MTF holds at the sensor Nyquist band under the conditions on each product page.
Lens Picks by Resolution Requirement
| 해상도 등급 | 추천 렌즈 | 마운트 | F# | 지원되는 최소 픽셀 피치 | 참고 |
|---|---|---|---|---|---|
| 1~2MP 진입 검사 | CIL028 2.6mm | M12 | 제품 페이지 보기 | 1–2MP 구간에서는 결정적인 제약 요인이 아님 | Covers up to 6MP at 2.2µm; pick the lowest-cost lens that covers your format. |
| 5MP 범용 | CIL059 5.9mm | M12 | F/1.7–F/5.6 | 제품 페이지 보기 | Fixed-aperture M12 variants chosen at purchase. The F/1.7 build is rated 4–6MP; the F/4.0 build reaches 12MP as residual aberrations drop. |
| 8~12MP 검사 | CIL160 16mm | M12 | F/1.9–F/5.6 | 제품 페이지 보기 | F/2.8–F/4.0에서 12MP로 평가되는 고정 조리개 모델들입니다. F/5.6 모델의 경우 회절 현상이 심해지면서 해상도가 8MP로 떨어집니다. |
| 8~12MP 계측 | CIL514 25mm | C-마운트 | F/2.8–F/16 | 3.45µm | Adjustable iris. The Airy disk reaches two pixel pitches near F/5.1 at 550nm. |
| 8–12MP 미세 피치 | CIL535 35mm | C-마운트 | F/2.0–F/16 | 2.2µm | Adjustable iris, rated for 2.2µm pixels at 12MP. At 550nm the Airy disk reaches two pixel pitches near F/3.3, so buy depth of field with working distance or focal length, not the iris. |
Above 12MP on formats larger than about 1.1 inch, fixed-focal C-mount FA lenses from Kowa, Fujinon, and Moritex are the established choices. The Commonlands M12 and C-mount optics above target the 1/4" to 1.1" formats. Size the field of view for any pick in the FOV calculator.
초점 거리 제어: 시야각(FOV) 및 픽셀당 mm 값 설정
조리개 제어: 회절의 장단점 조절
자주 묻는 질문
머신 비전에서 공간 분해능이란 무엇인가요?
Spatial resolution is the real-world size one pixel samples at the working distance, expressed in mm per pixel. Divide the field of view by the pixel count across it: a 100mm FOV on 2592 horizontal pixels gives 0.039mm per pixel. That is the sampling interval, not the smallest detectable feature: reliable detection needs a feature to span several pixels, typically 3 to 5.
머신 비전에서 감지 가능한 최소 크기는 얼마입니까?
최소 감지 크기는 비전 시스템이 안정적으로 식별할 수 있는 가장 작은 특징을 의미합니다. 공간 해상도에 해당 특징을 감지하는 데 필요한 픽셀 수를 곱하면 됩니다: (시야각(FOV) ÷ 픽셀 수) × 필요한 픽셀 수. 2048픽셀에서 100mm의 시야각(FOV)을 가질 경우 픽셀당 0.049mm가 되므로, 5픽셀 감지 대상의 경우 0.24mm 이상의 특징을 의미합니다.
카메라에서 IFOV란 무엇인가요?
IFOV (instantaneous field of view) is the angle subtended by one pixel. IFOV = FOV ÷ pixel count gives the average across the frame; the per-pixel value varies with field position. A camera with an 80° horizontal FOV and 3840 pixels averages about 0.021° per pixel, or 48 pixels per degree. Multiply IFOV in radians by working distance to get the pixel footprint on the object.
머신 비전 렌즈에서 ‘메가픽셀’이란 무엇을 의미하나요?
A megapixel rating describes the sensor class a lens is designed to cover, a combination of pixel pitch and format, not its optical resolving power. Resolving power is measured in lp/mm. Two lenses with different megapixel labels can resolve identically in lp/mm. The higher label often just reflects a larger image circle for a bigger sensor at the same pixel pitch.
머신 비전에서 회절 한계란 무엇인가요?
회절 한계는 빛의 파동적 특성에 의해 결정되는, 특정 조리개 값에서 렌즈가 만들어낼 수 있는 최소 흐림 점입니다. F/8, 550nm 조건에서 회절 한계에 도달한 렌즈는 대략 227 lp/mm 이상의 해상도를 구현할 수 없으며, 이 렌즈의 에어리 원반 크기는 10.7µm로, 3.45µm 센서 기준 3픽셀 이상에 해당합니다.
Match a Lens to Your Resolution Requirement
Send us the defect size, working distance, and sensor. The Commonlands engineering team will work through the FOV, pixel coverage, lp/mm, and aperture numbers with you, or you can run the math yourself first.