How do I calculate the smallest detail a camera can resolve at a given distance?
Asked 5/18/2020
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I’m using a camera in a measurement/control system and want to estimate the theoretical spatial resolution on the subject: the smallest real-world detail that corresponds to one pixel at a given working distance.
Camera data:
- Sensor size: 3.7 mm × 2.8 mm
- Resolution: 659 × 494 px
- Pixel size: 5.6 µm × 5.6 µm
- Focal length: 16 mm
- Distance to subject: 90–110 mm
I’m inspecting surface variability after machining using contrast analysis, so I need to know approximately how small a feature this setup can measure on the surface.
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
6y ago
2 Answers
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The magnification of an imaging system is the ratio of the size of an object on the sensor to the real-world size of the subject. This relation, when combined with the thin lens formula, and solving for subject size yields:
$$ \text{subject size} = \text{image size }\times\frac{\text{subject distance}-\text{focal length}}{\text{focal length}} $$
The smallest detail you can resolve corresponds to a single pixel in your resultant image, so the "image size" should just be your pixel size. Thus your minimal resolvable subject size is 5.6 µm x (100 mm – 16 mm) / 16 mm = 29 µm, or about 0.03 mm.
In order to resolve down to 0.01 mm, you need a magnification ratio of 5.6 / 10 = .56 or greater. With a 16 mm lens, this means a subject distance of no more than 25 mm.
Originally by user11924. Source · Licensed CC BY-SA 4.0
user11924
6y ago
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Generated from our catalog & community — verify before relying on it.
For this use, you want the object-space size of one pixel.
Using magnification with a thin lens, the subject detail corresponding to one pixel is approximately:
subject detail = pixel size × (subject distance − focal length) / focal length
With your numbers at about 100 mm working distance:
5.6 µm × (100 mm − 16 mm) / 16 mm ≈ 29 µm
So one pixel corresponds to about 0.029 mm, roughly 0.03 mm on the surface.
Across your 90–110 mm range, it’s about:
- 90 mm: 5.6 µm × 74/16 ≈ 26 µm
- 110 mm: 5.6 µm × 94/16 ≈ 33 µm
So the theoretical sampling resolution is roughly 0.026–0.033 mm per pixel.
Important: that is a best-case geometric estimate, not guaranteed measurement accuracy. Real resolving power can be worse because of lens sharpness, focus, contrast, lighting, noise, and the surface-analysis method. If you need to reliably resolve 0.01 mm features, this setup is likely insufficient at 100 mm distance; you’d need higher magnification (for example, a shorter working distance or different optics).
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