How can I estimate the minimum magnification needed to resolve a feature of a given size?
Asked 12/3/2014
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I want to estimate the minimum magnification, or equivalently the maximum subject distance, at which a camera system can still resolve a feature of a given size.
My starting idea is:
- convert system resolution (for example line pairs/mm at the sensor) into a minimum resolvable feature size on the sensor
- divide that sensor-space feature size by the real object-space feature size to get the required magnification
Example: for a Canon 7D, if the sensor were the limiting factor and I assume about 104 lp/mm:
- 1 / 104 lp/mm = 9.6 µm on the sensor
- 9.6 µm / 100 µm (roughly a human hair) ≈ 0.096× magnification
That would imply individual hairs should not be expected to resolve once the field of view becomes much larger than roughly 235 × 156 mm on the 22.5 × 15 mm sensor.
Is that reasoning basically sound, or am I missing important factors such as lens resolution, diffraction, or aperture?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
11y ago
2 Answers
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I think I get what you are asking - we can assume the sensor limits resolution, and if we know magnification of the system we can then relate this to an object space resolution limit.
Your approach is going in the right direction, but you should use the rayleigh criterion as the definition of resolution on the sensor (this assumes diffraction limit. Aberration limit would be much harder to calculate without actual lens data). This is proportional to F/#, so as noted in one of the other answers focal length does come into this. We set it so that the radius of the airy disk that results from diffraction covers 2 pixels. If you know magnification you can relate this to object space information, or you can use h=f*tan(HFOV) where h is the height on the detector (2 pixels), f is the focal length and HFOV is the half field of view. This will give you an angular limit that two points can approach and still be resolved. From this angle you can find separation if you know distance, and vice versa.
Please let me know if you have any questions, this can be a difficult subject to follow.
Originally by user35710. Source · Licensed CC BY-SA 4.0
user35710
11y ago
0
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Your reasoning is broadly in the right direction: if you know the smallest resolvable detail at the sensor, dividing by the object’s real size gives the required magnification.
But the important caveat is that the sensor is only one limit. Real system resolution depends on both sensor and lens, plus aperture/diffraction. So a simple lp/mm-to-feature-size conversion is only valid if the sensor truly is the bottleneck.
In practice:
- Required magnification is approximately sensor-space minimum detail / object-space feature size.
- But sensor-space minimum detail should come from the whole optical system, not just pixel pitch.
- Diffraction matters, and it depends on f-number.
- Lens quality and aberrations also matter.
- Focal length enters indirectly because magnification and field of view depend on it.
A practical way to verify the limit is to test the camera/lens combination with a resolution target such as a 1951 USAF chart.
So: yes, the structure of your calculation is reasonable, but it is only an approximation unless you include lens performance and diffraction, or measure the system directly.
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