# Determining the size of the smallest resolvable detail for a given camera

My generic question:

Given camera specifications, e.g:

• sensor resolution,
• sensor image area,
• pixel size (area),
• optical size,
• focal length (ratio),
• fov (horizontal and/or vertical)

and distance to an object to be view, how can i determine the smallest resolvable detail by this camera?

Context:

I am trying to build a detector for detecting defects in my products (plastic beads of about 3 mm). These defect have a range of sizes, on average they are about 100 micron but we would like to be able to detect 50 micron and up. These plastic beads will be falling down through a pipe and i will have the camera capture an image as it passes and use a processing step (based on color difference mostly) to find any defects on the bead. I want defects of size 50 micron and up to be resolved quite well, i.e. 50 micron defects have several tens to hundreds of pixels.

• I'm voting to close this question as off-topic because this question is about building a detector, not the production of photographs, and the technical answers you want aren't the same as answers that would be useful for the art and science of photography. – mattdm Dec 9 '17 at 1:13
• @mattdm if the technical answers that the OP wants aren't part of the science of photography, what is? – Brandon Dube Dec 9 '17 at 1:35
• @BrandonDube The science of photography is the science of making images with light. This is about computer vision. The things that are important here aren't the same as the things that are important for making a photograph for the sake of the photograph. – mattdm Dec 9 '17 at 2:36
• We disagree on the definition of the science of photography. – Brandon Dube Dec 9 '17 at 2:54
• @nluigi this is one of the "XY problem". You are asking not to how solve your real problem (detect defects) but how to implement your proposed solution. At least it is less effective. This might clear things meta.stackexchange.com/questions/66377/what-is-the-xy-problem – aaaaaa Dec 9 '17 at 11:34

If you want tens to hundreds of pixels per 50 micron area, you need a microscope. Based on your object size, with that resolution, you want at least 10px/50um * 3000um/50um a 600px wide view of your bead, and up to a 6000px wide view of your bead.

Common sensor sizes are 24x36mm, 16x24mm, and smaller in industrial cameras.

You're going to need, roughly, 3-5x magnification for the bigger sensor sizes (36mm and 24mm), and lower for smaller sensor sizes (closer to 1x).

Shop for microscope objectives with this sort of field of view. They will mostly all be diffraction limited, ish, at pretty big apertures (f/2 and faster). You can use 2.44*wavelength * fno to get the spot size. In vis, that's about 2.44*.55*2 = 2.684 microns.

A 16mm wide sensor with 2.64 micron pixels is 5500px wide.

So you have not violated any resolution limits, but you are operating close to them for your 100px/50um target.

I do not expect you will find a system that can get images out of a camera at this speed, and processed, in anything resembling real time. Your best possible speed is probably 1-3fps.

The working distance of microscopes is usually/always short. If that is not suitable for your needs, you need a custom system (be prepared to spend upwards of \$100,000/system) that would be near the limits of what is possible re: element sizes and resolution.

• Thank you for your answer. I am wondering how you determined which magnification was needed from the required field of fiew and the image sensor size? Don't you need a working distance for this? – nluigi Dec 9 '17 at 10:32
• Your object is 3mm wide, and you want it to fit on the sensor. So the image can be at most [short dimension] long, usually a bit less to allow some positioning error. 16/3 ~= 5, I rounded that to 3-5x. Significantly underfilling the sensor will requiring processing lots of "waste" pixels and also increase the resolution requirements of the system. – Brandon Dube Dec 9 '17 at 20:11