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Trying to Find the Right Proximity Sensor

Hi, I've been trying to find a distance sensor with certain specifics for the last few days and haven't quite been able to find what I'm looking for.

I need the distance sensor to either be ultrasonic or inductive; it's going to be measuring the distance of a steel beam so either of these would work.

It also needs to have a fairly high resolution, no lower than 2mm.

It's going to be used in an outside environment so it needs to be able to function in as low as -40 degrees celsius.

The sensor range needs to be fairly short; minimum range no greater than 4mm, maximum range no lower than 40mm.

The sensor also needs to have an analog voltage output, or something similar that can be wired to a PLC to read the distance at all times.

If anybody knows where I could find a sensor with these specifics, I'd greatly appreciate any info shared.

Thanks.
 
maybe saying the specific problem would help to get suggestions of other ways to tackle the problem
 
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