Need some sort of sensor that can measure deflection high resolution high accuracy

Basically what I am trying to do is measure the deflection of a plastic ceiling panel when it is backloaded(weight placed ontop from behind the panel). Need to be able to measure with a resolution better than atleast 3mm. Multiple different areas on the panel would be measured. I was looking at time of flight sensors (ultrasonic and laser) but couldnt find anything with good enough resolution + accuracy and i'm not even sure if they are suitable for this application. Also tried exploring alternate methods with an accelerometer and similar but does not seem plausible.

Touch here for the full post on the Arduino Apprentices tumblr

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