Accurate (1 mm) short range (0-10 cm) distance sensor?

Hello everybody,

I'm pretty new to Arduino and still looking around at all the components.
I'm interested in working out a project I had in mind for a while but I can't seem to find a fitting distance sensor.

I need a fairly accurate (+-1 mm) short range (0-10 cm) distance sensor.
Price doesn't really matter at this point but cheaper is better :slight_smile:

EDIT:
The material can be whatever, reflector or something else.
The object will always be there.

I'm currently looking at using these Adafruit VL6180X Time of Flight Distance Ranging Sensor (VL6180) [STEMMA QT] : ID 3316 : $13.95 : Adafruit Industries, Unique & fun DIY electronics and kits or Adafruit VL53L0X Time of Flight Distance Sensor - ~30 to 1000mm : ID 3317 : $14.95 : Adafruit Industries, Unique & fun DIY electronics and kits and changing my design a bit.

Any suggestion?
Thanks.

It's very important to state the material that you're trying to detect because there are sensors specific to different material types...

Updated my post.

Err, I meant what is the material of the object that you're sensing the position of? Is it electrically conductive for instance? Or magnetic? Or spaghetti? This may determine the most effective sensor.

It would be fabric, but I can attach a piece of metal or a magnet to the fabric if needed.