nice to see helpful people 
@AWOL: So the packages are max 8bits. How big can the data(number) be inside this package?
Is this 28=256 bits so I have an accuracy of 2mm/256=0,0078mm? Or do I also need some start and stop bits, if this is the case how much bits are those start and stop bits per package?
@zoomket: Just discovered the third pin on a potentiometer :). This is an easy solution indeed, thanks for the tip.
@Radman: I was also also thinking about sending the data to a laptop because they most probably are going to use the data on a pc. The Smart phone would just be handy to see a quick result. It’s a small and handy interface; also if I can show this to my teachers, they will be stunned I think. We do need the bluetoothconnection because the place where the sensor is mounted is really hard to reach at some places.
@wildbill: the range of my sensor is from 0,5mm to 2mm with an accuracy of 10µm. The accuracy of our whole measurementmachine needs to be minimum 0,05mm. Thanks for giving me the advice of the max and min. Where can I find a good manual for the programming? I already learned to program in Java so I almost understand everything about the commands.
@MarkT: The impedance of the sensor would be 5000 ohm. Is this good? And why do I need to check this?
Thanks again for the help and the tips 8)