Measuring the distance to an obstacle not with ultrasound or laser, but with what?

Question

Electronics

Greetings!
In general, it is required to determine on the machine when processing the material the presence of an obstacle (non-conductive)
at a certain distance, for example 5 cm. As such, the distance is not important, it is only important to find out either the obstacle further or closer with a maximum resolution of 2mm:
D :DD and don't take up much space :DDD
Ultrasonic as well as infra-red sensors didn't fit - too much interference.
Contacts don't work either.

Answer 1

1) two cameras and a backlight
2) a capacitive sensor, the accuracy is really no